The full syllabus, broken into 39 topics and 93 distinct question types — from the basics of
linear equations through to histograms and the sine/cosine rule. Every question regenerates fresh each time,
so practice never runs dry.
Linear equations
Solve for x
3x + 7 = 22
3 levels
Expanding & simplifying
Multiply out and collect terms
3(x + 4) + 2x
2 levels
Factorising quadratics
Factorise fully
x² + 8x + 15
2 levels
Factorise, formula, and completing the square
x² − 2x − 15 = 0
4 levels
Simultaneous equations
Solve for x and y
2x + y = 11
2 levels
Percentages
Of, change, and reverse
15% of 240
3 levels
Ratio
Share, name, and reverse
2 : 3
3 levels
Laws of indices
Multiply, divide, and powers
x⁵ × x³
3 levels
Angle facts
Form and solve equations from angle rules
2x° + (x + 30)° = 180°
2 levels
Pythagoras
Right-angled triangles
legs 3 cm and 4 cm
2 levels
SOHCAHTOA with a drawn triangle
sin(30°) = opposite / hypotenuse
2 levels
Circle theorems
Centre/circumference, semicircle, cyclic quads, tangents, alternate segment
angle at centre = 2 × angle at circumference
5 levels
Transformations
Translate, reflect, rotate, enlarge
(x, y) → (x, -y)
4 levels
Statistics
Averages, charts, grouped data, box plots
5, 7, 7, 9, 12
5 levels
Sequences
Linear and quadratic nth terms
5, 8, 11, 14, …
3 levels
Substitution
Substitute values into expressions
3x + 2y
2 levels
Rearranging formulae
Change the subject
y = ax + b
2 levels
Fractions
Add, subtract, multiply, divide
2/3 + 1/4
2 levels
Standard form
Convert to and from standard form
3.2 × 10⁴
2 levels
Probability
Single events and complements
P(red) = 3/10
2 levels
Rounding & sig figs
Decimal places and significant figures
12.345 → 12.3
2 levels
Proportion
Direct and inverse proportion
y ∝ x
2 levels
Area & perimeter
Rectangles, triangles, and circles
A = ½ × base × height
2 levels
Inequalities
Solve linear inequalities
3x + 2 < 17
1 level
Compound measures
Speed, distance, time, and density
speed = distance ÷ time
2 levels
Bearings
Three-figure bearings
bearing of B from A is 065°
1 level
Probability trees
Combined events without replacement
P(red, then blue)
1 level
Vectors
Add, subtract, and scale column vectors
a = (3, 2), b = (-1, 4)
1 level
Upper & lower bounds
Bounds of a rounded measurement
15 cm to the nearest cm
1 level
Graphs
Gradients, y-intercepts, and quadratic curves
y = mx + c
3 levels
3D shapes
Volume & surface area — cuboids, cylinders, cones, spheres
V = l × w × h
5 levels
Sine & cosine rule
Non-right-angled triangles
a ÷ sin(A) = b ÷ sin(B)
3 levels
Surds
Simplify, multiply, and rationalise
√72 = 6√2
3 levels
Function notation
Evaluate, compose, and invert
f(x) = 2x + 3
3 levels
Similar shapes
Length, area, and volume scale factors
area scale factor = k²
1 level
Real-life graphs
Velocity-time graphs — area = distance
distance = area under the graph
3 levels
Cumulative frequency
Running totals from grouped data
0–5, 5–10, 10–15...
1 level
Venn diagrams
Union, intersection, and complement
A ∩ B
1 level
Histograms
Frequency density with unequal class widths
frequency density = frequency ÷ width
2 levels