Mathematics HKDSE Free Practice Test

Q: What is included in Math Premium?

Premium opens a guided route for Mathematics: higher-volume topic practice, timed sets, active-recall flashcards, spaced rechecks, saved mistake review, complete worked explanations, cross-device history, and dashboard progress. AceDSE uses these tools as one study loop, so students can move from a weak-topic signal to focused practice and then verify whether the weakness has improved.

Q: How is the next practice tailored to the student?

AceDSE uses the student's answers, pace, repeated weak topics, saved mistakes, and recent review history to recommend the next useful focus. The purpose is not to label a student permanently: recommendations change as new answers show improvement or expose another gap, and the student can still choose a different topic or timed set at any time.

Q: How can Premium save revision time?

Students spend less time searching through random worksheets, travelling to collect exercises, or deciding what to do next. A short diagnostic and the saved progress signals point to a focused set, while explanations, rechecks, and mistake review stay in the same workspace. Students can use short study blocks at home, between lessons, or while travelling and continue at their own pace.

Q: Do Premium questions include useful explanations?

Yes. Published practice includes a complete explanation designed to show why the correct answer works, the key exam method or evidence, and the common trap behind plausible wrong choices where relevant. Explanations are quality-checked and may be corrected when a verified content issue, syllabus change, or clearer solution method is identified.

Q: What progress appears in the dashboard?

For the selected Premium subject, the signed-in dashboard can show completed practice, recent activity, study streak, repeated weak topics, saved mistakes, review history, and readiness signals. These indicators help students and an optional read-only parent view decide what needs attention next; they are study guidance, not an official predicted DSE grade.

Q: Does 8,000+ mean every subject has 8,000 Premium questions?

No. 8,000+ is the owner-supplied platform-wide Premium practice inventory across AceDSE, not a promise of 8,000 questions in every subject. Subject catalog cards show separately verified counts where those counts are available; checkout availability does not turn the platform-wide figure into a per-subject promise.

Q: Does one subscription include every subject?

No. Each HKD 399/month subscription unlocks one selected subject. The subject shown in Stripe Checkout is the subject added to that account. Opening another subject requires its own subscription, so always check the subject name before confirming.

Q: How does the 3-day trial, billing, and cancellation work?

Stripe shows the selected subject, trial end, and HKD 399 monthly price before confirmation. Unless cancelled first, the initial charge is scheduled for the displayed trial end and the subscription then renews monthly until cancelled. Use Manage subscription in the signed-in dashboard to open Stripe's secure portal; cancel before the trial end to avoid the first scheduled charge.

Q: What can I use without Premium?

Every subject has exactly 30 free questions: one six-question diagnostic followed by a separate 24-question practice bank, with answers, complete written explanations, local progress, the exam blueprint, and the syllabus map. Free practice needs no payment card and remains separate from the Premium trial.

Q: Is Premium checkout available for this subject?

Mathematics is currently a supported Premium subject. If live checkout or immediate access delivery is temporarily unavailable, AceDSE sends you to the subject-aware pricing information instead of attempting a payment that may not deliver access.

Free HKDSE practice

30 free Math practice questions

Maps the Compulsory Part plus Extended Part Module 1 (calculus and statistics) and Module 2 (algebra and calculus).

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30free practice questions
8,000+Premium questions across AceDSE
HKDSEfull syllabus coverage

30 free practice questions

Start with the diagnostic, then open the practice bank

Start one complete 30-question free runner. Questions 1-6 also power the optional diagnostic report, while questions 7-30 remain local practice. Every answer includes an explanation.

Study engine

Mathematics

0Answered

30Questions

59Modules

Question preview Topic: Number and algebra

1/30

Free practice

Which equation matches the graph?

2027 assessment blueprint

Know what the real Mathematics assessment includes

AceDSE's free questions are a short multiple-choice diagnostic. They check selected concepts; they are not a past paper, predicted paper, or complete simulation of every assessed skill.

65% Compulsory Part Paper 1 · Conventional questions

35% Compulsory Part Paper 2 · Multiple choice

• Extended Part · M1 or M2 conventional paper

CP, M1 and M2 are separate study routes; an MCQ check cannot represent the whole assessment.

Framework checked August 2026 · Choose the framework for your own exam year Verify with HKEAA

AceDSE study map

Topic checkpoints mapped to official source boundaries

Use this AceDSE Mathematics map as a revision index. It is organised within HKEAA and EDB source boundaries, but the official documents remain the final authority.

12curriculum sections

59AceDSE checkpoints

3official source links

Compulsory Part: Number and Algebra

Quadratic equations in one unknown

Quadratic equations in one unknown belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.50

Prerequisites Start node

Unlocks

Functions and graphs

Related

Exponential and logarithmic functions Inequalities and linear programming

Mastery evidence

Explain Quadratic equations in one unknown using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Quadratic equations in one unknown.
Practise common HKDSE question formats for Quadratic equations in one unknown.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Quadratic equations in one unknown using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Quadratic equations in one unknown before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Quadratic equations in one unknown but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: Quadratic equations in one unknown Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

Functions and graphs

Functions and graphs belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.83

Prerequisites

Quadratic equations in one unknown

Unlocks

Exponential and logarithmic functions More about graphs of functions

Related

More about polynomials More about graphs of functions

Mastery evidence

Explain Functions and graphs using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Functions and graphs.
Practise common HKDSE question formats for Functions and graphs.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Functions and graphs using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Functions and graphs before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Functions and graphs but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: Functions and graphs Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

Exponential and logarithmic functions

Exponential and logarithmic functions belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

Functions and graphs

Unlocks

More about polynomials

Related

Quadratic equations in one unknown More about equations

Mastery evidence

Explain Exponential and logarithmic functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Exponential and logarithmic functions.
Practise common HKDSE question formats for Exponential and logarithmic functions.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Exponential and logarithmic functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Exponential and logarithmic functions before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Exponential and logarithmic functions but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: Exponential and logarithmic functions Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

More about polynomials

More about polynomials belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

Exponential and logarithmic functions

Unlocks

More about equations

Related

Functions and graphs Variations

Mastery evidence

Explain More about polynomials using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for More about polynomials.
Practise common HKDSE question formats for More about polynomials.
Record mistakes and link them to adjacent topics.

Exam skills

Explain More about polynomials using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for More about polynomials before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise More about polynomials but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: More about polynomials Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

More about equations

More about equations belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

More about polynomials

Unlocks

Variations Inequalities and linear programming

Related

Exponential and logarithmic functions Arithmetic and geometric sequences and their summations

Mastery evidence

Explain More about equations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for More about equations.
Practise common HKDSE question formats for More about equations.
Record mistakes and link them to adjacent topics.

Exam skills

Explain More about equations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for More about equations before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise More about equations but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: More about equations Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

Variations

Variations belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

More about equations

Unlocks

Arithmetic and geometric sequences and their summations

Related

More about polynomials Inequalities and linear programming

Mastery evidence

Explain Variations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Variations.
Practise common HKDSE question formats for Variations.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Variations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Variations before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Variations but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: Variations Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

Arithmetic and geometric sequences and their summations

Arithmetic and geometric sequences and their summations belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

Variations

Unlocks

Inequalities and linear programming

Related

More about equations More about graphs of functions

Mastery evidence

Explain Arithmetic and geometric sequences and their summations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Arithmetic and geometric sequences and their summations.
Practise common HKDSE question formats for Arithmetic and geometric sequences and their summations.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Arithmetic and geometric sequences and their summations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Arithmetic and geometric sequences and their summations before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Arithmetic and geometric sequences and their summations but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: Arithmetic and geometric sequences and their summations Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

Inequalities and linear programming

Inequalities and linear programming belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

Arithmetic and geometric sequences and their summations More about equations

Unlocks

More about graphs of functions

Related

Variations Quadratic equations in one unknown

Mastery evidence

Explain Inequalities and linear programming using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Inequalities and linear programming.
Practise common HKDSE question formats for Inequalities and linear programming.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Inequalities and linear programming using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Inequalities and linear programming before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Inequalities and linear programming but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: Inequalities and linear programming Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Number and Algebra

More about graphs of functions

More about graphs of functions belongs to Compulsory Part: Number and Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.67

Prerequisites

Inequalities and linear programming Functions and graphs

Unlocks No direct unlock yet

Related

Arithmetic and geometric sequences and their summations Functions and graphs

Mastery evidence

Explain More about graphs of functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for More about graphs of functions.
Practise common HKDSE question formats for More about graphs of functions.
Record mistakes and link them to adjacent topics.

Exam skills

Explain More about graphs of functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Number and Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for More about graphs of functions before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise More about graphs of functions but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Number and Algebra: More about graphs of functions Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Measures, Shape and Space

Equations of straight lines

Equations of straight lines belongs to Compulsory Part: Measures, Shape and Space. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites Start node

Unlocks

Basic properties of circles Equations of circles

Related

Loci Equations of circles

Mastery evidence

Explain Equations of straight lines using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Equations of straight lines.
Practise common HKDSE question formats for Equations of straight lines.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Equations of straight lines using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Equations of straight lines before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Equations of straight lines but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Measures, Shape and Space: Equations of straight lines Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Measures, Shape and Space

Basic properties of circles

Basic properties of circles belongs to Compulsory Part: Measures, Shape and Space. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.67

Prerequisites

Equations of straight lines

Unlocks

Loci

Related

Equations of circles More about trigonometry

Mastery evidence

Explain Basic properties of circles using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Basic properties of circles.
Practise common HKDSE question formats for Basic properties of circles.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Basic properties of circles using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Basic properties of circles before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Basic properties of circles but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Measures, Shape and Space: Basic properties of circles Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Measures, Shape and Space

Loci

Loci belongs to Compulsory Part: Measures, Shape and Space. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.67

Prerequisites

Basic properties of circles

Unlocks

Equations of circles

Related

Equations of straight lines More about trigonometry

Mastery evidence

Explain Loci using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Loci.
Practise common HKDSE question formats for Loci.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Loci using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Loci before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Loci but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Measures, Shape and Space: Loci Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Measures, Shape and Space

Equations of circles

Equations of circles belongs to Compulsory Part: Measures, Shape and Space. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.83

Prerequisites

Loci Equations of straight lines

Unlocks

More about trigonometry

Related

Basic properties of circles Equations of straight lines

Mastery evidence

Explain Equations of circles using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Equations of circles.
Practise common HKDSE question formats for Equations of circles.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Equations of circles using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Equations of circles before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Equations of circles but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Measures, Shape and Space: Equations of circles Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Measures, Shape and Space

More about trigonometry

More about trigonometry belongs to Compulsory Part: Measures, Shape and Space. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

Equations of circles

Unlocks

More about trigonometric functions

Related

Loci Basic properties of circles

Mastery evidence

Explain More about trigonometry using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for More about trigonometry.
Practise common HKDSE question formats for More about trigonometry.
Record mistakes and link them to adjacent topics.

Exam skills

Explain More about trigonometry using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Measures, Shape and Space task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for More about trigonometry before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise More about trigonometry but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Measures, Shape and Space: More about trigonometry Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Data Handling

Permutations and combinations

Permutations and combinations belongs to Compulsory Part: Data Handling. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.50

Prerequisites Start node

Unlocks

More about probability

Related

Measures of dispersion Measures of dispersion

Mastery evidence

Explain Permutations and combinations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Permutations and combinations.
Practise common HKDSE question formats for Permutations and combinations.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Permutations and combinations using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Permutations and combinations before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Permutations and combinations but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Data Handling: Permutations and combinations Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Data Handling

More about probability

More about probability belongs to Compulsory Part: Data Handling. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Permutations and combinations

Unlocks

Measures of dispersion

Related

Uses and abuses of statistics Uses and abuses of statistics

Mastery evidence

Explain More about probability using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for More about probability.
Practise common HKDSE question formats for More about probability.
Record mistakes and link them to adjacent topics.

Exam skills

Explain More about probability using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for More about probability before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise More about probability but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Data Handling: More about probability Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Data Handling

Measures of dispersion

Measures of dispersion belongs to Compulsory Part: Data Handling. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

More about probability

Unlocks

Uses and abuses of statistics

Related

Permutations and combinations Permutations and combinations

Mastery evidence

Explain Measures of dispersion using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Measures of dispersion.
Practise common HKDSE question formats for Measures of dispersion.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Measures of dispersion using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Measures of dispersion before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Measures of dispersion but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Data Handling: Measures of dispersion Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Data Handling

Uses and abuses of statistics

Uses and abuses of statistics belongs to Compulsory Part: Data Handling. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.50

Prerequisites

Measures of dispersion

Unlocks No direct unlock yet

Related

More about probability More about probability

Mastery evidence

Explain Uses and abuses of statistics using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Uses and abuses of statistics.
Practise common HKDSE question formats for Uses and abuses of statistics.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Uses and abuses of statistics using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Data Handling task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Uses and abuses of statistics before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Uses and abuses of statistics but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Data Handling: Uses and abuses of statistics Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Further Learning Units

Further applications

Further applications belongs to Compulsory Part: Further Learning Units. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.17

Prerequisites Start node

Unlocks

Inquiry and investigation

Related No related node yet

Mastery evidence

Explain Further applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Further Learning Units task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Further applications.
Practise common HKDSE question formats for Further applications.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Further applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Further Learning Units task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Further applications before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Further applications but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Further Learning Units: Further applications Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Compulsory Part: Further Learning Units

Inquiry and investigation

Inquiry and investigation belongs to Compulsory Part: Further Learning Units. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Learning strategy · 0.17

Prerequisites

Further applications

Unlocks No direct unlock yet

Related No related node yet

Mastery evidence

Explain Inquiry and investigation using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Further Learning Units task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Inquiry and investigation.
Practise common HKDSE question formats for Inquiry and investigation.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Inquiry and investigation using precise subject language.
Choose evidence, formulae, examples, or data that match the Compulsory Part: Further Learning Units task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Inquiry and investigation before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Inquiry and investigation but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Compulsory Part: Further Learning Units: Inquiry and investigation Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Foundation Knowledge

Binomial expansion

Binomial expansion belongs to Module 1: Foundation Knowledge. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.17

Prerequisites Start node

Unlocks

Exponential and logarithmic functions

Related No related node yet

Mastery evidence

Explain Binomial expansion using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Binomial expansion.
Practise common HKDSE question formats for Binomial expansion.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Binomial expansion using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Binomial expansion before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Binomial expansion but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Foundation Knowledge: Binomial expansion Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Foundation Knowledge

Exponential and logarithmic functions

Exponential and logarithmic functions belongs to Module 1: Foundation Knowledge. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.17

Prerequisites

Binomial expansion

Unlocks No direct unlock yet

Related No related node yet

Mastery evidence

Explain Exponential and logarithmic functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Exponential and logarithmic functions.
Practise common HKDSE question formats for Exponential and logarithmic functions.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Exponential and logarithmic functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Exponential and logarithmic functions before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Exponential and logarithmic functions but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Foundation Knowledge: Exponential and logarithmic functions Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Calculus

Derivative of a function

Derivative of a function belongs to Module 1: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.50

Prerequisites Start node

Unlocks

Differentiation of a function

Related

Second derivative Definite integration and its applications

Mastery evidence

Explain Derivative of a function using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Derivative of a function.
Practise common HKDSE question formats for Derivative of a function.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Derivative of a function using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Derivative of a function before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Derivative of a function but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Calculus: Derivative of a function Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Calculus

Differentiation of a function

Differentiation of a function belongs to Module 1: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 1.00

Prerequisites

Derivative of a function

Unlocks

Second derivative Applications of differentiation Indefinite integration and its applications

Related

Applications of differentiation Approximation of definite integrals using the trapezoidal rule

Mastery evidence

Explain Differentiation of a function using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Differentiation of a function.
Practise common HKDSE question formats for Differentiation of a function.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Differentiation of a function using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Differentiation of a function before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Differentiation of a function but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Calculus: Differentiation of a function Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Calculus

Second derivative

Second derivative belongs to Module 1: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

Differentiation of a function

Unlocks

Applications of differentiation

Related

Derivative of a function Indefinite integration and its applications

Mastery evidence

Explain Second derivative using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Second derivative.
Practise common HKDSE question formats for Second derivative.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Second derivative using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Second derivative before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Second derivative but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Calculus: Second derivative Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Calculus

Applications of differentiation

Applications of differentiation belongs to Module 1: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

Second derivative Differentiation of a function

Unlocks

Indefinite integration and its applications

Related

Differentiation of a function Definite integration and its applications

Mastery evidence

Explain Applications of differentiation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Applications of differentiation.
Practise common HKDSE question formats for Applications of differentiation.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Applications of differentiation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Applications of differentiation before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Applications of differentiation but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Calculus: Applications of differentiation Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Calculus

Indefinite integration and its applications

Indefinite integration and its applications belongs to Module 1: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

Applications of differentiation Differentiation of a function

Unlocks

Definite integration and its applications

Related

Second derivative Approximation of definite integrals using the trapezoidal rule

Mastery evidence

Explain Indefinite integration and its applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Indefinite integration and its applications.
Practise common HKDSE question formats for Indefinite integration and its applications.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Indefinite integration and its applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Indefinite integration and its applications before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Indefinite integration and its applications but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Calculus: Indefinite integration and its applications Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Calculus

Definite integration and its applications

Definite integration and its applications belongs to Module 1: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Indefinite integration and its applications

Unlocks

Approximation of definite integrals using the trapezoidal rule

Related

Applications of differentiation Derivative of a function

Mastery evidence

Explain Definite integration and its applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Definite integration and its applications.
Practise common HKDSE question formats for Definite integration and its applications.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Definite integration and its applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Definite integration and its applications before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Definite integration and its applications but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Calculus: Definite integration and its applications Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Calculus

Approximation of definite integrals using the trapezoidal rule

Approximation of definite integrals using the trapezoidal rule belongs to Module 1: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.50

Prerequisites

Definite integration and its applications

Unlocks No direct unlock yet

Related

Indefinite integration and its applications Differentiation of a function

Mastery evidence

Explain Approximation of definite integrals using the trapezoidal rule using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Approximation of definite integrals using the trapezoidal rule.
Practise common HKDSE question formats for Approximation of definite integrals using the trapezoidal rule.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Approximation of definite integrals using the trapezoidal rule using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Approximation of definite integrals using the trapezoidal rule before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Approximation of definite integrals using the trapezoidal rule but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Calculus: Approximation of definite integrals using the trapezoidal rule Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Conditional probability and Bayes' theorem

Conditional probability and Bayes' theorem belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.50

Prerequisites Start node

Unlocks

Discrete random variables

Related

Probability distribution, expectation and variance Sampling distribution and point estimates

Mastery evidence

Explain Conditional probability and Bayes' theorem using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Conditional probability and Bayes' theorem.
Practise common HKDSE question formats for Conditional probability and Bayes' theorem.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Conditional probability and Bayes' theorem using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Conditional probability and Bayes' theorem before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Conditional probability and Bayes' theorem but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Conditional probability and Bayes' theorem Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Discrete random variables

Discrete random variables belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

Conditional probability and Bayes' theorem

Unlocks

Probability distribution, expectation and variance

Related

The binomial distribution Confidence interval for a population mean

Mastery evidence

Explain Discrete random variables using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Discrete random variables.
Practise common HKDSE question formats for Discrete random variables.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Discrete random variables using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Discrete random variables before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Discrete random variables but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Discrete random variables Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Probability distribution, expectation and variance

Probability distribution, expectation and variance belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Discrete random variables

Unlocks

The binomial distribution

Related

Conditional probability and Bayes' theorem The Poisson distribution

Mastery evidence

Explain Probability distribution, expectation and variance using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Probability distribution, expectation and variance.
Practise common HKDSE question formats for Probability distribution, expectation and variance.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Probability distribution, expectation and variance using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Probability distribution, expectation and variance before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Probability distribution, expectation and variance but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Probability distribution, expectation and variance Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

The binomial distribution

The binomial distribution belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

Probability distribution, expectation and variance

Unlocks

The Poisson distribution Applications of the binomial and Poisson distributions

Related

Discrete random variables Applications of the binomial and Poisson distributions

Mastery evidence

Explain The binomial distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for The binomial distribution.
Practise common HKDSE question formats for The binomial distribution.
Record mistakes and link them to adjacent topics.

Exam skills

Explain The binomial distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for The binomial distribution before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise The binomial distribution but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: The binomial distribution Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

The Poisson distribution

The Poisson distribution belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

The binomial distribution

Unlocks

Applications of the binomial and Poisson distributions

Mastery evidence

Explain The Poisson distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for The Poisson distribution.
Practise common HKDSE question formats for The Poisson distribution.
Record mistakes and link them to adjacent topics.

Exam skills

Explain The Poisson distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for The Poisson distribution before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise The Poisson distribution but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: The Poisson distribution Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Applications of the binomial and Poisson distributions

Applications of the binomial and Poisson distributions belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

The Poisson distribution The binomial distribution

Unlocks

Basic definition and properties of normal distribution

Related

The binomial distribution Standardisation of a normal variable and use of the standard normal table

Mastery evidence

Explain Applications of the binomial and Poisson distributions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Applications of the binomial and Poisson distributions.
Practise common HKDSE question formats for Applications of the binomial and Poisson distributions.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Applications of the binomial and Poisson distributions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Applications of the binomial and Poisson distributions before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Applications of the binomial and Poisson distributions but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Applications of the binomial and Poisson distributions Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Basic definition and properties of normal distribution

Basic definition and properties of normal distribution belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Applications of the binomial and Poisson distributions

Unlocks

Standardisation of a normal variable and use of the standard normal table

Related

The Poisson distribution Applications of the normal distribution

Mastery evidence

Explain Basic definition and properties of normal distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Basic definition and properties of normal distribution.
Practise common HKDSE question formats for Basic definition and properties of normal distribution.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Basic definition and properties of normal distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Basic definition and properties of normal distribution before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Basic definition and properties of normal distribution but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Basic definition and properties of normal distribution Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Standardisation of a normal variable and use of the standard normal table

Standardisation of a normal variable and use of the standard normal table belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.67

Prerequisites

Basic definition and properties of normal distribution

Unlocks

Applications of the normal distribution

Related

Applications of the binomial and Poisson distributions Sampling distribution and point estimates

Mastery evidence

Explain Standardisation of a normal variable and use of the standard normal table using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Standardisation of a normal variable and use of the standard normal table.
Practise common HKDSE question formats for Standardisation of a normal variable and use of the standard normal table.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Standardisation of a normal variable and use of the standard normal table using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Standardisation of a normal variable and use of the standard normal table before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Standardisation of a normal variable and use of the standard normal table but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Standardisation of a normal variable and use of the standard normal table Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Applications of the normal distribution

Applications of the normal distribution belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Standardisation of a normal variable and use of the standard normal table

Unlocks

Sampling distribution and point estimates

Related

Basic definition and properties of normal distribution Confidence interval for a population mean

Mastery evidence

Explain Applications of the normal distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Applications of the normal distribution.
Practise common HKDSE question formats for Applications of the normal distribution.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Applications of the normal distribution using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Applications of the normal distribution before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Applications of the normal distribution but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Applications of the normal distribution Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Sampling distribution and point estimates

Sampling distribution and point estimates belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Applications of the normal distribution

Unlocks

Confidence interval for a population mean

Mastery evidence

Explain Sampling distribution and point estimates using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Sampling distribution and point estimates.
Practise common HKDSE question formats for Sampling distribution and point estimates.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Sampling distribution and point estimates using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Sampling distribution and point estimates before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Sampling distribution and point estimates but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Sampling distribution and point estimates Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Statistics

Confidence interval for a population mean

Confidence interval for a population mean belongs to Module 1: Statistics. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.50

Prerequisites

Sampling distribution and point estimates

Unlocks No direct unlock yet

Related

Applications of the normal distribution Discrete random variables

Mastery evidence

Explain Confidence interval for a population mean using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Confidence interval for a population mean.
Practise common HKDSE question formats for Confidence interval for a population mean.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Confidence interval for a population mean using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Statistics task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Confidence interval for a population mean before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Confidence interval for a population mean but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Statistics: Confidence interval for a population mean Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 1: Further Learning Unit

Inquiry and investigation

Inquiry and investigation belongs to Module 1: Further Learning Unit. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Learning strategy · 0.00

Prerequisites Start node

Unlocks No direct unlock yet

Related No related node yet

Mastery evidence

Explain Inquiry and investigation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Further Learning Unit task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Inquiry and investigation.
Practise common HKDSE question formats for Inquiry and investigation.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Inquiry and investigation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 1: Further Learning Unit task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Inquiry and investigation before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Inquiry and investigation but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 1: Further Learning Unit: Inquiry and investigation Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Foundation Knowledge

Odd and even functions

Odd and even functions belongs to Module 2: Foundation Knowledge. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.50

Prerequisites Start node

Unlocks

Mathematical induction

Related

The binomial theorem More about trigonometric functions

Mastery evidence

Explain Odd and even functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Odd and even functions.
Practise common HKDSE question formats for Odd and even functions.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Odd and even functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Odd and even functions before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Odd and even functions but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Foundation Knowledge: Odd and even functions Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Foundation Knowledge

Mathematical induction

Mathematical induction belongs to Module 2: Foundation Knowledge. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Odd and even functions

Unlocks

The binomial theorem

Related

More about trigonometric functions Introduction to e

Mastery evidence

Explain Mathematical induction using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Mathematical induction.
Practise common HKDSE question formats for Mathematical induction.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Mathematical induction using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Mathematical induction before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Mathematical induction but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Foundation Knowledge: Mathematical induction Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Foundation Knowledge

The binomial theorem

The binomial theorem belongs to Module 2: Foundation Knowledge. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.67

Prerequisites

Mathematical induction

Unlocks

More about trigonometric functions

Related

Odd and even functions Introduction to e

Mastery evidence

Explain The binomial theorem using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for The binomial theorem.
Practise common HKDSE question formats for The binomial theorem.
Record mistakes and link them to adjacent topics.

Exam skills

Explain The binomial theorem using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for The binomial theorem before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise The binomial theorem but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Foundation Knowledge: The binomial theorem Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Foundation Knowledge

More about trigonometric functions

More about trigonometric functions belongs to Module 2: Foundation Knowledge. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.83

Prerequisites

The binomial theorem More about trigonometry

Unlocks

Introduction to e

Related

Mathematical induction Odd and even functions

Mastery evidence

Explain More about trigonometric functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for More about trigonometric functions.
Practise common HKDSE question formats for More about trigonometric functions.
Record mistakes and link them to adjacent topics.

Exam skills

Explain More about trigonometric functions using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for More about trigonometric functions before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise More about trigonometric functions but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Foundation Knowledge: More about trigonometric functions Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Foundation Knowledge

Introduction to e

Introduction to e belongs to Module 2: Foundation Knowledge. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.50

Prerequisites

More about trigonometric functions

Unlocks No direct unlock yet

Related

The binomial theorem Mathematical induction

Mastery evidence

Explain Introduction to e using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Introduction to e.
Practise common HKDSE question formats for Introduction to e.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Introduction to e using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Foundation Knowledge task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Introduction to e before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Introduction to e but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Foundation Knowledge: Introduction to e Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Calculus

Limits

Limits belongs to Module 2: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.50

Prerequisites Start node

Unlocks

Differentiation

Related

Applications of differentiation Definite integration

Mastery evidence

Explain Limits using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Limits.
Practise common HKDSE question formats for Limits.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Limits using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Limits before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Limits but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Calculus: Limits Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Calculus

Differentiation

Differentiation belongs to Module 2: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

Limits

Unlocks

Applications of differentiation Indefinite integration and its applications

Related

Indefinite integration and its applications Applications of definite integration

Mastery evidence

Explain Differentiation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Differentiation.
Practise common HKDSE question formats for Differentiation.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Differentiation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Differentiation before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Differentiation but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Calculus: Differentiation Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Calculus

Applications of differentiation

Applications of differentiation belongs to Module 2: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Differentiation

Unlocks

Indefinite integration and its applications

Related

Limits Definite integration

Mastery evidence

Explain Applications of differentiation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Applications of differentiation.
Practise common HKDSE question formats for Applications of differentiation.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Applications of differentiation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Applications of differentiation before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Applications of differentiation but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Calculus: Applications of differentiation Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Calculus

Indefinite integration and its applications

Indefinite integration and its applications belongs to Module 2: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.83

Prerequisites

Applications of differentiation Differentiation

Unlocks

Definite integration

Related

Differentiation Applications of definite integration

Mastery evidence

Explain Indefinite integration and its applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Indefinite integration and its applications.
Practise common HKDSE question formats for Indefinite integration and its applications.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Indefinite integration and its applications using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Indefinite integration and its applications before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Indefinite integration and its applications but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Calculus: Indefinite integration and its applications Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Calculus

Definite integration

Definite integration belongs to Module 2: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Indefinite integration and its applications

Unlocks

Applications of definite integration

Related

Applications of differentiation Limits

Mastery evidence

Explain Definite integration using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Definite integration.
Practise common HKDSE question formats for Definite integration.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Definite integration using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Definite integration before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Definite integration but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Calculus: Definite integration Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Calculus

Applications of definite integration

Applications of definite integration belongs to Module 2: Calculus. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.50

Prerequisites

Definite integration

Unlocks No direct unlock yet

Related

Indefinite integration and its applications Differentiation

Mastery evidence

Explain Applications of definite integration using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Applications of definite integration.
Practise common HKDSE question formats for Applications of definite integration.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Applications of definite integration using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Calculus task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Applications of definite integration before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Applications of definite integration but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Calculus: Applications of definite integration Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Algebra

Determinants

Determinants belongs to Module 2: Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Concept · 0.50

Prerequisites Start node

Unlocks

Matrices

Related

Systems of linear equations Scalar product and vector product

Mastery evidence

Explain Determinants using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Determinants.
Practise common HKDSE question formats for Determinants.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Determinants using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Determinants before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Determinants but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Algebra: Determinants Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Algebra

Matrices

Matrices belongs to Module 2: Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.67

Prerequisites

Determinants

Unlocks

Systems of linear equations

Related

Introduction to vectors Applications of vectors

Mastery evidence

Explain Matrices using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Matrices.
Practise common HKDSE question formats for Matrices.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Matrices using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Matrices before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Matrices but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Algebra: Matrices Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Algebra

Systems of linear equations

Systems of linear equations belongs to Module 2: Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Method · 0.67

Prerequisites

Matrices

Unlocks

Introduction to vectors

Related

Determinants Scalar product and vector product

Mastery evidence

Explain Systems of linear equations using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Systems of linear equations.
Practise common HKDSE question formats for Systems of linear equations.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Systems of linear equations using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Systems of linear equations before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Systems of linear equations but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Algebra: Systems of linear equations Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Algebra

Introduction to vectors

Introduction to vectors belongs to Module 2: Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.67

Prerequisites

Systems of linear equations

Unlocks

Scalar product and vector product

Related

Matrices Applications of vectors

Mastery evidence

Explain Introduction to vectors using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Introduction to vectors.
Practise common HKDSE question formats for Introduction to vectors.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Introduction to vectors using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Introduction to vectors before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Introduction to vectors but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Algebra: Introduction to vectors Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Algebra

Scalar product and vector product

Scalar product and vector product belongs to Module 2: Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.67

Prerequisites

Introduction to vectors

Unlocks

Applications of vectors

Related

Systems of linear equations Determinants

Mastery evidence

Explain Scalar product and vector product using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Scalar product and vector product.
Practise common HKDSE question formats for Scalar product and vector product.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Scalar product and vector product using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Scalar product and vector product before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Scalar product and vector product but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Algebra: Scalar product and vector product Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Algebra

Applications of vectors

Applications of vectors belongs to Module 2: Algebra. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Representation · 0.50

Prerequisites

Scalar product and vector product

Unlocks No direct unlock yet

Related

Introduction to vectors Matrices

Mastery evidence

Explain Applications of vectors using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Applications of vectors.
Practise common HKDSE question formats for Applications of vectors.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Applications of vectors using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Algebra task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Applications of vectors before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Applications of vectors but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Algebra: Applications of vectors Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Module 2: Further Learning Unit

Inquiry and investigation

Inquiry and investigation belongs to Module 2: Further Learning Unit. Use it as one official curriculum checkpoint before moving into timed practice.

Knowledge graph Learning strategy · 0.00

Prerequisites Start node

Unlocks No direct unlock yet

Related No related node yet

Mastery evidence

Explain Inquiry and investigation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Further Learning Unit task.
Show working or reasoning clearly enough for marker-friendly review.

Source boundary HKEAA Category A listHKEAA assessment frameworkEDB Mathematics curriculum

Checkpoints

Know the core ideas and vocabulary for Inquiry and investigation.
Practise common HKDSE question formats for Inquiry and investigation.
Record mistakes and link them to adjacent topics.

Exam skills

Explain Inquiry and investigation using precise subject language.
Choose evidence, formulae, examples, or data that match the Module 2: Further Learning Unit task.
Show working or reasoning clearly enough for marker-friendly review.

Practice route

Recall the key ideas for Inquiry and investigation before opening questions.
Attempt a short diagnostic task, then mark the exact reason for any lost mark.
Redo one adjacent topic so the checkpoint stays connected instead of isolated.

Weak signals

You recognise Inquiry and investigation but cannot choose the right method under time pressure.
Your answer uses the right keyword but lacks the required evidence, step, or example.
The same mistake appears again after reading the explanation.

Premium memory path Mind map: Module 2: Further Learning Unit: Inquiry and investigation Flashcards: Definitions, method triggers, examples, and common mistakes Spaced repetition: Review after 1 day, 3 days, and before the next timed mixed set

Algebra laws

Keep the operation visible: products, quotients, powers, and logarithms should not be buried inside one sentence.

Indices

Multiply powers

a^m\cdot a^n=a^{m+n}

Divide powers

\frac{a^m}{a^n}=a^{m-n}

Power of a power

(a^m)^n=a^{mn}

Zero index

a^0=1\quad(a\ne0)

Same-base rules. Keep the base; operate on the indices.

Logarithms

Product law

\log_a(xy)=\log_a x+\log_a y

Quotient law

\log_a\!\left(\frac{x}{y}\right)=\log_a x-\log_a y

Power law

\log_a(x^n)=n\log_a x

Use when $a>0$ , $a\ne1$ , and all log inputs are positive.

Quadratic equations

Separate the formula from the discriminant so students can check the root conditions before solving.

Quadratic formula

Standard form

ax^2+bx+c=0\quad(a\ne0)

Solutions

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

The whole denominator is $2a$ ; keep the $\pm$ sign.

Discriminant

Definition

\Delta=b^2-4ac

Root count

\begin{cases}\Delta>0&\text{two distinct real roots}\\ \Delta=0&\text{repeated real root}\\ \Delta<0&\text{no real roots}\end{cases}

Use the sign of $\Delta$ before deciding how many real roots there are.

Sequences

Put the general term, finite sum, and infinity condition on their own lines for quick comparison.

Arithmetic sequence

General term

u_n=a+(n-1)d

Sum of first n terms

S_n=\frac{n}{2}\{2a+(n-1)d\}

$a$ is the first term and $d$ is the common difference.

Geometric sequence

General term

u_n=ar^{n-1}

Finite sum

S_n=\frac{a(1-r^n)}{1-r}\quad(r\ne1)

Sum to infinity

S_{\infty}=\frac{a}{1-r}\quad(|r|<1)

$S_{\infty}$ only applies when the common ratio satisfies $|r|<1$ .

Focus session

Run a timed Math study block

Pick a short timer, keep the checklist visible, and turn the free questions into a real revision session instead of a quick scroll.

DSE focus timer

15:00

Choose a task, start the timer, then answer without switching tabs.

Completed on this device 0 sessions

Free session checklist

Open the question bank and answer until the timer ends.
Mark one weak topic or one careless mistake.
Write the next action before leaving the page.

Open free questions

Suggested starts

Quadratic equations in one unknown

Recall the key ideas for Quadratic equations in one unknown before opening questions.

You recognise Quadratic equations in one unknown but cannot choose the right method under time pressure.

Functions and graphs

Recall the key ideas for Functions and graphs before opening questions.

You recognise Functions and graphs but cannot choose the right method under time pressure.

Exponential and logarithmic functions

Recall the key ideas for Exponential and logarithmic functions before opening questions.

You recognise Exponential and logarithmic functions but cannot choose the right method under time pressure.

More about polynomials

Recall the key ideas for More about polynomials before opening questions.

You recognise More about polynomials but cannot choose the right method under time pressure.

Cheatsheet

Mathematics quick reference

Keep this open while practising so formulas, answer frames, and common checkpoints stay visible.

Algebra, indices, and sequences

Indices

Multiply powers
$a^m\cdot a^n=a^{m+n}$

Divide powers
$\frac{a^m}{a^n}=a^{m-n}$

Power of a power
$(a^m)^n=a^{mn}$

Zero index
$a^0=1\quad(a\ne0)$
Logarithms

Product law
$\log_a(xy)=\log_a x+\log_a y$

Quotient law
$\log_a\!\left(\frac{x}{y}\right)=\log_a x-\log_a y$

Power law
$\log_a(x^n)=n\log_a x$

Use when $a>0$ , $a\ne1$ , and inputs are positive.
Quadratic formula

Standard form
$ax^2+bx+c=0\quad(a\ne0)$

Solutions
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Discriminant

Definition
$\Delta=b^2-4ac$

Root count
$\begin{cases}\Delta>0&\text{two distinct real roots}\\ \Delta=0&\text{repeated real root}\\ \Delta<0&\text{no real root}\end{cases}$
Arithmetic sequence

General term
$u_n=a+(n-1)d$

Sum of first n terms
$S_n=\frac{n}{2}\{2a+(n-1)d\}$
Geometric sequence

General term
$u_n=ar^{n-1}$

Finite sum
$S_n=\frac{a(1-r^n)}{1-r}\quad(r\ne1)$

Sum to infinity
$S_{\infty}=\frac{a}{1-r}\quad(|r|<1)$

Coordinate geometry

Distance

$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Midpoint

$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$
Slope

$m=\frac{y_2-y_1}{x_2-x_1}$

$m_1=m_2$ : parallel

$m_1m_2=-1$ : perpendicular
Straight line

$y=mx+c$

$y-y_1=m(x-x_1)$

$ax+by+c=0$
Circle

$(x-h)^2+(y-k)^2=r^2$

Centre $(h,k)$ , radius $r$ .

Trigonometry and geometry

Right triangle

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$
Identities

$\sin^2\theta+\cos^2\theta=1$

$\tan\theta=\frac{\sin\theta}{\cos\theta}$
Sine and cosine rules

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

$a^2=b^2+c^2-2bc\cos A$
Triangle area

$A=\frac{1}{2}ab\sin C$

$A=\sqrt{s(s-a)(s-b)(s-c)}$
Radians

$\ell=r\theta$

$A=\frac{1}{2}r^2\theta$

Mensuration and similarity

Circle

$C=2\pi r$

$A=\pi r^2$
Cylinder

$\text{curved area}=2\pi rh$

$V=\pi r^2h$
Cone

$\text{curved area}=\pi rl$

$V=\frac{1}{3}\pi r^2h$
Sphere

$A=4\pi r^2$

$V=\frac{4}{3}\pi r^3$
Similar figures

$\text{length ratio}=a:b$

$\text{area ratio}=a^2:b^2$

$\text{volume ratio}=a^3:b^3$

Statistics and probability

Mean

$\bar{x}=\frac{\sum x}{n}$

$\bar{x}=\frac{\sum wx}{\sum w}$
Variance and standard deviation

$\sigma^2=\frac{\sum (x-\bar{x})^2}{n}$

$\sigma=\sqrt{\sigma^2}$
Probability

$P(A')=1-P(A)$

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Conditional probability

$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$
Counting

${}^nP_r=\frac{n!}{(n-r)!}$

${}^nC_r=\frac{n!}{r!(n-r)!}$
Expected value

$E(X)=\sum xP(X=x)$

Extended Part calculus quick list

Derivatives

$\frac{d}{dx}x^n=nx^{n-1}$

$\frac{d}{dx}\sin x=\cos x$

$\frac{d}{dx}\cos x=-\sin x$

$\frac{d}{dx}e^x=e^x$
Product and quotient rules

$(uv)'=u'v+uv'$

$\left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v^2}$
Chain rule

$\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$
Integration

$\int x^n\,dx=\frac{x^{n+1}}{n+1}+C,\quad n\ne -1$
Definite integral

$\text{area}=\int_a^b f(x)\,dx,\quad f(x)\ge0$

Formula recall

Test the formula before you look

Use this as a two-minute retrieval drill before starting the maths questions. Reveal only after you have tried writing the formula from memory.

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Premium opens a guided route for Mathematics: higher-volume topic practice, timed sets, active-recall flashcards, spaced rechecks, saved mistake review, complete worked explanations, cross-device history, and dashboard progress. AceDSE uses these tools as one study loop, so students can move from a weak-topic signal to focused practice and then verify whether the weakness has improved.

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