UK GCSE Maths (9–1)

UK GCSE (9–1) — Road to Grade 9

Aligned to Edexcel (1MA1), AQA & OCR UK GCSE Maths from Grade 1 foundations to Grade 9 mastery — train freely at your target grade.

Choose Syllabus:
Grades 1–9 Booklets (PDF)
3

Grade 3 Mastery

Recommended for your current XP Level

Print Grade 3 Booklet (PDF)
Number

Estimation

Estimating calculations and real-world word problems

Number

Limits of Accuracy

Upper and lower bounds (Error intervals)

Number

Fractions (+/-)

Add/Subtract Fractions

Number

Fractions (x/÷)

Multiply/Divide Fractions

Number

Reciprocals

Finding the reciprocal of numbers and fractions

Number

Percentages of an Amount

Without and with a calculator

Number

Percentage Change

Profit, loss, and percentage increase/decrease

Number

Simple Interest

Fixed interest calculated on the original amount

Ratio, Proportion and Rates of Change

Simplifying Ratios

Writing ratios in their simplest form and as 1:n

Ratio, Proportion and Rates of Change

Sharing in a Ratio

Dividing an amount into a given ratio

Ratio, Proportion and Rates of Change

Recipes

Scaling ingredients and yields

Ratio, Proportion and Rates of Change

Exchange Rates

Currency conversion and comparing costs

Ratio, Proportion and Rates of Change

Best Buys

Value for money and special offers

Ratio, Proportion and Rates of Change

Unit Conversions

Converting metric units for length, area, and volume

Ratio, Proportion and Rates of Change

Scale Drawings & Maps

Using scales to find real-life distances

Geometry and Measures

Area & Circumference

Circles, semi-circles, and compound shapes

Geometry and Measures

Parts of a Circle

Radius, Diameter, Circumference, Chord, Arc, Tangent, Sector, Segment

Geometry and Measures

Area of Compound Shapes

Finding areas by adding and subtracting shapes

Geometry and Measures

3D Solids, Plans & Elevations

Faces, edges, vertices, nets, plan views and front/side elevations

Probability

Frequency Trees

Completing logic branches and calculating probabilities

Probability

Two-Way Tables

Completing logic grids and cross-sectional data

4

Grade 4 Mastery

Advance your XP Level to master these easier

Print Grade 4 Booklet (PDF)
Number

Percentage Multipliers

Increasing and decreasing by a percentage

Number

Compound Interest

Growth and decay over time

Number

Prime Factor Trees

Expressing as a product of primes

Number

HCF & LCM

Using Venn diagrams to find HCF and LCM

Number

Laws of Indices

Multiplying, dividing, and powers

Number

Indices with Numbers & Letters

Applying laws to algebraic terms

Algebra

Brackets (Single)

Expanding and factorising single brackets

Algebra

Forming & Solving Equations

Unknowns on both sides, word problems and shapes

Algebra

Linear Inequalities

Number lines and solving linear inequalities

Algebra

Linear & Special Sequences

Generating terms, linear nth term, Fibonacci & geometric

Ratio, Proportion and Rates of Change

Real Life Graphs

Distance-time, cost, and flow rate graphs

Geometry and Measures

Angles in Parallel Lines

Alternate, corresponding and co-interior angles

Geometry and Measures

Angles in Polygons

Interior and exterior angles of regular and irregular polygons

Geometry and Measures

Bearings

Three-figure bearings, back bearings and scale/trigonometry problems

Geometry and Measures

Translations, Reflections & Rotations

Translating, reflecting and rotating 2D shapes on a coordinate grid

Geometry and Measures

Constructions & Loci

Ruler and compass bisectors, perpendiculars, triangles and shading loci regions

Geometry and Measures

Pythagoras' Theorem

Finding missing sides in 2D shapes

Geometry and Measures

Surface Area

Calculating total surface area of prisms and cylinders

Geometry and Measures

Volume of Prisms

Finding the volume of basic and compound prisms

Geometry and Measures

Cylinders

Finding volume and surface area of cylinders

Statistics

Averages from Tables

Calculating averages from frequency and grouped tables

Probability

Relative Frequency

Expected outcomes and complex probability tables

Statistics

Scatter Graphs

Correlation, lines of best fit, and extrapolation

5

Grade 5 Mastery

Advance your XP Level to master these easier

Print Grade 5 Booklet (PDF)
Number

Reverse Percentages

Finding the original amount

Number

Standard Form (Converting)

Writing numbers in standard form

Number

Standard Form (Calculating)

Adding, multiplying and dividing

Algebra

Changing the Subject

Rearranging formulae to make a letter the subject

Algebra

Gradient of a Line

Finding gradients from graphs and coordinates

Algebra

Equation of a Line

Finding y = mx + c

Algebra

Expanding & Factorising Quadratics

Double brackets and factorising x² + bx + c

Algebra

Solving Quadratics by Factorising

Solving x² + bx + c = 0 by factorisation

Algebra

Linear Simultaneous Equations

Elimination, substitution and worded simultaneous equations

Algebra

Solving Equations Graphically

Solving simultaneous equations using intersecting lines

Algebra

Quadratic, Cubic & Reciprocal Graphs

Tables of values, turning points, roots and recognising curve shapes

Ratio, Proportion and Rates of Change

Ratio Contexts

Multi-step contextual problems

Ratio, Proportion and Rates of Change

Ratios & Fractions

Linking ratios to fractions

Ratio, Proportion and Rates of Change

Combining Ratios

Given A:B and B:C, finding A:B:C

Ratio, Proportion and Rates of Change

Linear Direct Proportion

Finding the constant k in linear proportion y = kx

Ratio, Proportion and Rates of Change

Direct & Inverse Prop

Unitary methods and formulas

Ratio, Proportion and Rates of Change

Speed, Distance, Time

Calculating speed and average speed

Ratio, Proportion and Rates of Change

Density, Mass, Volume

Using the density formula

Ratio, Proportion and Rates of Change

Pressure, Force, Area

Using the pressure formula

Geometry and Measures

Sector Area & Arc Length

Finding arc lengths and sector areas

Geometry and Measures

Enlargements

Positive integer, decimal and fractional scale factors and ray lines

Geometry and Measures

Vectors

Column vectors and geometric paths

Geometry and Measures

Spheres and Cones

Calculating volume and surface area using formulae

Geometry and Measures

Congruent Triangles

Recognising SSS, SAS, ASA, and RHS congruence

Geometry and Measures

Trigonometry Exact Values

Calculating missing sides using exact trig values

Geometry and Measures

SOHCAHTOA

Using sine, cosine, and tangent in right-angled triangles

Probability

Venn Diagrams

Set notation, 2-circle and 3-circle Venn diagrams

Probability

Probability Trees

Multiplying and adding probabilities

7

Grade 7 Mastery

Advance your XP Level to master these easier

Print Grade 7 Booklet (PDF)
Number

Simplifying Surds (Higher)

Finding square factors

Number

Expanding with Surds (Higher)

Multiplying and expanding brackets

Number

Rationalising the Denominator (Higher)

Removing surds from the bottom

Number

Calculating with Bounds (Higher)

Min/Max values in calculations (Higher)

Algebra

Rearranging Harder Formulae (Higher)

Where the subject appears twice (Higher)

Algebra

Factorising Harder Quadratics (Higher)

Factorising ax² + bx + c where a > 1 (Higher)

Algebra

The Quadratic Formula (Higher)

Solving ax² + bx + c = 0 using the formula (Higher)

Algebra

Quadratic Sequences (Higher)

Finding the nth term of quadratic sequences (Higher)

Algebra

Functions (Higher)

Composite and inverse functions

Algebra

Trig & Exponential Graphs (Higher)

Graphs of sin, cos, tan and exponential curves y = pq^x (Higher)

Algebra

Algebraic Fractions (Higher)

Simplifying, adding, multiplying and solving (Higher)

Ratio, Proportion and Rates of Change

Algebraic Proportion (Higher)

Direct and inverse proportion with powers and roots (Higher)

Geometry and Measures

Similar Shapes: Area, Volume & Frustums (Higher)

Area and volume scale factors and frustums (Higher)

Geometry and Measures

3D Pythagoras & Trig (Higher)

Finding lengths and angles in 3D shapes

Geometry and Measures

The Sine Rule (Higher)

Finding lengths and angles in non-right-angled triangles

Geometry and Measures

The Cosine Rule (Higher)

Using sides and included angles in non-right-angled triangles

Geometry and Measures

Area of Any Triangle (Higher)

Using 1/2 ab sin(C) to find areas

Probability

Conditional Probability (Higher)

Without replacement and complex tree diagrams

Statistics

Histograms (Higher)

Calculating frequency density and estimating from areas

Grandmaster

You have reached the peak of the GCSE Mathematics curriculum.