GCSE Notes and Worksheets (for Years 7 to 11)

Here you will find notes, practice questions and solutions for GCSE, arranged by subject area (Number, Algebra, Shape and Space, Handling Data), and by topic. There are also other notes and worksheets for years 7 to 11.

The topics are arranged according to the Edexcel IGCSE specification, so there are a handful of topics not relevant to GCSE. But 95% of the material is relevant to both.

The notes may be useful to a student without access to a teacher or a textbook. Or possibly to a teacher looking for a quick source of some examples on a particular topic.

The worksheets (WS) may be of use to teachers looking for a quick source of some extra questions. They are probably not much use to students as they do not have answers, except where stated. (In some cases I may be able to supply answers if requested.)

The past paper questions (PPQs) may be be useful to students, since they have worked solutions.

Topic

Notes

Worksheets

Past Paper Questions

Number

   
Arithmetic with Decimals
Notes
WS-Decimal division (with answers)
Fractions
Notes v1
Notes v2
Notes v3 (problems)
WS-Comparing Fractions
WS-Fractions Revision 1
WS-Fractions Revision 2
WS-Multiplying and Dividing Fractions
Fractions and Decimals
Notes v1
Notes v2
WS-Fractions and Decimals
Percentages
Notes
Notes (Table method)
WS-Finding Percentage Increase and Decrease
WS-Mental Test - Percentages
WS-Percentage Increase and Decrease
WS-Percentage Increases and Decreases
WS-Percentage Problems 1
WS-Percentage Problems 2 - Increase & Decrease
WS-Percentage Problems 3
WS-Percentages - Compound
WS-Y7 Percentages Revision
WS-Y8 Percentages Revision
PPQs
PPQAnswers
Ratio and Proportion (including inverse proportion)
Notes
WS-Ratio - Inverse Proportion
WS-Ratio and Proportion
WS-Ratio and Proportion 1
WS-Ratio and Proportion 2
WS-Y9 Homework - Ratio
Approximation (dps, sig figs) & estimation
Notes
WS-Back of an Envelope
WS-Sig Figs and Dec Places
Upper and lower bounds
Notes
WS-Upper and Lower Bounds
WS-Upper and Lower Bounds 2
WS-Y10 Upper and Lower Bounds
PPQs
PPQAnswers
Metric System for length, area, volume, mass, etc
Notes
WS-Problem in Metric Units 2
WS-Problems in Metric Units
WS-Problems in Metric Units 2
Time, Distance, Speed
Notes
WS-Time, Distance and Speed
WS-Time, Distance and Speed HWK
WS-Time Distance Speed 2
WS-Time Distance Speed 3
Standard Form
Notes
WS-Std Form & Sig Figs Revision
PPQs
PPQAnswers
Primes, Factors, LCM, HCF, etc
Notes
Notes (Divisibility Tests)
WS-Prime Factor Form
WS-Prime Factors and Related Topics
WS-Prime factors - investigate
WS-Product Codes
WS-Triangular Square and Cube Numbers
WS-Y7 Sets and Factors
PPQs
PPQAnswers
Negative and fractional indices
Notes
WS-Negative and Fractional Indices
PPQs
PPQAnswers
Surds
Notes
WS-Simplifying Surds - with answers
PPQs
PPQAnswers
Converting recurring decimals to fractions
Notes
WS-Recurring decimals (with solutions)
BIDMAS
Notes
Mental Arithmetic
WS-Mental Test 1
WS-Mental Test 2
WS-Multiplying Decimals Mentally
WS-Quick Mental Arithmetic Samples
WS-Y9 MENTAL TEST 1
WS-Y9 MENTAL TEST 2
Calculator Practice
WS-Calculator Practice
WS-Y7 Calculator Practice
Positive and Negative Numbers
Notes
WS-Negative Numbers
WS-Negative Numbers 2
WS-Quick Mental Arithmetic Test - Negative Numbers
WS-True, False, and Iffy Negative Number Statements
WS-True False and Iffy Negative Number Statements

Algebra

   
Formation of expressions
Notes
WS-Diagonals of a Polygon
WS-Setting up Expressions
WS-Setting up Expressions (easier version 1)
WS-Setting up Expressions (easier version 2)
PPQs
PPQAnswers
Simplification of expressions
Notes
WS-Factorisation
WS-Simplification - mixed
WS-Simplification Practice 1
WS-Simplification Practice 2
WS-Simplifying brackets
WS-Simplifying like terms
WS-Substitution
WS-Substitution (Positive Numbers)
PPQs
PPQAnswers
Multiplying Two Brackets
Notes
WS-Expanding Brackets
Solving equations
Notes
WS-Solving Equations
WS-Solving Equations 2
Solving Problems using Equations
Notes
WS-Algebra Problems (Harder)
WS-How old is Tom
Algebraic fractions
Notes
WS-Algebraic Fractions 1
WS-Algebraic Fractions 2
WS-Simplifying Algebraic Fractions
PPQs
PPQAnswers
Simultaneous Equations - Linear
Notes v1
Notes v2
WS-Introduction to Simultaneous Equations
WS-Simultaneous Eqns (with answers)
PPQs
PPQAnswers
Simultaneous Equations - One linear, one quadratic
Notes
WS-Simultaneous Equations - One Linear, One Quadratic
WS-with worked answers-Sim Eqns - One Lin One Quad
Inequalities
Notes
WS-Inequalities
PPQs
PPQAnswers
Changing the subject of a formula
Notes
Notes (more examples)
WS-Changing the subject of a formula
PPQs
PPQAnswers
Sequences
Notes
WS-Dots round a circle
WS-Rules for Number Sequences
WS-Sequences (linear)
WS-Sequences - complete
WS-Tables and Sequences
Direct and inverse proportionality
Notes
WS-Proportionality
WS-Proportionality 1
WS-Proportionality 2
WS-Proportionality Homework
PPQs
PPQAnswers
Functions
Notes
WS-Function Composition
WS-Function Inversion
WS-Functions
WS-Functions 2
WS-Functions Specimen Questions
Quadratic Expressions - Factorising
Notes
WS-Factorising Quadratics 1
WS-Factorising Quadratics 2
WS-Giant Factorising Quadratics Practice Sheet
WS-Mixed Factorization
WS-Simplifying Calculations Using Factorisation
PPQs
PPQAnswers
Quadratic Equations
Notes
WS-Problems solved by Quadratic Equations
WS-Quadratic Equations
Straight Line Graphs, gradient etc (y=mx+c)
Notes (basics)
Notes (y=mx+c)
WS-Drawing Graphs (Y7)
WS-Equations of straight line graphs
WS-Gradients
WS-Gradients
WS-Perpendicular Lines
WS-Straight Line Graphs
WS-Straight Line Graphs - Problems
Uses of graphs
Notes
WS-Graphs - vt graph
WS-Reading Scales on Graphs
WS-Scales and Graphs
PPQs
PPQAnswers
Regions on graphs defined by inequalities
Notes
WS-Inequalities and regions on graphs
Curved graphs (including use to solve equations)
Notes
WS-Graphs - Sketching and Transformations
WS-Graphs - Sketching and Transformations
WS-Graphs - plotting, solving eqns (with solutions)
WS-Identifying Algebraic Graphs
WS-Transformations of Graphs Short Test
WS-Using graphs to solve eqns
WS-Using graphs to solve eqns (solns to Q1)
WS-Using graphs to solve eqns 2
WS-Using graphs to solve eqns 3
WS-Using graphs to solve problems 1
WS-Using graphs to solve problems 1 - Answers
WS-Using graphs to solve problems 2
PPQs
PPQAnswers
Calculus
Notes
WS-Calculus Practice
WS-Differentiation (Y11)
WS-IGCSE Calculus Questions A5
WS-Velocity, Acceleration and other Rates of Change
Sets and Set Notation
Notes
WS-Set Language and Notation A5 brochure
WS-Set Notation (with answers)
WS-Venn diagram questions (3 circles)

Shape and Space

   
Angles - triangles and parallel lines
Notes
WS-Angle Problems
WS-Bearings and Scale Drawing
Quadrilaterals (kite, rhombus etc) & Polygons
Notes
WS-Angles in Polygons
WS-Quadrilateral Questions
WS-True, False, and Iffy Shape Statements
Angles in circles
Notes
PPQs
PPQAnswers
Intersecting Chords
Notes
WS-Intersecting Chords with solutions
WS-Intersecting Chords with solutions
Transformations
Notes
Notes (enlargements)
WS-More Enlargements
WS-Patterns & Transformations
WS-Transformations - Mixed
WS-Transformations 1 - Translations
WS-Transformations 2 - Rotations
WS-Transformations 3 - Reflections
WS-Transformations 4 - Enlargements
Symmetry
Notes
Vectors
Notes
WS-Vector Questions
WS-Vectors in component form
PPQs
PPQAnswers
Area of triangle, parallelogram, trapezium
Notes
Pi - circles, sectors and arcs
Notes 1 (circles)
Notes 2 (circles and simple sectors)
Notes 3 (arcs, sectors and segments)
WS-Circles, sectors and arcs
WS-Segments and chords
PPQs
PPQAnswers
Prisms and Cylinders
Notes
WS-Cylinders
WS-Prisms & Cylinders
Volume, surface area of prism, pyramid, cone, sphere
Notes
WS-Cones
WS-Curved Surface area of a cone
Pythagoras Theorem
Notes
WS-Pythagoras Problems
WS-Pythagoras Problems
WS-Pythagoras Qs in 3D
WS-Pythagoras Theorem
Congruent Triangles
WS-Congruent Triangles (with answers)
Similar Triangles and other similar shapes
Notes v1
Notes v2
WS-Similar Triangles
WS-Similar Triangles 1
WS-Similar Triangles 2
WS-Similar Triangles Further Problems
PPQs
PPQAnswers
Similar shapes - ratios of areas and volumes
Notes
WS-Similar Shapes- Area & Volume
PPQs
PPQAnswers
Trigonometry
Notes
Notes (solving problems)
WS-Bearings Problems
WS-Trig Practice
WS-Trig Problems
WS-Trig Problems 2
WS-Trig Qs in 3D
WS-Trigonometry Homework
WS-Trigonometry Homework - Answers
PPQs
PPQAnswers
Sine Rule, Cosine Rule
Notes
WS-Sine and Cosine Rule
PPQs
PPQAnswers
Trigonometric Graphs
Notes
WS-Trig Eqns and Graphs
Constructions
Notes
WS-Ruler and Compass Constructions
WS-Ruler and Compass Constructions (IGCSE Version)
PPQs

Handling Data

   
Statistical Graphs
Notes
Grouped frequency distributions, histograms
Notes
WS-Grouped Frequency Distributions and Histograms
WS-Histograms (varying class width)
PPQs
PPQAnswers
Scattergraphs
Notes
WS-Scattergraphs
Averages and measures of spread
Notes v1
Notes v2
WS-Averages & measures of Spread (Ind data items)
WS-Mean and median from Frequency tables
Cumulative Frequency, quartiles, IQR, etc
Notes
WS-Answers to CF Graphs
WS-Cum Freq Graphs
PPQs
PPQAnswers
Probability Laws (including tree diagrams)
Notes (possibility spaces)
Notes (probability laws and tree diagrams)
Notes (theory vs experiment)
WS-Probabilities - Combining
WS-Probability Revision Qs
WS-Probability Trees
PPQs
PPQAnswers