HKDSE Maths (Core) study plan

Classify every question in a 40-question mixed set by Paper 1 (long-form, working required) versus Paper 2 (multiple choice) format and by topic, then rank the topics by how many marks you lost on a cold diagnostic attempt

Solve 25 quadratic equations using factorisation, completing the square and the quadratic formula, and state for each which method was fastest and why

Derive the discriminant condition for real, repeated and no real roots, then use it to answer 10 'find the range of k' style questions without solving the equation

Sketch 8 quadratic graphs from completed-square form, labelling the vertex, axis of symmetry and y-intercept, and connect each feature to the algebraic form

Apply all three index laws and the laws of logarithms to simplify 20 expressions, including changing base and solving a^x = b by taking logarithms

Solve 15 simultaneous equations, mixing one linear plus one quadratic with two linear, and verify each answer by substitution

Formulate and solve 10 word problems by translating them into equations (age, rate, mixture and consecutive-integer types) and define the variable explicitly before solving

Prove 5 algebraic identities using the difference of two squares and perfect-square expansions, writing each line as a logical step rather than a jump

State and apply the remainder theorem and factor theorem to find unknown coefficients in 12 polynomial questions

Perform long division and synthetic division of polynomials and express results in the form dividend = divisor x quotient + remainder

Use the factor theorem to factorise cubics completely and hence solve cubic equations

Handle variation problems (direct, inverse, joint, partial) by first writing the proportionality statement, then substituting to find the constant

Solve 15 equations involving absolute values, rational expressions and surds, and identify and reject extraneous roots

Apply the midpoint, distance, slope and section formula to 12 coordinate geometry problems, including finding a locus equation

Find the equation of a straight line in general, slope-intercept and point-slope forms and convert between them fluently

Solve linear inequalities in one unknown and represent the solution on a number line, including compound 'and/or' cases

State and apply the sine, cosine and area formulae for triangles, and use the cosine formula to find an unknown side or angle in 12 problems

Apply the sine and cosine rules to 3D figures by identifying the correct planar triangle and drawing the diagram before calculating

Use bearings and angles of elevation/depression in 8 multi-step problems, sketching the north line and marking all given angles

Solve trigonometric equations for a given range and state the general solution pattern

Compute arc length, sector area, volume and surface area of prisms, pyramids, cylinders, cones and spheres, and solve similar-solid ratio problems

Apply the properties of circles (angle at centre, angle in semicircle, cyclic quadrilateral, tangent-radius) to prove 8 geometric statements

Write two-column or paragraph proofs for congruent and similar triangles, justifying every statement with a named reason

Solve 10 mensuration word problems involving composite solids and rate of flow

Compute mean, median, mode, range, interquartile range and standard deviation from raw data and from grouped frequency tables

Construct and interpret box-and-whisker plots, histograms and cumulative frequency curves, and read quartiles and percentiles from them

Apply basic probability rules including the addition rule, independent events and conditional probability to 15 problems

Distinguish permutation from combination and solve 10 arrangement problems with repetition and restriction cases

Complete a full Paper 1 under exam conditions in 135 minutes and a full Paper 2 in 75 minutes back-to-back on separate days

Mark both papers against a marking scheme and classify every lost mark as knowledge gap, method error, careless slip or time pressure

Re-drill the top 5 recurring error types from weeks 1 to 7 with 10 targeted questions each

Build a final one-page 'exam-day sheet' of formulas, common traps and timing checkpoints, then reproduce it from memory