Mathematics Free Practice Test
This diagnostic test mirrors the HKDSE Mathematics examination structure, covering compulsory part topics and including extension module reference items. Work through the problems to gauge your understanding and timing.
Topic Coverage
Reliable algebra, clear geometry, probability reasoning, modelling, and step-by-step presentation.
Measures, shape, and space
Data handling and probability
Coordinate geometry and trigonometry
Mathematical applications and modelling
Extended Module 1: calculus and statistics
Extended Module 2: algebra and calculus
Common Study Questions
Use these topic questions to decide what to revise next before starting the diagnostic set.
DSE Math quadratic equation roots and coefficients practice
Use sum and product of roots to simplify symmetric algebraic expressions and substitute.
DSE Math volume melting recast cylinder cone
In melting and recasting, volume is conserved. Compute original volume, then solve for the unknown in the new shape.
DSE probability combination draw socks same colour
Count total combinations, then favorable combinations; probability is favorable over total.
DSE circle equation diameter endpoints practice
Midpoint is center, half the distance is radius; plug into standard form.
DSE linear programming profit maximization constraints
Set up constraints and objective function, find vertices of feasible region, evaluate to maximize profit.
M1 differentiation polynomial derivative practice
Apply power rule term by term.
M2 integration expand quadratic indefinite integral
Expand the integrand, then integrate term by term, adding constant C.
Free Practice
Choose one answer for each original question, then check your score and explanations.
Source Grounding
Practice content is original and should be checked against official documents for final exam decisions.