HKDSE Mathematics · Compulsory Part · Study guides
The topics that cost the most marks, explained properly
8 long-form guides, one per topic. Each names what the question type actually asks, the two or three ways people get it wrong and why each wrong turn feels right, then works an example through with our own numbers — and hands you a drill on the same topic.
What this is (and isn't)
Every guide is written from scratch, from the syllabus learning objectives. The worked examples use our own numbers. No exam question wording, numbers, figures, answer options or examiner-report text is reproduced here or anywhere else on this site.
Congruent and similar figures: correspondence, conditions and scale
Why the order of the letters in a similarity statement decides every ratio you write, what actually licenses you to call two figures similar, and the squaring step that turns a length scale factor into an area one.
Updated 5 September 2026
Volume and surface area: picking the right solid, and the right height
The one-third that separates a cone from a cylinder, why slant height and vertical height are not interchangeable, and what happens to volume when every length is doubled.
Updated 5 September 2026
Angles in 3-D figures: what the diagram is not telling you
Why a right angle in a 3-D sketch is usually not a right angle, how to find the angle between a line and a plane without guessing, and the test an angle between two planes has to pass.
Updated 5 September 2026
Angles and polygons: deducing what the diagram refuses to show
Why an angle that looks acute may be forced to be obtuse, the difference between the interior angle of a regular polygon and the angle at its centre, and how to stop reading equal lengths off a drawing.
Updated 5 September 2026
Straight lines: slope from general form, and signs from a sketch
The two operations in 'negative reciprocal' and why doing one of them is the commonest slip, how to read coefficient signs off a sketch without assuming they are positive, and where the minus sign in the slope comes from.
Updated 5 September 2026
The discriminant: which inequality, and which direction
Why 'two distinct real roots' needs a strict inequality, how a sign error turns one condition into its opposite, and the branch of the answer that quietly goes missing.
Updated 5 September 2026
Mean, median and mode: when the question asks for the largest possible one
Why a data set can have two modes, what changes when a question says 'greatest possible', and how to build the arrangement that answers it instead of reading off the one you were shown.
Updated 5 September 2026
Range, interquartile range and standard deviation: what moves and what does not
Why adding a constant to every value leaves the spread untouched while multiplying does not, the difference between range and interquartile range, and how to answer a 'greatest possible spread' question.
Updated 5 September 2026
Original study notes by Dsetopia, written from the EDB syllabus learning objectives. Not affiliated with the HKEAA; no exam content is reproduced.
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