# 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.

### 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 Answers to worksheets
Cumulative Frequency, quartiles, IQR, etc
 Notes
 WS-Cum Freq Graphs Answers to worksheets
 PPQs PPQAnswers
Scattergraphs
 Notes
 WS-Scattergraphs Answers to worksheets

#### IGCSE only

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