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AQA GCSE Maths (Higher)

Study Notes

1. Number

1.1.1 Identifying Numbers 1.1.2 Advanced Number Types 1.1.3 Number Conversions and Applications

1.2.1 Set Basics 1.2.2 Set Operations and Examples

1.3.1 Basic Powers and Roots 1.3.2 Advanced Powers and Roots

1.4.1 Understanding and Usage of Fractions, Decimals, and Percentages 1.4.2 Equivalence and Conversion of Fractions, Decimals, and Percentages

1.5.1 Quantitative Ordering

1.6.1 Basic Operations 1.6.2 Practical Applications of the Four Operations

1.7.1 Basic Indices 1.7.2 Indices Calculations

1.8.1 Understanding Standard Form 1.8.2 Calculations in Standard Form

1.9.1 Rounding and Accuracy 1.9.2 Making Estimates

1.10.1 Understanding Limits of Accuracy

1.11.1 Calculator Efficiency 1.11.2 Calculator in Calculations

1.12.1 Calculating with Time 1.12.2 Time Management Skills

1.13.1 Money Calculations

1.14.1 Basics of Surds 1.14.2 Rationalizing the Denominator

1.1.1 Identifying Numbers 1.1.2 Advanced Number Types 1.1.3 Number Conversions and Applications

1.2.1 Set Basics 1.2.2 Set Operations and Examples

1.3.1 Basic Powers and Roots 1.3.2 Advanced Powers and Roots

1.4.1 Understanding and Usage of Fractions, Decimals, and Percentages 1.4.2 Equivalence and Conversion of Fractions, Decimals, and Percentages

1.5.1 Quantitative Ordering

1.6.1 Basic Operations 1.6.2 Practical Applications of the Four Operations

1.7.1 Basic Indices 1.7.2 Indices Calculations

1.8.1 Understanding Standard Form 1.8.2 Calculations in Standard Form

1.9.1 Rounding and Accuracy 1.9.2 Making Estimates

1.10.1 Understanding Limits of Accuracy

1.11.1 Calculator Efficiency 1.11.2 Calculator in Calculations

1.12.1 Calculating with Time 1.12.2 Time Management Skills

1.13.1 Money Calculations

1.14.1 Basics of Surds 1.14.2 Rationalizing the Denominator

2. Algebra

2.1.1 Representation with Letters 2.1.2 Substitution in Expressions

2.2.1 Simplifying Expressions 2.2.2 Expanding Products 2.2.3 Factorization

2.3.1 Understanding Indices 2.3.2 Indices Calculations

2.4.1 Constructing Expressions and Equations 2.4.2 Solving Linear Equations 2.4.3 Simultaneous Linear Equations 2.4.4 Changing the Subject of Formulas

2.5.1 Representing Inequalities 2.5.2 Inequalities on a Number Line

2.6.1 Continuing Sequences 2.6.2 nth Term of Sequences

2.7.1 Interpreting Practical Graphs 2.7.2 Drawing Graphs from Data

2.8.1 Constructing and Interpreting Graphs 2.8.2 Solving Equations Graphically

2.9.1 Recognizing and Sketching Graphs

2.10.1 Estimating Gradients of Curves 2.10.2 Using Derivatives 2.10.3 Applying Differentiation 2.10.4 Discriminating Maxima and Minima

2.11.1 Understanding Functions 2.11.2 Inverse Functions 2.11.3 Composite Functions

2.1.1 Representation with Letters 2.1.2 Substitution in Expressions

2.2.1 Simplifying Expressions 2.2.2 Expanding Products 2.2.3 Factorization

2.3.1 Understanding Indices 2.3.2 Indices Calculations

2.4.1 Constructing Expressions and Equations 2.4.2 Solving Linear Equations 2.4.3 Simultaneous Linear Equations 2.4.4 Changing the Subject of Formulas

2.5.1 Representing Inequalities 2.5.2 Inequalities on a Number Line

2.6.1 Continuing Sequences 2.6.2 nth Term of Sequences

2.7.1 Interpreting Practical Graphs 2.7.2 Drawing Graphs from Data

2.8.1 Constructing and Interpreting Graphs 2.8.2 Solving Equations Graphically

2.9.1 Recognizing and Sketching Graphs

2.10.1 Estimating Gradients of Curves 2.10.2 Using Derivatives 2.10.3 Applying Differentiation 2.10.4 Discriminating Maxima and Minima

2.11.1 Understanding Functions 2.11.2 Inverse Functions 2.11.3 Composite Functions

3. Ratio, proportion and rates of change

3.1.1 Understanding Ratios 3.1.2 Proportional Reasoning

3.2.1 Common Measures of Rate 3.2.2 Advanced Rate Calculations

3.3.1 Basic Percentage Calculations 3.3.2 Advanced Percentage Applications

3.4.1 Understanding Exponential Changes

3.1.1 Understanding Ratios 3.1.2 Proportional Reasoning

3.2.1 Common Measures of Rate 3.2.2 Advanced Rate Calculations

3.3.1 Basic Percentage Calculations 3.3.2 Advanced Percentage Applications

3.4.1 Understanding Exponential Changes

4. Geometry and measures
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4.1.1 Cartesian Coordinates

4.2.1 Creating Straight-Line Graphs

4.3.1 Finding and Calculating Gradient

4.4.1 Length of a Line Segment 4.4.2 Midpoint Coordinates

4.5.1 Interpreting and Formulating Linear Equations

4.6.1 Equations of Parallel Lines

4.7.1 Gradient and Equation of Perpendicular Lines 4.7.2 Finding Perpendicular Lines 4.7.3 Perpendicular Lines Practical Examples

4.8.1 Circle Vocabulary 4.8.2 Polygons 4.8.3 Solids

4.9.1 Drawing Lines and Angles 4.9.2 Constructing Triangles 4.9.3 Drawing and Interpreting Nets

4.10.1 Creating and Interpreting Scale Drawings 4.10.2 Understanding Bearings

4.11.1 Lengths in Similar Shapes 4.11.2 Area and Volume in Similar Shapes

4.12.1 Line and Rotational Symmetry 4.12.2 Symmetry in 3D Shapes

4.13.1 Calculating Angles in Shapes 4.13.2 Angles in Parallel Lines

4.14.1 Understanding Circle Theorems 4.14.2 Applying Circle Theorems (Extended Only)

4.15.1 Metric Units and Conversions

4.16.1 Calculations for Common Shapes

4.17.1 Circumference and Area of Circles 4.17.2 Arc Length and Sector Area

4.18.1 Calculations for Solids

4.19.1 Compound Shapes Perimeters and Areas 4.19.2 Compound Solids Surface Areas and Volumes

4.20.1 Application of Pythagoras' Theorem

4.21.1 Trigonometric Ratios 4.21.2 Pythagoras and Trigonometry 4.21.3 Elevation and Depression

4.22.1 Known Exact Values

4.23.1 Recognising and Sketching Graphs 4.23.2 Solving Trigonometric Equations

4.24.1 Sine and Cosine Rules 4.24.2 Area of Triangles

4.25.1 3D Calculations

4.26.1 Reflection 4.26.2 Rotation 4.26.3 Enlargement 4.26.4 Translation

4.27.1 Describing Translations 4.27.2 Vector Operations

4.28.1 Vector Magnitude Calculation

4.29.1 Vector Representation 4.29.2 Expressing Vectors

4.1.1 Cartesian Coordinates

4.2.1 Creating Straight-Line Graphs

4.3.1 Finding and Calculating Gradient

4.4.1 Length of a Line Segment 4.4.2 Midpoint Coordinates

4.5.1 Interpreting and Formulating Linear Equations

4.6.1 Equations of Parallel Lines

4.7.1 Gradient and Equation of Perpendicular Lines 4.7.2 Finding Perpendicular Lines 4.7.3 Perpendicular Lines Practical Examples

4.8.1 Circle Vocabulary 4.8.2 Polygons 4.8.3 Solids

4.9.1 Drawing Lines and Angles 4.9.2 Constructing Triangles 4.9.3 Drawing and Interpreting Nets

4.10.1 Creating and Interpreting Scale Drawings 4.10.2 Understanding Bearings

4.11.1 Lengths in Similar Shapes 4.11.2 Area and Volume in Similar Shapes

4.12.1 Line and Rotational Symmetry 4.12.2 Symmetry in 3D Shapes

4.13.1 Calculating Angles in Shapes 4.13.2 Angles in Parallel Lines

4.14.1 Understanding Circle Theorems 4.14.2 Applying Circle Theorems (Extended Only)

4.15.1 Metric Units and Conversions

4.16.1 Calculations for Common Shapes

4.17.1 Circumference and Area of Circles 4.17.2 Arc Length and Sector Area

4.18.1 Calculations for Solids

4.19.1 Compound Shapes Perimeters and Areas 4.19.2 Compound Solids Surface Areas and Volumes

4.20.1 Application of Pythagoras' Theorem

4.21.1 Trigonometric Ratios 4.21.2 Pythagoras and Trigonometry 4.21.3 Elevation and Depression

4.22.1 Known Exact Values

4.23.1 Recognising and Sketching Graphs 4.23.2 Solving Trigonometric Equations

4.24.1 Sine and Cosine Rules 4.24.2 Area of Triangles

4.25.1 3D Calculations

4.26.1 Reflection 4.26.2 Rotation 4.26.3 Enlargement 4.26.4 Translation

4.27.1 Describing Translations 4.27.2 Vector Operations

4.28.1 Vector Magnitude Calculation

4.29.1 Vector Representation 4.29.2 Expressing Vectors

5. Probability
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5.1.1 Probability Scale 5.1.2 Probability Notation 5.1.3 Single Event Probability 5.1.4 Complementary Probability

5.2.1 Relative Frequency 5.2.2 Expected Frequencies

5.3.1 Diagrams for Combined Events 5.3.2 Combined Events without Replacement

5.4.1 Calculating Conditional Probability

5.1.1 Probability Scale 5.1.2 Probability Notation 5.1.3 Single Event Probability 5.1.4 Complementary Probability

5.2.1 Relative Frequency 5.2.2 Expected Frequencies

5.3.1 Diagrams for Combined Events 5.3.2 Combined Events without Replacement

5.4.1 Calculating Conditional Probability

6. Statistics
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6.1.1 Data Classification

6.2.1 Data Interpretation 6.2.2 Data Comparison

6.3.1 Central Tendencies 6.3.2 Spread Measures

6.4.1 Chart Creation

6.5.1 Scatter Diagrams and Correlation 6.5.2 Line of Best Fit

6.6.1 Cumulative Frequency Analysis

6.7.1 Histogram Interpretation

6.1.1 Data Classification

6.2.1 Data Interpretation 6.2.2 Data Comparison

6.3.1 Central Tendencies 6.3.2 Spread Measures

6.4.1 Chart Creation

6.5.1 Scatter Diagrams and Correlation 6.5.2 Line of Best Fit

6.6.1 Cumulative Frequency Analysis

6.7.1 Histogram Interpretation

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