Your journey to excellence in
By Revision Genie
Number
Unit 1
Ordering Integers and Decimals
Using Symbols for Comparisons
Four Operations with Integers
Four Operations with Decimals
Four Operations with Fractions
Understanding Place Value
Relationships Between Operations
Inverse Operations in Calculations
Priority of Operations (BIDMAS)
Prime Numbers and Their Properties
Factors and Multiples
Highest Common Factor (HCF)
Lowest Common Multiple (LCM)
Prime Factorisation
Systematic Listing Strategies
Product Rule for Counting
Positive Integer Powers
Real Roots of Numbers
Estimating Powers and Roots
Calculations with Roots
Calculations with Integer Indices
Calculations with Fractional Indices
Exact Calculations with Fractions
Exact Calculations with Surds
Simplifying Surd Expressions
Rationalising Denominators
Calculations in Standard Form
Interpreting Calculator Displays in Standard Form
Terminating Decimals and Corresponding Fractions
Recurring Decimals to Fractions
Fractions in Ratio Problems
Fractions and Percentages as Operators
Using Standard Units of Measure
Metric Conversion Factors
Estimating Answers in Calculations
Using Approximation to Check Calculations
Rounding to Decimal Places
Rounding to Significant Figures
Error Intervals Using Inequality Notation
Limits of Accuracy
Upper and Lower Bounds in Calculations
Unit 2
Algebra
Using Algebraic Notation
Simplifying Algebraic Expressions
Substituting Values into Expressions
Understanding Expressions and Equations
Understanding Formulae and Identities
Expanding Single Brackets
Expanding Double Brackets
Factorising Linear Expressions
Factorising Quadratic Expressions
Simplifying Algebraic Fractions
Using the Laws of Indices
Rearranging Formulae
Understanding Functions and Inverse Functions
Composite Functions
Plotting Linear Graphs
Understanding y = mx + c
Identifying Parallel and Perpendicular Lines
Finding the Equation of a Line
Sketching Quadratic Graphs
Identifying Roots and Turning Points
Completing the Square
Sketching Cubic and Reciprocal Graphs
Sketching Exponential Graphs
Transforming Graphs of Functions
Using Graphs to Solve Equations
Solving Linear Equations
Solving Quadratic Equations by Factorisation
Solving Quadratic Equations with the Formula
Solving Quadratic Equations by Completing the Square
Solving Simultaneous Linear Equations
Solving Linear and Quadratic Simultaneous Equations
Solving Inequalities on a Number Line
Solving Quadratic Inequalities
Representing Inequalities on Graphs
Generating Terms of a Sequence
Finding the nth Term of Linear Sequences
Finding the nth Term of Quadratic Sequences
Recognising Special Sequences
Working with Fibonacci-Type Sequences
Understanding Arithmetic Progressions
Understanding Geometric Progressions
Using Iterative Methods to Solve Equations
Interpreting Distance-Time Graphs
Interpreting Velocity-Time Graphs
Calculating Gradients of Graphs
Calculating Areas Under Graphs
Understanding the Equation of a Circle
Finding Tangents to Circles
Unit 3
Ratio, Proportion and Rates of Change
Converting Between Units of Measure
Using Compound Units: Speed
Using Compound Units: Rates of Pay
Using Compound Units: Unit Pricing
Using Compound Units: Density
Using Compound Units: Pressure
Understanding Scale Factors
Using Scale Diagrams and Maps
Expressing One Quantity as a Fraction of Another
Understanding and Simplifying Ratios
Dividing Quantities in a Given Ratio
Applying Ratios to Real-Life Contexts
Comparing Values Using Ratios
Understanding Proportion as Equality of Ratios
Relating Ratios to Fractions
Relating Ratios to Linear Functions
Defining and Understanding Percentages
Converting Between Percentages, Fractions, and Decimals
Calculating Percentage Increases and Decreases
Solving Original Value Problems with Percentages
Working with Percentages Greater Than 100%
Understanding and Solving Simple Interest Problems
Solving Direct Proportion Problems
Solving Inverse Proportion Problems
Graphical Representation of Direct Proportion
Graphical Representation of Inverse Proportion
Using Compound Measures in Comparisons
Comparing Lengths Using Ratio Notation
Comparing Areas Using Ratio Notation
Comparing Volumes Using Ratio Notation
Understanding and Interpreting Direct Proportion Equations
Understanding and Interpreting Inverse Proportion Equations
Constructing Equations for Direct Proportion
Constructing Equations for Inverse Proportion
Interpreting Gradients as Rates of Change
Recognising Graphs of Direct Proportion
Recognising Graphs of Inverse Proportion
Understanding Instantaneous Rate of Change
Calculating Average Rate of Change
Applying Gradients of Chords and Tangents
Using Rates of Change in Numerical Contexts
Using Rates of Change in Algebraic Contexts
Using Rates of Change in Graphical Contexts
Understanding Growth and Decay Problems
Calculating Compound Interest
Solving Iterative Growth and Decay Problems
Setting Up Growth and Decay Equations
Interpreting Solutions to Growth and Decay Problems
Unit 4
Geometry and Measures
Points, Lines, and Planes
Parallel and Perpendicular Lines
Polygons and Their Properties
Regular Polygons and Symmetry
Drawing Diagrams from Descriptions
Basic Ruler and Compass Constructions
Constructing Perpendicular Bisectors
Constructing Perpendicular Lines
Bisecting Angles with Compass
Solving Loci Problems
Angles at a Point and on a Line
Vertically Opposite Angles
Alternate and Corresponding Angles
Angle Sum in Triangles and Polygons
Properties of Special Quadrilaterals
Types of Triangles and Their Properties
Congruence Criteria for Triangles
Triangle Congruence and Simple Proofs
Base Angles of Isosceles Triangles
Identifying Congruent Shapes
Identifying Similar Shapes
Transformations: Rotation, Reflection, Translation
Enlargement with Fractional Scale Factors
Enlargement with Negative Scale Factors
Combining Transformations
Circle Definitions and Properties
Tangents and Chords in Circles
Angle Subtended by Arcs
Angles in a Semicircle
Angles in the Same Segment
Cyclic Quadrilaterals
Tangents and Radius Perpendicularity
Tangents from External Points
Perpendicular Bisector of a Chord
Alternate Segment Theorem
Geometric Problems on Coordinate Axes
Properties of 3D Shapes
Plans and Elevations of 3D Shapes
Constructing Plans and Elevations
Standard Units of Measure
Measuring Line Segments and Angles
Interpreting Maps and Bearings
Area of Triangles and Parallelograms
Area of Trapezia
Volume of Cuboids and Prisms
Circumference of a Circle
Area of a Circle
Perimeters of 2D Shapes
Surface Area of Spheres and Cones
Volume of Spheres and Cones
Frustums and Composite Solids
Arc Lengths and Areas of Sectors
Congruence Relationships in Similar Figures
Similarity Relationships in Lengths
Similarity Relationships in Areas and Volumes
Pythagoras’ Theorem in 2D Figures
Pythagoras’ Theorem in 3D Figures
Trigonometric Ratios in Right-Angled Triangles
Trigonometric Ratios in General Triangles
Exact Values of Trigonometric Ratios
The Sine Rule
The Cosine Rule
Area of Triangles Using Sine
Describing Translations as Vectors
Adding and Subtracting Vectors
Multiplying Vectors by Scalars
Geometric Proofs Using Vectors
Unit 5
Probability
Recording Outcomes of Experiments
Using Frequency Tables
Using Frequency Trees
Randomness and Fairness in Probability
Equally Likely Events
Expected Outcomes of Experiments
Relative Frequency vs Theoretical Probability
Probability Scale from 0 to 1
Exhaustive Outcomes Summing to 1
Mutually Exclusive Events Summing to 1
Empirical Samples and Theoretical Distributions
Enumerating Sets Systematically
Using Tables to Enumerate Sets
Using Grids to Enumerate Sets
Using Venn Diagrams to Enumerate Sets
Using Tree Diagrams to Enumerate Sets
Constructing Possibility Spaces for Single Experiments
Constructing Possibility Spaces for Combined Experiments
Calculating Theoretical Probabilities from Possibility Spaces
Independent Combined Events
Dependent Combined Events
Tree Diagrams for Combined Events
Adding Probabilities for Combined Events
Multiplying Probabilities for Combined Events
Conditional Probability Basics
Expected Frequencies in Two-Way Tables
Tree Diagrams for Conditional Probability
Venn Diagrams for Conditional Probability
Common Mistakes in Probability Calculations
Interpreting Real-Life Probability Scenarios
Unit 6
Statistics
What is Sampling?
Limitations of Sampling
Primary vs Secondary Data
Discrete vs Continuous Data
Frequency Tables for Categorical Data
Bar Charts for Categorical Data
Pie Charts for Categorical Data
Pictograms for Categorical Data
Vertical Line Charts for Ungrouped Data
Tables for Time Series Data
Line Graphs for Time Series Data
Grouped Data Frequency Tables
Histograms with Equal Class Intervals
Histograms with Unequal Class Intervals
Cumulative Frequency Graphs
Box Plots and Their Uses
Mean as a Measure of Central Tendency
Median as a Measure of Central Tendency
Mode and Modal Class
Range as a Measure of Spread
Outliers in Data Sets
Quartiles and Interquartile Range
Describing Populations Using Statistics
Scatter Graphs for Bivariate Data
Understanding Correlation Types
Correlation vs Causation
Drawing Lines of Best Fit
Interpolating Trends in Data
Extrapolating Trends in Data
Dangers of Extrapolation
Positive, Negative, and No Correlation
Weak vs Strong Correlation
