OCR GCSE Maths: Higher
Exam Questions

Mathematical Symbols, Order of Operations (BIDMAS/BODMAS), Irrational Numbers, Negative Numbers, Addition & Subtraction, Multiplication & Division, Related Calculations, Money Calculations, Systematic Lists, Product Rule for Counting

Types of Number, Prime Factor Decomposition, Uses of Prime Factor Decomposition, HCF & LCM

Basic Fractions, Mixed Numbers & Improper Fractions, Adding & Subtracting Fractions, Multiplying & Dividing Fractions

Basic Percentages, Percentage Increases & Decreases, Reverse Percentages

Converting Fractions, Decimals & Percentages, Recurring Decimals, Ordering Fractions, Decimals & Percentages

Powers & Roots, Laws of Indices, Converting to & from Standard Form, Operations with Standard Form

Simplifying Surds, Rationalising Denominators

Rounding & Estimation, Upper & Lower Bounds

Using a Calculator

Introduction to Ratios, Sharing in a Ratio, Working with Proportion

Ratios with Fractions, Decimals & Percentages, Multiple Ratios

Direct Proportion, Inverse Proportion

Exchange Rates, Best Buys

Simple Interest, Compound Interest, Depreciation, Exponential Growth & Decay

Algebraic Notation, Algebraic Vocabulary, Substitution, Collecting Like Terms

Algebraic Roots & Indices

Expanding & Simplifying Single Brackets, Expanding Double Brackets, Expanding Triple Brackets

Factorising Out Terms, Factorising by Grouping, Factorising Simple Quadratics, Factorising Harder Quadratics, Difference of Two Squares, Deciding the Factorisation Method

Completing the Square

Simplifying Algebraic Fractions, Adding & Subtracting Algebraic Fractions, Multiplying & Dividing Algebraic Fractions, Solving Equations with Algebraic Fractions

Formulas where Subject Appears Once, Formulas where Subject Appears Twice

Algebraic Proof

Solving Linear Equations

Solving Quadratics by Factorising, The Quadratic Formula, Completing the Square, Deciding the Quadratic Method

Solving Linear Inequalities, Solving Quadratic Inequalities

Linear Simultaneous Equations, Quadratic Simultaneous Equations

Iteration, Sign-Change Methods

Forming Equations from Words, Forming Equations from Shapes, Problem Solving with Equations

Introduction to Functions, Composite Functions, Inverse Functions

Introduction to Sequences, Types of Sequences, nth Terms of Linear Sequences, Quadratic Sequences

2D Coordinates, Midpoint of a Line, Gradient of a Line, Length of a Line

Equations of Straight Lines (y = mx + c), Drawing Straight Line Graphs, Parallel Lines, Perpendicular Lines

Representing Inequalities as Regions, Finding Inequalities from Regions

Types of Graphs, Quadratic Graphs, Drawing Graphs from Tables, Solving Equations Using Graphs, Trigonometric Graphs, Solving Trig Equations

Equation of a Circle, Equation of a Tangent

Finding Gradients of Tangents, Finding Areas under Graphs

Distance-Time Graphs, Speed-Time Graphs, Conversion Graphs, Rates of Change of Graphs

Translations of Graphs, Reflections of Graphs

Rotational Symmetry, Lines of Symmetry, Planes of Symmetry, 2D Shapes, 3D Shapes, Plans & Elevations

Basic Angle Properties, Angles in Polygons, Angles in Parallel Lines

Angles at Centre & Circumference, Angle in a Semicircle, Theorems with Chords & Tangents, Angles in Cyclic Quadrilaterals, Angles in the Same Segment, The Alternate Segment Theorem, Circle Theorem Proofs

Congruence, Congruent Triangles, Similarity, Similar Lengths, Geometrical Proof

Similar Areas & Volumes

Introduction to Column Vectors, Representing Vectors as Diagrams, Length of a Vector, Position & Displacement Vectors, Finding Vector Paths, Problem Solving with Vectors

Translations, Reflections, Rotations, Enlargements, Combination of Transformations

Time, Converting between Units, Squared & Cubic Units, Compound Measures, Speed, Density & Pressure

Bearings, Scale, Constructing Triangles, Constructions, Loci

Perimeter, Area Formulae, Adding & Subtracting Areas, Problem Solving with Areas

Area & Circumference of Circles, Arcs & Sectors

Volume, Problem Solving with Volumes, Surface Area

Pythagoras Theorem, SOHCAHTOA, Elevation & Depression, Exact Trig Values

Sine Rule, Cosine Rule, Area of a Triangle, Deciding the Trig Rule

3D Pythagoras & Trigonometry

Basic Probability, Sample Space, Relative & Expected Frequency

Two-Way Tables, Frequency Trees, Set Notation & Venn Diagrams

Probability Tree Diagrams

Combined Probabilities, Conditional Probability, Combined Conditional Probabilities

Mean, Median & Mode, Calculations with the Mean, Averages from Tables, Averages from Grouped Data, Range & Interquartile Range, Comparing Data Sets, Population & Sampling

Bar Charts & Pictograms, Pie Charts, Time Series Graphs, Reading & Interpreting Statistical Diagrams, Comparing Statistical Diagrams

Frequency Density, Drawing Histograms, Interpreting Histograms

Cumulative Frequency, Drawing Cumulative Frequency Diagrams, Interpreting Cumulative Frequency Diagrams, Box Plots

Scatter Graphs & Correlation, Lines of Best Fit