HKDSE Maths notes & practice
Notes and practice for every topic in the HKDSE Mathematics Compulsory Part, from quadratic equations to statistics.
- 1
Quadratic Equations
Solve quadratic equations three ways, use the discriminant to tell how many roots there are, and work with the sum and product of roots.
- 2
Functions and Graphs
Function notation, domain and range, the vertex of a quadratic graph by completing the square, and how graphs move under transformations.
- 3
Exponential and Logarithmic Functions
Laws of indices and logarithms, graphs of exponential and log functions, and solving equations like 3ˣ = 20 in real-life growth problems.
- 4
Polynomials
Long division of polynomials, the remainder and factor theorems, factorising cubics, and simplifying rational functions.
- 5
More about Equations
Simultaneous equations with one linear and one quadratic, and equations that reduce to quadratics: fractional, exponential and logarithmic.
- 6
Variations
Direct, inverse, joint and partial variation, and how a percentage change in one quantity changes another.
- 7
Arithmetic and Geometric Sequences
General terms and sums of arithmetic and geometric sequences, the sum to infinity, and word problems like bouncing balls and savings plans.
- 8
Inequalities and Linear Programming
Compound linear inequalities, quadratic inequalities solved with a sketch, and linear programming: finding the greatest or least value over a shaded region.
- 9
Equations of Straight Lines
Slopes, parallel and perpendicular lines, the forms of a straight-line equation, intercepts, and points of division.
- 10
Basic Properties of Circles
The circle theorems on chords, angles, cyclic quadrilaterals and tangents, with the standard reasons you must write in HKDSE answers.
- 11
Equations of Circles
Standard and general forms of the equation of a circle, finding the centre and radius, and how a line meets a circle.
- 12
Trigonometry
Trig identities and graphs, solving trig equations from 0° to 360°, and the sine rule, cosine rule and area formulas for any triangle.
- 13
Permutations and Combinations
The addition and multiplication principles, permutations and combinations, and arrangements with conditions like 'together' or 'not next to each other'.
- 14
Probability
Basic probability, the addition and multiplication laws, drawing with and without replacement, conditional probability and expected value.
- 15
Statistics and Dispersion
Mean, median and mode, measures of dispersion, box-and-whisker diagrams, standard scores and the normal distribution.