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Number Operations and Properties
Unit 1
Adding Integers
Subtracting Integers
Multiplying Integers
Dividing Integers
Adding Decimals
Subtracting Decimals
Multiplying Decimals
Dividing Decimals
Order of Operations (BIDMAS)
Understanding Place Value
Rounding to Decimal Places
Rounding to Significant Figures
Finding Factors
Finding Multiples
Highest Common Factor (HCF)
Lowest Common Multiple (LCM)
Prime Numbers and Prime Factorization
Square Numbers and Square Roots
Cube Numbers and Cube Roots
Fraction Basics and Simplification
Converting Fractions to Decimals
Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions
Working with Mixed Numbers
Calculating a Fraction of a Quantity
Expressing One Quantity as a Fraction of Another
Understanding Percentages
Calculating Percentage of a Quantity
Expressing One Quantity as a Percentage of Another
Percentage Increase and Decrease
Equivalences Between Fractions, Decimals, and Percentages
Using a Calculator Effectively
Inverse Operations
Understanding Powers and Roots
Index Notation for Squares and Cubes
Index Laws for Multiplication and Division
Efficient Written Methods for Operations
Decimal Notation in Money Calculations
Solving Problems with Profit and Loss
Solving Problems with Discounts
Solving Problems with Wages and Salaries
Simple Interest Calculations
Budgeting and Debt Calculations
Annual Percentage Rate (APR)
Annual Equivalent Rate (AER)
Estimating and Checking Calculations
Unit 2
Algebraic Expressions and Equations
Simplifying Algebraic Expressions
Collecting Like Terms
Expanding Single Brackets
Expanding Double Brackets
Factorising Linear Expressions
Factorising Quadratic Expressions
Difference of Two Squares
Substituting Values into Expressions
Writing Expressions from Word Problems
Solving Linear Equations
Linear Equations with Unknowns on Both Sides
Solving Equations with Fractions
Solving Quadratic Equations by Factorisation
Solving Quadratic Equations Using the Formula
Completing the Square for Quadratic Equations
Solving Simultaneous Equations Algebraically
Solving Simultaneous Equations Graphically
Solving Linear Inequalities
Representing Inequalities on a Number Line
Simplifying Algebraic Fractions
Adding and Subtracting Algebraic Fractions
Multiplying and Dividing Algebraic Fractions
Changing the Subject of a Formula
Rearranging Formulas with Powers
Rearranging Formulas with Roots
Finding the nth Term of a Sequence
Linear Sequences and nth Terms
Non-Linear Sequences and nth Terms
Generating Points for Quadratic Graphs
Plotting Quadratic Graphs
Interpreting the Solutions of Quadratic Graphs
Direct Proportion Problems
Inverse Proportion Problems
Using Graphs for Proportion Problems
Identifying an Equation from a Graph
Finding the Gradient and Intercept
Equations of Parallel Lines
Equations of Perpendicular Lines
Recognising and Using Algebraic Identities
Common Errors in Algebraic Manipulation
Exam Techniques for Algebra Questions
Unit 3
Sequences and Graphs
Understanding Arithmetic Sequences
Finding the nth Term of an Arithmetic Sequence
Identifying Geometric Sequences
Calculating Terms in Geometric Sequences
Exploring Fibonacci and Other Special Sequences
Generating Sequences Using Term-to-Term Rules
Generating Sequences Using Position-to-Term Rules
Recognising Linear Graphs from Equations
Plotting Linear Graphs Using a Table of Values
Understanding the Gradient of a Linear Graph
Finding the Equation of a Line from a Graph
Exploring Parallel and Perpendicular Lines
Graphing Quadratic Functions
Finding the Vertex of a Quadratic Graph
Interpreting Roots of Quadratic Graphs
Sketching Quadratic Graphs Using Key Points
Graphing Cubic Functions
Understanding Reciprocal Graphs
Sketching Exponential Graphs
Using Graphs for Real-Life Situations
Distance-Time Graphs and Their Interpretation
Using Conversion Graphs
Interpreting Graphs of Direct Proportion
Interpreting Graphs of Inverse Proportion
Identifying Key Features of Graphs
Understanding the Equation of a Circle
Finding the Tangent to a Circle at a Point
Using Graphs to Solve Quadratic and Linear Systems
Exploring Transformations of Graphs
Reflecting Graphs in Axes
Translating Graphs Vertically and Horizontally
Stretching Graphs by Scale Factors
Recognising Graphs of Trigonometric Functions
Plotting and Sketching Sine Graphs
Plotting and Sketching Cosine Graphs
Plotting and Sketching Tangent Graphs
Understanding Graphical Solutions to Inequalities
Using Graphs to Solve Real-World Problems
Common Errors in Graph Plotting
Exam Practice: Graphing Linear Functions
Exam Practice: Graphing Quadratic Functions
Exam Practice: Graphing Other Functions
Exam Practice: Interpreting Graphs in Context
Unit 4
Geometry and Measures
Properties of Points and Lines
Vertices, Edges, and Faces
Parallel and Perpendicular Lines
Right Angles and Polygons
Regular Polygons and Symmetry
Labeling Sides and Angles
Drawing Shapes from Descriptions
Angles at a Point
Angles on a Straight Line
Vertically Opposite Angles
Alternate Angles on Parallel Lines
Corresponding Angles on Parallel Lines
Circle Definitions and Properties
Properties of Triangles
Properties of Quadrilaterals
Properties of 3D Shapes
Nets, Plans, and Elevations
Metric Units of Measurement
Estimating Measures
Converting Metric Units
Length, Area, Volume, and Capacity
Mass, Time, and Temperature
Measuring Line Segments and Angles
Compound Measures and Units
Calculating Perimeters of Shapes
Areas of Triangles and Rectangles
Areas of Composite Shapes
Circumference of Circles
Area of Circles
Surface Area of Cubes and Cuboids
Volume of Cubes and Cuboids
Imperial Measures and Metric Equivalents
Maps and Scale Drawings
Angle Sum in Triangles
Angle Sum in Polygons
Single Transformations: Reflection
Single Transformations: Rotation
Single Transformations: Translation
Single Transformations: Enlargement
Drawing Shapes with Ruler and Protractor
Bearings and Direction
Interior and Exterior Angles of Polygons
Combined Transformations
Reflections in Diagonal Lines
Enlargement by Fractional Scale Factor
Enlargement by Negative Scale Factor
Effect of Enlargement on Area
Effect of Enlargement on Volume
Congruent Shapes
Standard Ruler and Compass Constructions
Loci of Points
Using Pythagoras’ Theorem in 2D
Using Pythagoras’ Theorem in 3D
Trigonometric Ratios: Sine, Cosine, Tangent
Angles of Elevation and Depression
The Sine Rule
The Cosine Rule
Area of a Triangle Using Trigonometry
Ratios in Similar 2D Shapes
Ratios in Similar 3D Shapes
Frustums and Complex Mensuration Problems
Unit 5
Handling Data and Statistics
The Handling Data Cycle
Understanding Populations and Samples
Simple Random Sampling
Effect of Sample Size on Reliability
Designing Experiments and Surveys
Creating Data-Collection Sheets
Types of Data: Qualitative and Quantitative
Identifying Sources of Bias
Sorting Data with Venn Diagrams
Extracting Data from Tables and Lists
Designing and Using Two-Way Tables
Calculating the Mean from a List
Calculating the Median from a List
Calculating the Mode from a List
Calculating the Range from a List
Mean from Ungrouped Frequency Tables
Mode and Median from Ungrouped Frequency Tables
Frequency Tables and Diagrams
Constructing Pictograms
Constructing Bar Charts
Constructing Pie Charts
Constructing Line Graphs
Frequency Trees and Flow Charts
Identifying Misleading Graphs
Examining Data for Patterns and Exceptions
Comparing Distributions
Making Inferences from Data
Scatter Diagrams and Correlation
Types of Correlation
Interpreting Lines of Best Fit
Estimating Mean from Grouped Frequency Data
Modal Class and Median Class
Cumulative Frequency Tables
Cumulative Frequency Curves
Estimating Median and Quartiles from Curves
Box Plots and Interquartile Range
Outliers in Data Sets
Correlation vs Causation
Probability Vocabulary
Probability Scale from 0 to 1
Listing Outcomes for Single Events
Listing Outcomes for Combined Events
Calculating Probabilities as Fractions or Decimals
Mutually Exclusive Outcomes
Sum of Probabilities Equals One
Probability of Event Not Occurring
Using Tree Diagrams for Independent Events
Using Tree Diagrams for Non-Independent Events
Systematic Listing Strategies
Using Probability to Calculate Expectation
Unit 6
Ratio, Proportion, and Rates of Change
Understanding Ratios
Simplifying Ratios
Expressing Ratios in Different Forms
Dividing Quantities in a Given Ratio
Ratio Problems in Real-Life Contexts
Introduction to Proportion
Direct Proportion
Inverse Proportion
Solving Proportional Problems
Scaling Quantities Up or Down
Using Ratios and Proportions in Recipes
Working with Scale Factors
Interpreting Maps and Scale Drawings
Speed as a Rate of Change
Calculating Average Speed
Using Distance-Time Graphs
Density as a Rate of Change
Calculating Density Problems
Population Density Applications
Solving Best-Buy Problems with Ratios
Currency Conversion Using Ratios
Mixing Solutions and Concentrations
Understanding Percentages in Proportions
Compound Percentage Change
Using Ratios in Financial Contexts
Exchange Rates and Proportions
Worked Examples: Ratio Problems
Worked Examples: Proportion Problems
Common Exam Traps in Ratio Questions
Common Exam Traps in Proportion Questions
Rates of Change in Graphical Representations
Real-Life Applications of Rates of Change
Interpreting Compound Measures
Using Ratios and Proportions in Geometry
Scaling Areas and Volumes
Understanding Growth and Decay Rates
Problem-Solving Strategies for Rates of Change
Exam-Style Questions: Ratios
Exam-Style Questions: Proportions
Exam-Style Questions: Rates of Change
Unit 7
Bounds and Accuracy
Understanding Rounding
Estimating Calculations
Error Intervals from Rounding
Truncation and Error Intervals
Defining Upper and Lower Bounds
Calculating Upper and Lower Bounds for Addition
Calculating Upper and Lower Bounds for Subtraction
Calculating Upper and Lower Bounds for Multiplication
Calculating Upper and Lower Bounds for Division
Using Bounds in Real-Life Problems
Interpreting Error Intervals in Measurements
Significant Figures in Scientific Contexts
Common Mistakes in Rounding
Identifying Over-Estimation Errors
Identifying Under-Estimation Errors
Functional Use of Bounds in Estimation
Exam Trap: Misinterpreting Bounds in Context
Worked Example: Bounds in Area Calculations
Worked Example: Bounds in Speed Calculations
Worked Example: Bounds in Financial Problems
Choosing Appropriate Accuracy Levels
Impact of Rounding on Final Results
Combining Bounds in Multi-Step Calculations
Bounds and Accuracy in Statistical Data
Exam Trap: Misusing Significant Figures
Exam Trap: Misapplying Bounds Rules
Using Bounds in Problem-Solving Strategies
Understanding Accuracy in Everyday Contexts
Worked Example: Error Intervals in Geometry
Worked Example: Error Intervals in Physics Problems
Practical Applications of Bounds in Engineering
Bounds and Accuracy in Scientific Research
Exam Practice: Mixed Bounds Questions
Exam Practice: Rounding and Estimation Problems
Exam Practice: Error Interval Interpretation
Unit 8
Probability and Expectation
Introduction to Probability
The Probability Scale (0 to 1)
Mutually Exclusive Events
Sum of Probabilities Equals 1
Complementary Events
Calculating Probability as Fractions
Calculating Probability as Decimals
Experimental Probability vs Theoretical Probability
Relative Frequency in Probability
Using Venn Diagrams for Probability
Two-Way Tables in Probability
Tree Diagrams for Combined Events
Independent Events in Probability
Dependent Events in Probability
Adding Probabilities for Mutually Exclusive Events
Multiplying Probabilities for Independent Events
Using Tree Diagrams Step-by-Step
Common Errors in Tree Diagram Calculations
Probability in Real-Life Contexts
Understanding Expectation in Probability
Calculating Expected Outcomes
Expectation in Games of Chance
Expectation in Decision Making
Probability and Risk Assessment
Interpreting Probability in Exam Questions
Common Probability Misconceptions
Probability of Multiple Events Combined
Using Probability to Solve Problems
Probability in Sampling Techniques
Probability and Stratified Sampling
Constructing Probability Models
Probability in Everyday Situations
Probability and Insurance Calculations
Unit 9
Advanced Algebra and Functions
Definition of Surds
Simplifying Surds
Multiplying Surds
Dividing Surds
Expanding Expressions with Surds
Rationalising the Denominator
Using Surds in Exact Calculations
Index Laws: Multiplication
Index Laws: Division
Index Laws: Zero Powers
Index Laws: Negative Powers
Index Laws: Fractional Powers
Simplifying Algebraic Expressions with Indices
Solving Linear Simultaneous Equations Algebraically
Solving Linear Simultaneous Equations Graphically
Solving Non-Linear Simultaneous Equations
Transformations of Functions: Translation
Transformations of Functions: Reflection
Transformations of Functions: Stretching
Transformations of Functions: Combining Transformations
Finding the nth Term of Linear Sequences
Finding the nth Term of Non-Linear Sequences
Sketching Linear Graphs
Sketching Quadratic Graphs
Sketching Cubic Graphs
Sketching Reciprocal Graphs
Finding Intersections of Linear and Quadratic Graphs
Direct Proportion: Algebraic Representation
Direct Proportion: Graphical Representation
Indirect Proportion: Algebraic Representation
Indirect Proportion: Graphical Representation
Changing the Subject of a Formula: Simple Cases
Changing the Subject of a Formula: Complex Cases
Using Functions as Inputs and Outputs
Factorising Using the Difference of Two Squares
Understanding Rational and Irrational Numbers
Converting Recurring Decimals to Fractions
Examining Common Errors in Algebraic Manipulation
Examining Common Errors in Graph Sketching
Examining Common Errors in Transformations of Functions
Unit 10
Circle Theorems and Geometry
Parts of a Circle
The Angle at the Centre Theorem
The Angle in a Semicircle Theorem
Angles in the Same Segment Theorem
The Cyclic Quadrilateral Theorem
The Tangent and Radius Theorem
Tangents from a Point Theorem
Alternate Segment Theorem
Proofs of Circle Theorems
Using Circle Theorems in Problems
Finding Missing Angles in Circles
Constructing Tangents to Circles
Using Cyclic Quadrilaterals in Geometry
Intersection of Chords in a Circle
Arc Length Formula
Sector Area Formula
Segment Area Formula
Solving Mensuration Problems with Circles
Using Pythagoras in Circle Geometry
Using Trigonometry in Circle Geometry
Finding the Equation of a Circle
Finding Tangents to a Circle Equation
Circle Geometry in Coordinate Plane
Common Errors in Circle Theorems
Exam Strategies for Circle Geometry Questions
Unit 11
Growth, Decay, and Exponential Functions
Understanding Exponential Functions
Properties of Exponential Functions
Exponential Growth Formula
Exponential Decay Formula
Graphing Exponential Functions
Identifying Growth and Decay from Graphs
The Role of the Base in Exponential Functions
Exponential Growth in Real-Life Contexts
Exponential Decay in Real-Life Contexts
Compound Interest Formula
Calculating Compound Interest Step-by-Step
Continuous Growth and Decay Models
Using Exponential Functions in Word Problems
Solving Exponential Equations
Interpreting Parameters in Exponential Models
Examining the Asymptote of Exponential Graphs
Transformations of Exponential Graphs
Exponential Functions vs Linear Functions
Real-Life Examples of Compound Interest
Population Growth Models
Radioactive Decay Calculations
Half-Life and Exponential Decay
Examining Doubling Time in Growth Problems
Logarithms as the Inverse of Exponentials
Using Logarithms to Solve Growth and Decay Problems
Common Errors in Exponential Calculations
The Impact of Changing the Growth Rate
Graphing Compound Interest Scenarios
Comparing Simple vs Compound Interest
Understanding Exponential Multipliers
Application of Exponential Models in Finance
Exam Traps in Growth and Decay Problems
Using Exponential Graphs to Predict Trends
The Role of Time in Growth and Decay
Exponential Functions in Technology Applications
Step-by-Step Half-Life Problems
Real-World Decay Examples (e.g., Carbon Dating)
Modeling Investment Growth
Understanding Continuous Compound Interest
Examining Exponential Growth in Biology
Examining Exponential Decay in Physics
Solving Multi-Step Exponential Growth Problems
Solving Multi-Step Exponential Decay Problems
Predicting Future Values Using Exponential Models
Exponential Functions in Environmental Science
Key Features of Exponential Graphs
Using Exponential Models in Economics
Examining Decay Constant in Exponential Problems
Unit 12
Trigonometry and 3D Geometry
Understanding the Sine Rule
Using the Sine Rule to Find Angles
Using the Sine Rule to Find Sides
Understanding the Cosine Rule
Using the Cosine Rule to Find Angles
Using the Cosine Rule to Find Sides
Comparing Sine and Cosine Rules
Calculating the Area of a Triangle Using Trigonometry
Using 𝐴 = 1/2 𝑎𝑏 sin 𝐶 Formula
Solving 2D Problems with Trigonometry
Identifying Angles of Elevation and Depression
Applying Trigonometry to Real-Life 2D Problems
Understanding Pythagoras’ Theorem in 3D
Using Pythagoras’ Theorem in 3D Problems
Introduction to 3D Trigonometry
Finding Angles in 3D Shapes with Trigonometry
Finding Lengths in 3D Shapes with Trigonometry
Solving 3D Problems with Mixed Techniques
Visualizing 3D Geometry Problems
Using Trigonometric Ratios in 3D Contexts
Understanding Similarity in 3D Shapes
Relating Lengths, Areas, and Volumes in Similar Shapes
Examining Common Errors in Trigonometry Problems
Interpreting 3D Diagrams and Elevations
Constructing 3D Geometry Problems
Using Bearings in Trigonometric Problems
Understanding the Relationship Between Ratios and Angles
Using Trigonometry in Compound Shapes
Breaking Down Complex 3D Problems
Exam Techniques for Trigonometry Questions
Using Exact Values for Trigonometric Ratios
Understanding the Unit Circle in Trigonometry
Applying Trigonometry to Real-Life 3D Problems
Unit 13
Sampling and Probability Techniques
Understanding Sampling and Populations
Simple Random Sampling Technique
Identifying Sources of Bias in Sampling
Designing Data Collection Sheets
Introduction to Stratified Sampling
Calculating Stratified Sampling Proportions
Advantages and Disadvantages of Stratified Sampling
Histograms for Continuous Data
Constructing Histograms with Equal Intervals
Constructing Histograms with Unequal Intervals
Interpreting Histograms
Using Histograms to Compare Distributions
Probability Vocabulary and Scale
Calculating Probabilities of Simple Events
Dependent and Independent Events
Calculating Probability of Independent Events
Calculating Probability of Dependent Events
Using Tree Diagrams for Dependent Events
Experimental Probability and Relative Frequency
Comparing Experimental and Theoretical Probability
Impact of Sample Size on Probability Estimates
Common Errors in Probability Calculations
Using Probability to Solve Real-Life Problems
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