HKDSE Mathematics · Compulsory Part · Paper 2 · Topics
The ten topics Paper 2 asks about most
10 topics, each with what it covers in plain words and two original sample questions you can try, with the answer and a worked solution behind a click.
Where the samples come from
Every sample is generated by our own question engine from the syllabus learning objectives, with our own numbers, and checked by two independent methods. None is taken or adapted from an HKEAA paper. The samples here are fixed public examples: no mock paper on this site will ever give you these exact questions.
Polynomials
Polynomials are the algebra the rest of the paper is built on. Questions ask you to expand and simplify products, factorise expressions, use the remainder and factor theorems to find unknown coefficients, and work with the H.C.F. and L.C.M. of algebraic expressions.
Quadratic equations
Quadratics turn up in both sections of Paper 2. You need to solve quadratic equations, use the discriminant to decide how many real roots there are, use the sum and product of roots without solving, and find the greatest or least value of a quadratic function from its graph or by completing the square.
Congruence and similarity
This topic is about figures that have the same shape. You need the conditions for two triangles to be congruent or similar, and how lengths, areas and volumes scale between similar figures — most often a triangle cut by a line parallel to one side.
Trigonometry
Trigonometry in Paper 2 is about angles and lengths in plane figures, and about trigonometric expressions in their own right. Questions ask you to express a length or a ratio through sine, cosine and tangent, simplify with the basic identities, and solve trigonometric equations over a given interval.
Arithmetic and geometric sequences
Sequences start in Section A with number patterns and grow into arithmetic and geometric sequences in Section B. You need the general term and the sum to n terms of each kind, and the sum to infinity of a geometric sequence when it exists.
Logarithms
Logarithms let you work with powers by working with their exponents. Questions ask you to use the laws of logarithms and the change of base, solve equations involving logarithms, and compare or estimate very large numbers that a calculator cannot show in full.
Measures of dispersion
Dispersion is about how spread out a set of data is. You need to find the range, the inter-quartile range, the standard deviation and the variance, read them off diagrams, and know what happens to each when every datum is changed in the same way.
Equations of circles
This topic puts circles on the coordinate plane. You need to write the equation of a circle from its centre and radius or from other conditions, read the centre and radius off the general form, and decide how a circle and a straight line meet.
Equations of straight lines
Straight lines are the first step of coordinate geometry. You need to find the equation of a line from a point and a slope, or from two points, read the slope and intercepts off an equation, and use the conditions for two lines to be parallel or perpendicular.
Properties of circles
This topic is geometry inside a circle. Questions give you a figure with points on a circle and ask for an angle, using the facts about angles at the centre and at the circumference, angles in the same segment, cyclic quadrilaterals, and equal chords and arcs.
Original material by Dsetopia, written from the EDB syllabus learning objectives. Not affiliated with the HKEAA; no exam content is reproduced.
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