Higher GCSE

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Higher GCSE Topics

Practice questions for every GCSE topic with papers self-mark so you can track progress.

Add And Subtract Algebraic Fractions

Add and subtract algebraic fractions including factorising and finding common denominators

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Add and Subtract Fractions

Add and subtract fractions and mixed numbers including word problems

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Algebraic Indices Involving Brackets

Apply index laws to simplify expressions with brackets including negative and fractional indices

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Angle Properties

Angles on a parallel line, in an isosceles triangle and vertically opposite angles

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Angles With Algebra

Solve angle problems using algebra in triangles, parallel lines and shapes

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Applying Circle Theorems

Apply circle theorems to find angles and solve geometric problems involving circles

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Area and Circumference of Circle

Calculate circle area and circumference from the radius and diameter

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Area Scale Factors

Use area scale factors to find lengths, areas, surface areas and convert area units

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Averages From A List

Find mean, median, mode and range from a list of numbers

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Averages From Tables

Find mean, median and mode from frequency tables including grouped data

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Bounds From Calculations

Find upper and lower bounds from calculations

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Box plots

Construct and compare box plots using quartiles and median and find interquartile range

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Calculating Bearings

Calculate and interpret bearings using angles and real-world navigation problems

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Calculations With Standard Form

Multiply, divide, add and subtract standard form

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Completing The Square

Complete the square and solve quadratic equations including surd answers

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Composite and Inverse Functions

Work with composite functions and inverse functions including substitution and evaluation

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Compound Shapes

Area and perimeter of compound shapes including rectangles, triangles and missing parts

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Conditional Probability Tree Diagrams

Solve conditional probability problems using tree diagrams and calculate combined probabilities

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Congruent Triangles

Identify and prove congruent triangles

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Constructions And Loci

Construct triangles, bisectors, and loci using ruler and compass methods

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Convert to Fractions and Unit Ratios

Convert ratios and fractions including unit ratios and part comparisons

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Converting Standard Form

Convert to and from standard form

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Cosine Rule

Use the cosine rule to find missing sides, angles and perimeters in triangles

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Counting Strategies

List outcomes and use the product rule to find total possibilities

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Cumulative Frequency Graphs

Draw and interpret cumulative frequency graphs including median, quartiles, IQR and probability

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Curve Gradient and Area

Find gradients of curves, stationary points and estimate areas using the trapezium rule

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Cylinders and Spheres

Calculate volume and surface area of cylinders and spheres, including problem solving

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Decimal Arithmetic

Multiply and divide decimals including worded problems and integer calculations

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Density and Pressure

Calculate pressure, force and area and also calculate density, mass and volume

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Direct and Inverse Proportion

Work with direct and inverse proportion including forming and using equations

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Distance-Time Graphs

Interpret distance-time and velocity-time graphs to find speed, distance, velocity and displacement

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Draw And Describe Enlargements

Enlarge and describe enlargements using positive and negative scale factors

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Draw And Describe Reflections

Reflect and describe reflections using a mirror line

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Draw And Describe Rotations

Rotate and describe rotations using direction and turns

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Draw And Describe Scatter Graphs

Plot scatter graphs and identify correlation

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Draw And Describe Translations

Translate and describe translations using vectors

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Draw and Interpret Cubic and Reciprocal Graphs

Plot and interpret cubic and reciprocal functions

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Draw And Interpret Quadratic Graphs

Draw and interpret quadratic graphs, solve equations and find turning points

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Draw Straight-Line Graphs

Plot straight-line graphs using the y-intercept and gradient

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Drawing Histograms

Draw and interpret histograms from frequency tables and complete missing data

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Drawing Venn Diagrams

Complete and interpret Venn diagrams including set notation and sorting numbers into sets

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Estimate With Scatter Graphs

Draw and use the line of best fit to estimate values and find outliers

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Estimation

Estimate answers using facts, fractions and square roots in calculations

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Expand and Simplify Linear

Expand and simplify single brackets

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Expand/Factorise ax^2 + bx + c

Expand and factorise quadratic brackets where a is not 1

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Expand/Factorise x^2 + bx + c

Expand and factorise quadratic brackets where a is 1

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Experimental Probability

Use experimental probability to calculate frequencies and expected outcomes

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Exponential Graphs

Draw and interpret exponential graphs including growth, decay and finding equations from points

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Exterior Angles

Find exterior angles of polygons and use them to determine number of sides

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Factorise Linear

Factorise common factors including numbers, letters or both

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Find Equations Of Lines

Use gradients and y-intercepts to find y = mx + c

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Finding Bearings

Find and interpret bearings using angles and direction on diagrams

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Finding Bounds

Find upper and lower bounds and error intervals for rounded values

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Further Direct and Inverse Proportion

Direct and inverse proportion including powers and roots of x

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Gradients

Find gradients of straight-line graphs

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Graphic Transformations From Multiplications

Describe and apply graph transformations involving multiplications on cubic and quadratic functions

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Graphic Transformations From Translations

Describe and apply graph transformations involving translations of quadratic and cubic functions

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Graphical Inequalities

Solve and represent graphical inequalities including single and multiple boundary regions

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HCF and LCM

Find factors, multiples, highest common factors and lowest common multiples

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Identifying Circle Theorems

Identify and recognise key circle theorems including angles, tangents and cyclic quadrilaterals

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Increasing And Decreasing By Percentages

Use percentages to Increase and decrease values and calculate simple interest

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Independent And Frequency Tree Diagrams

Use independent events and frequency trees to calculate probabilities and complete diagrams

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Indices Calculations

Apply index laws including indices in fractions and brackets

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Inequalities On Number Lines

Show inequalities on number lines and interpret ranges of values

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Interior Angles

Find the interior angles of polygons and the number of sides

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Interpreting Histograms

Interpret histograms to estimate median, mean, proportions and percentages

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Interpreting Real-Life Graphs

Interpret real-life graphs including gradients, intercepts and modelling data

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Interpreting Venn Diagrams

Interpret Venn diagrams to find probabilities including union, intersection, complements and multi-set problems

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Iteration

Use Iterative methods to solve equations including quadratic and cubic solutions

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Kinematics Formulae

Use kinematics formulae (SUVAT) to solve motion problems with constant acceleration

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Lengths And Areas In Sectors

Calculate lengths and areas in circles including sectors, arcs and quarter circles

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Line Segments

Find midpoints of line segments using graphs and coordinates

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Linear Sequences

Find nth term rules and use linear sequences to generate or check terms

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Multiply And Divide Fractions

Multiply and divide fractions including mixed numbers and integers

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Negative and Fractional Indices

Simplify expressions with negative and fractional indices including powers of fractions and brackets

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Non-Linear Sequences

Work with non-linear sequences including Fibonacci, exponential patterns and quadratic nth terms

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Percentage Change and Reverse Percentages

Percentage increase, decrease, profit and reverse percentages

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Plans And Elevations

Draw and interpret plans and elevations including front, side and top views of 3D shapes

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Probability From Combined Events

Find probabilities from combined events using sample space diagrams and two-event outcomes

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Probability From Mutually Exclusive Events

Find probabilities using mutually exclusive events

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Product of Primes

Find product of prime factors and use them to find HCF and LCM

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Proportion Problems

Best value, recipes, exchange rates and worded problems

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Pyramids and Cones

Calculate surface area and volume of pyramids, cones, cylinders and hemispheres

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Pythagoras From Line Segment

Use Pythagoras’ theorem to find lengths of line segments from coordinates

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Pythagoras From Right-Angled Triangle

Use Pythagoras' theorem to find missing sides and recognise triples

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Quadratic and Linear Simultaneous Equations

Solve simultaneous equations involving a quadratic and a linear equation

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Quadratic Formula

Solve quadratic equations using the quadratic formula

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Rates

Solve rate problems including money, capacity, fuel consumption and filling prisms

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Rearranging Advanced Formulae

Rearrange advanced formulae including factorising and square root expressions

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Rearranging Formulae

Rearrange formulae to change the subject of equations

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Recurring Decimals

Convert recurring decimals to fractions and fractions to recurring decimals

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Repeated Percentages

Calculate compound interest and depreciation

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Resultant Of Vectors

Add, subtract and find resultant vectors including magnitude and algebraic vector expressions

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Sampling

Understand sampling methods including random and stratified sampling and capture-Recapture

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Sharing Ratios

Share amounts using ratios including two-part and three-part ratios from totals

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Similar Triangles

Use similar triangles to find missing lengths using scale factors

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Simplify Algebraic Fractions

Simplify algebraic fractions including quadratics and difference of squares expressions

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Simplify and Rationalise Advanced Surds

Simplify surds and rationalise including expansion and complex denominators

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Simplify and Rationalise Surds

Simplify surds and rationalise denominators including algebraic fractions and applications

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Simplifying Algebraic Indices

Simplify algebraic expressions using index laws including multiplication, division and missing powers

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Simplifying and Multiplying Ratios

Simplify ratios including decimals, different units and 3-part ratios

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Simultaneous Equations Different Coefficients

Solve simultaneous equations with different coefficients

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Simultaneous Equations Same/Similar Coefficients

Solve simultaneous equations with same or similar coefficients including rearranging

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Sine Rule

Use the sine rule to find missing sides and angles in triangles

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Solve Algebraic Fractions

Solve algebraic fraction equations involving quadratics

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Solve ax^2 + bx + c

Solve quadratic equations where a is not 1

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Solve Linear Inequalities

Solve inequalities including 3-part and bracketed expressions

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Solve Simultaneous Equations Graphically

Solve simultaneous equations graphically including linear, quadratic and circle intersections

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Solve with Brackets, Fractions and 4-Part

Solve equations involving brackets, fractions and four-term algebraic equations

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Solve x^2 + bx + c

Solve quadratic equations where a is 1

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Solving Equations

Solve equations including two-step algebraic equations

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Solving Vector Problems

Solve vector problems using triangles and parallelograms

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Speed And Acceleration

Work with speed and acceleration including unit conversions and average speed problems

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Stem and Leaf, Pie Charts and Frequency Polygons

Draw and interpret pie charts, stem and leaf diagrams and frequency polygons

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Time Series

Draw and interpret time series graphs including trends and seasonal patterns

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Trapeziums

Calculate area of trapezia and find missing sides using the trapezium formula

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Trigonometric Area of Triangle

Find area of triangles using the trigonometry formula

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Trigonometric Graphs

Draw and interpret sine, cosine and tangent graphs

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Trigonometric Transformations

Apply transformations to trigonometric graphs including stretches, reflections and translations

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Trigonometry From Right-Angled Triangle

Use sine, cosine and tangent to find angles and side lengths in triangles

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Two-Way Tables

Complete and interpret 2-way tables

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Understanding Function Notation

Use function notation to substitute values and manipulate functions

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Understanding Vectors

Understand vectors including drawing, column vectors and describing lines using vector notation

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Using Exact Trigonometric Values Non-Calculator

Recall values in trigonometry to find angles and side lengths in right-angled triangles

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Using Formulae

Write and interpret formulae including expressions and relationships between variables

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Using Pythagoras In 3D

Use Pythagoras theorem in 3D shapes including cubes, cuboids, prisms and pyramids

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Using Trigonometry In 3D

Use trigonometry in 3D shapes including cuboids, pyramids and cones to find lengths and angles

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Volume and Surface Area of Prisms

Find volume and surface area of prisms including cuboids and composite shapes

Grade
 
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9

Volume Scale Factors

Use volume scale factors to find lengths, areas, volumes and convert volume units

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