Years 7 to 11 (up to GCSE) Notes and Worksheets

Here you will find notes and worksheets for years 7 to 11, arranged by the broad subject areas in the (English) National Curriculum, and by topic. There are also worked practice questions for GCSE.

The topics with a pale blue background are those listed in the National Curriculum for Key Stage 4 (ages 14-16); the others are listed in the National Curriculum for Key Stage 3 (ages 11-14).

There are also a handful of topics which are only on IGCSE specifications - these are listed at the end.

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, or to students looking for extra practice. Answers to worksheets (where available) are included at the bottom of each topic. So far there are answers to all the KS3 topics, and more answers will be added over time. (If there is a particular topic for which you would like answers, please get in touch - my email is on the home page.)

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

Topic

Notes

Worksheets

Past Paper Questions

Number

   
Order of Operations
Notes
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
Answers to worksheets
Primes, Factors, LCM, HCF, etc
Notes
Notes (Divisibility Tests)
WS-Prime Factors and Related Topics
WS-Sets and Factors
WS-Triangular Square and Cube Numbers
WS-(Extension) Product Codes
WS-(Extension) Prime factors - investigate
WS-(Extension) Prime Factor Form
Answers to worksheets
PPQs
PPQAnswers
Standard Form
Notes
WS-Std Form Revision
Answers to worksheets
PPQs
PPQAnswers
Arithmetic with Decimals
Notes
WS-Decimal division (with answers)
Answers to worksheets
Fractions
Notes v1
Notes v2
Notes v3 (problems)
WS-Fractions Revision 1
WS-Fractions Revision 2
WS-Multiplying and Dividing Fractions
Answers to worksheets
Fractions and Decimals
Notes v1
Notes v2
WS-Fractions and Decimals
Answers to worksheets
Approximation (dps, sig figs) & estimation
Notes
WS-Sig Figs and Dec Places
WS-(Extension) Back of an Envelope
Answers to worksheets
Mental Arithmetic
WS-Quick Mental Arithmetic Samples
WS-Multiplying Decimals Mentally
WS-Y9 Mental Test 1
WS-Y9 Mental Test 2
WS-Mental Test 1
WS-Mental Test 2
Answers to worksheets
Calculator Practice
WS-Y7 Calculator Practice
WS-Calculator Practice
Answers to worksheets
Upper and lower bounds
Notes
WS-Y10 Upper and Lower Bounds
WS-Upper and Lower Bounds
WS-Upper and Lower Bounds 2
Answers to worksheets
PPQs
PPQAnswers
Negative and fractional indices
Notes
WS-Negative and Fractional Indices
WS-Further Indices
Answers to worksheets
PPQs
PPQAnswers
Surds
Notes
WS-Simplifying Surds - with answers
WS-Problems involving surds
WS-Rational & Irrational Numbers
Answers to worksheets
PPQs
PPQAnswers
Converting recurring decimals to fractions
Notes
WS-Recurring decimals (with solutions)

Algebra

   
Formation of expressions
Notes
WS-Setting up Expressions (easier version 1)
WS-Setting up Expressions (easier version 2)
WS-Setting up Expressions
Answers to worksheets
PPQs
PPQAnswers
Substitution
WS-Substitution (Positive Numbers only)
WS-Substitution
Answers to worksheets
Simplification of expressions
Notes
Notes (Multiplying Two Brackets)
WS-Simplifying like terms
WS-Simplification Practice 1 2 and 3
WS-Simplification Practice
WS-Simplifying brackets
WS-Expanding Brackets
WS-Simplification - mixed
WS-Factorisation
Answers to worksheets
PPQs
PPQAnswers
Solving equations
Notes
WS-Solving Equations 1
WS-Solving Equations 2
Answers to worksheets
Solving Problems using Equations
Notes
WS-How old is Tom
Answers to worksheets
Changing the subject of a formula
Notes
Notes (more examples)
WS-Changing the subject of a formula
Answers to worksheets
PPQs
PPQAnswers
Sequences
Notes
WS-Sequences (linear)
WS-Tables and Sequences
WS-Sequences - complete (including extension Qs)
WS-Dots round a circle
WS-Rules for Number Sequences
Answers to worksheets
Simultaneous Equations - Linear
Notes v1
Notes v2
WS-Simultaneous Eqns (with answers)
WS-Introduction to Simultaneous Equations
WS-Algebra Problems (Harder)
Answers to worksheets
PPQs
PPQAnswers
Inequalities
Notes
WS-Inequalities
Answers to worksheets
PPQs
PPQAnswers
Algebraic fractions
Notes
WS-Algebraic Fractions 1
WS-Algebraic Fractions 2
WS-Algebraic Fractions 3
Answers to worksheets
PPQs
PPQAnswers
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
Answers to worksheets
PPQs
PPQAnswers
Quadratic Equations
Notes
Notes (including completing the square)
WS-Quadratic Equations
WS-Problems solved by Quadratic Equations
WS-Completing the Square
Answers to worksheets
Simultaneous Equations - One linear, one quadratic
Notes
WS-Sim Eqns - One Linear One Quadratic (with worked answers)
Straight Line Graphs, gradient etc (y=mx+c)
Notes (basics)
Notes (y=mx+c)
WS-Drawing Graphs (Y7)
WS-Gradients
WS-Gradients 2
WS-Equations of straight line graphs
WS-Straight Line Graphs
WS-Straight Line Graphs - Problems
WS-Perpendicular Lines
Answers to worksheets
Regions on graphs defined by inequalities
Notes
WS-Inequalities and regions on graphs
Answers to worksheets
Curved graphs (including use to solve equations)
Notes
Notes (Transformations of graphs)
WS-Graphs - plotting, solving equations
WS-Identifying Algebraic Graphs
WS-Using graphs to solve eqns 1
WS-Using graphs to solve eqns 2
WS-Using graphs to solve eqns 3
WS-Finding Gradients of Curved Graphs
WS-Graphs - Sketching and Transformations
WS-Transformations of Graphs Short Test
Answers to worksheets
PPQs
PPQAnswers
Uses of graphs
Notes
WS-Reading Scales
WS-Reading Scales on Graphs
WS-Using graphs to solve problems 1
WS-Using graphs to solve problems 2
WS-Velocity - time graph
Answers to worksheets
PPQs
PPQAnswers
Trigonometric Graphs
Notes
WS-Trig Eqns and Graphs
Answers to worksheets

Ratio proportion and rates of change

   
Metric System for length, area, volume, mass, etc
Notes
WS-Problems in Metric Units
WS-Problems in Metric Units 2
Answers to worksheets
Time, Distance, Speed
Notes
WS-Time Distance Speed 1
WS-Time Distance Speed 2
WS-Time Distance Speed 3
WS-Time Distance Speed 4
Answers to worksheets
Ratio and Proportion (including inverse proportion)
Notes
WS-Ratio and Proportion 1
WS-Ratio and Proportion 2
WS-Ratio - Inverse Proportion
WS-Ratio and Proportion 3
Answers to worksheets
Percentages
Notes
Notes (Table method)
WS-Mental Arithmetic - Percentages
WS-Percentage Problems 1
WS-Percentage Problems 2 - Increase & Decrease
WS-Percentage Problems 3
WS-Percentage Increase and Decrease
WS-Percentage Increases and Decreases
Answers to worksheets
PPQs
PPQAnswers
Direct and inverse proportionality
Notes
WS-Proportionality 1
WS-Proportionality 2
WS-Proportionality Homework
Answers to worksheets
PPQs
PPQAnswers

Geometry and Measures

   
Constructions
Notes
Notes (template)
WS-Ruler and Compass Constructions
WS-Ruler and Compass Constructions (IGCSE Version)
WS-More Loci and Constructions
PPQs
Angles - triangles and parallel lines
Notes
WS-Angle Problems
Answers to worksheets
Quadrilaterals (kite, rhombus etc) & Polygons
Notes
Notes (template for quadrilateral qroperties)
WS-Angles in Polygons
WS-Quadrilateral Questions
WS-Diagonals of a Polygon
WS-True, False, and Iffy Shape Statements
Answers to worksheets
Symmetry
Notes
Congruent Triangles
WS-Congruent Triangles (with answers)
Bearings and Scale Drawing
WS-Bearings and Scale Drawing
Answers to worksheets
Angles in circles
Notes
Notes (summary)
WS-Angles in circles
Answers to worksheets
PPQs
PPQAnswers
Intersecting Chords
Notes
WS-Intersecting Chords with solutions
Coordinates and Transformations
WS-Mystery Coordinates
WS-Patterns & Transformations
Answers to worksheets
Combining Transformations
Notes
Notes (enlargements)
WS-Transformations 1 - Translations
WS-Transformations 2 - Rotations
WS-Transformations 3 - Reflections
WS-Transformations 4 - Enlargements
WS-Transformations 5 - More Enlargements
WS-Transformations - Extension Qs
Answers to worksheets
Area of triangle, parallelogram, trapezium
Notes
Pi - circles
Notes
WS-Circles
Answers to worksheets
Pi - Sectors and arcs
Notes 1 (circles and simple sectors)
Notes 2 (arcs, sectors and segments)
WS-Sectors and arcs
WS-Segments and chords
Answers to worksheets
PPQs
PPQAnswers
Prisms and Cylinders
Notes
WS-Prisms & Cylinders
WS-Cylinders
Answers to worksheets
Volume, surface area of prism, pyramid, cone, sphere
Notes
WS-Cones
WS-Curved Surface area of a cone
Answers to worksheets
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
Answers to worksheets
PPQs
PPQAnswers
Similar shapes - ratios of areas and volumes
Notes
WS-Similar Shapes- Area & Volume
Answers to worksheets
PPQs
PPQAnswers
Pythagoras Theorem
Notes
Notes (3D example)
WS-Pythagoras Theorem
WS-Pythagoras Problems
WS-Pythagoras Qs in 3D
Answers to worksheets
Trigonometry
Notes
Notes (solving problems)
WS-Trig Practice (finding sides only)
WS-Trig Practice
WS-Trigonometry Homework (with solutions)
WS-Trig Problems
WS-Trig Problems 2
WS-Trig Qs in 3D
WS-Bearings Problems
Answers to worksheets
PPQs
PPQAnswers
Sine Rule, Cosine Rule
Notes
WS-Sine and Cosine Rule
Answers to worksheets
PPQs
PPQAnswers
Vectors
Notes
WS-Vectors in component form
WS-Vector Questions
WS-Vector equation of a line
Answers to worksheets
PPQs
PPQAnswers

Probability

   
Theory vs Experiment and Possibility Spaces
Notes (possibility spaces)
Notes (theory vs experiment)
WS-Probability Experiments
Sets and Set Notation
Notes
WS-Sets
WS-Set Notation (with answers)
WS-(Extension) Venn diagram questions (3 sets)
WS-(Extension) Set Language and Notation
Answers to worksheets
Probability Laws and tree diagrams
Notes
WS-Probabilities - Combining
WS-Probability Trees
WS-Probability Revision Qs
Answers to worksheets
PPQs
PPQAnswers

Statistics

   
Statistical Graphs
Notes
WS-Stem & leaf
Answers to worksheets
Grouped frequency distributions, histograms
Notes
WS-Grouped Frequency Distributions and Histograms
WS-Histograms (varying class width)
Answers to worksheets
PPQs
PPQAnswers
Averages and measures of spread
Notes v1
Notes v2
WS-Averages & measures of Spread (Ind data items)
WS-Mean and median from Frequency tables
WS-More frequency distribution Qs
Cumulative Frequency, quartiles, IQR, etc
Notes
WS-Cum Freq Graphs
PPQs
PPQAnswers
Scattergraphs
Notes
WS-Scattergraphs

IGCSE only

   
Functions
Notes
WS-Functions
WS-Function Composition
WS-Function Inversion
WS-Functions Specimen Questions
Calculus
Notes
WS-Differentiation (Y11)
WS-Velocity, Acceleration and other Rates of Change
WS-Calculus Practice
WS-IGCSE Calculus Questions A5
Dimensional Algebra
WS-Dimensional Algebra