By Revision Genie
Number
Unit 1
Natural Numbers
Integers: Positive, Zero, Negative
Prime Numbers
Square Numbers
Cube Numbers
Common Factors and Multiples
Rational and Irrational Numbers
Reciprocals
Expressing Numbers in Words
Prime Factorization
Highest Common Factor (HCF)
Lowest Common Multiple (LCM)
Set Notation Basics
Venn Diagrams with Two Sets
Union and Intersection of Sets
Powers: Squares and Cubes
Roots: Square and Cube Roots
Other Powers and Roots
Proper Fractions
Improper Fractions and Mixed Numbers
Decimals and Percentages
Converting Between Fractions, Decimals, and Percentages
Simplifying Fractions
Ordering Quantities by Magnitude
Symbols: =, ≠, >, <, ⩾, ⩽
Four Operations with Integers
Four Operations with Fractions
Four Operations with Decimals
Order of Operations and Brackets
Positive, Zero, and Negative Indices
Rules of Indices
Standard Form Conversion
Calculations in Standard Form
Rounding to Decimal Places
Rounding to Significant Figures
Estimation in Calculations
Upper and Lower Bounds
Ratio Simplification
Dividing Quantities in a Given Ratio
Proportional Reasoning in Contexts
Common Measures of Rate
Average Speed Calculations
Currency Exchange Rates
Percentage of a Quantity
Expressing One Quantity as a Percentage of Another
Percentage Increase and Decrease
Simple Interest Calculations
Compound Interest Calculations
Efficient Calculator Use
Interpreting Calculator Displays
Time Calculations: Units and Conversions
24-Hour and 12-Hour Clock Conversions
Reading Clocks and Timetables
Money Calculations
Currency Conversion Problems
Unit 2
Algebra and Graphs
Substituting Values into Expressions
Collecting Like Terms
Expanding Single Brackets
Expanding Double Brackets
Factorising Simple Expressions
Factorising Quadratic Expressions
Simplifying Algebraic Fractions
Solving Linear Equations
Solving Simultaneous Equations
Changing the Subject of a Formula
Representing Inequalities on a Number Line
Solving Linear Inequalities
Finding the nth Term of Linear Sequences
Finding the nth Term of Quadratic Sequences
Sketching Linear Graphs
Sketching Quadratic Graphs
Sketching Cubic Graphs
Sketching Reciprocal Graphs
Sketching Exponential Graphs
Interpreting Distance-Time Graphs
Interpreting Speed-Time Graphs
Using Gradient as Rate of Change
Solving Equations Graphically
Finding Roots of Quadratic Equations Graphically
Understanding Domain and Range of Functions
Finding Inverse Functions
Forming Composite Functions
Differentiating ax^n Functions
Using Derivatives to Find Gradients
Finding Stationary Points
Determining Maxima and Minima
Using Tangents to Estimate Gradients
Understanding Cartesian Coordinates
Finding the Gradient of a Line
Finding the Equation of a Line
Finding the Midpoint of a Line Segment
Calculating the Length of a Line Segment
Equations of Parallel Lines
Equations of Perpendicular Lines
Unit 3
Coordinate Geometry
Cartesian Coordinates System
Plotting Points on a Grid
Understanding Quadrants
Reading Coordinates from a Graph
Drawing Straight-Line Graphs
Linear Equations in y = mx + c Form
Finding the Gradient from a Graph
Calculating Gradient Using Two Points
Understanding Positive and Negative Gradients
Finding the y-Intercept of a Line
Equations of Lines Parallel to Given Lines
Equations of Lines Perpendicular to Given Lines
Midpoint Formula for a Line Segment
Finding Midpoints Between Two Points
Length of a Line Segment Using Coordinates
Distance Formula Between Two Points
Using Linear Graphs to Solve Equations
Intersection of Two Linear Graphs
Graphical Representation of Inequalities
Transforming Equations to y = mx + c Form
Understanding Horizontal and Vertical Lines
Finding Equations of Horizontal Lines (y = k)
Finding Equations of Vertical Lines (x = k)
Using Graphs to Represent Real-Life Situations
Identifying Parallel Lines from Equations
Identifying Perpendicular Lines from Equations
Exam Trap: Misinterpreting Gradients
Exam Trap: Incorrect Use of Distance Formula
Exam Trap: Confusing Midpoint with Gradient
Worked Example: Gradient Calculation
Worked Example: Finding Midpoint
Worked Example: Distance Between Points
Worked Example: Parallel Line Equation
Worked Example: Perpendicular Line Equation
Worked Example: Solving Equations Graphically
Worked Example: Intersection of Two Lines
Worked Example: Graphing Real-Life Problems
Unit 4
Geometry
Basic Geometrical Terms
Properties of Triangles
Properties of Quadrilaterals
Properties of Polygons
Vocabulary of Circles
Nets of 3D Shapes
Drawing and Measuring Angles
Constructing Triangles with Compass and Ruler
Drawing and Interpreting Scale Drawings
Understanding Bearings
Line Symmetry in 2D Shapes
Rotational Symmetry in 2D Shapes
Angle Sum of a Triangle
Angle Sum of a Quadrilateral
Angles at a Point and on a Line
Vertically Opposite Angles
Angles in Parallel Lines
Interior and Exterior Angles of Polygons
Congruence and Similarity
Calculating Lengths in Similar Shapes
Circle Theorems: Angle in a Semicircle
Circle Theorems: Angle Between Tangent and Radius
Circle Theorems: Angles in the Same Segment
Circle Theorems: Opposite Angles in a Cyclic Quadrilateral
Circle Theorems: Alternate Segment Theorem
Equal Chords and Perpendicular Bisectors
Tangents from an External Point
Using Scale Factor in Similar Shapes
Using Scale Factor in Similar Solids
Common Exam Traps in Circle Theorems
Worked Examples: Angle Problems in Circles
Worked Examples: Bearings and Scale Drawings
Worked Examples: Symmetry in Shapes
Worked Examples: Angle Problems in Polygons
Exam Trap: Misinterpreting Bearings
Exam Trap: Incorrect Use of Circle Theorems
Unit 5
Mensuration
Metric Units of Length, Area, and Volume
Converting Between Metric Units
Perimeter of Rectangles and Triangles
Perimeter of Parallelograms and Trapeziums
Area of Rectangles and Squares
Area of Triangles
Area of Parallelograms
Area of Trapeziums
Circumference of a Circle
Area of a Circle
Arc Length of a Circle
Sector Area of a Circle
Surface Area of a Cuboid
Surface Area of a Prism
Surface Area of a Cylinder
Surface Area of a Sphere
Surface Area of a Cone
Surface Area of a Pyramid
Volume of a Cuboid
Volume of a Prism
Volume of a Cylinder
Volume of a Sphere
Volume of a Cone
Volume of a Pyramid
Perimeter and Area of Compound Shapes
Surface Area of Compound Solids
Volume of Compound Solids
Parts of Shapes: Perimeter and Area
Parts of Solids: Surface Area and Volume
Working with Shapes in Terms of π
Examining Units in Area and Volume Problems
Common Mistakes in Mensuration Calculations
Strategies for Solving Real-Life Mensuration Problems
Using Formulas Provided in the Exam
Understanding Frustums and Their Calculations
Relationship Between Dimensions in Similar Shapes
Scaling Areas and Volumes in Similar Solids
Practical Applications of Mensuration in Everyday Contexts
Unit 6
Trigonometry
Understanding Pythagoras' Theorem
Using Pythagoras' Theorem to Find a Side
Using Pythagoras' Theorem to Find the Hypotenuse
Introduction to Trigonometric Ratios
The Sine Ratio in Right-Angled Triangles
The Cosine Ratio in Right-Angled Triangles
The Tangent Ratio in Right-Angled Triangles
Finding Unknown Sides Using Trigonometry
Finding Unknown Angles Using Trigonometry
Solving Two-Dimensional Problems with Trigonometry
Angles of Elevation and Depression
Exact Trigonometric Values for Key Angles
Introduction to the Sine Rule
Using the Sine Rule to Find Angles
Using the Sine Rule to Find Sides
Introduction to the Cosine Rule
Using the Cosine Rule to Find Angles
Using the Cosine Rule to Find Sides
Area of a Triangle Using Trigonometry
Sketching the Sine Graph (0° to 360°)
Sketching the Cosine Graph (0° to 360°)
Sketching the Tangent Graph (0° to 360°)
Solving Trigonometric Equations with Sine
Solving Trigonometric Equations with Cosine
Solving Trigonometric Equations with Tangent
Understanding the Ambiguous Case of the Sine Rule
Trigonometry in Three Dimensions
Using Pythagoras' Theorem in 3D Problems
Calculating the Angle Between a Line and a Plane
Common Errors in Trigonometric Calculations
Choosing Between the Sine and Cosine Rules
Using Bearings in Trigonometric Problems
Using Trigonometry for Real-Life Applications
Interpreting Trigonometric Problems in Context
Exam Tips for Trigonometry Questions
Unit 7
Transformations and Vectors
Understanding Transformations
Reflection in Horizontal Lines
Reflection in Vertical Lines
Reflection in Diagonal Lines
Describing Reflections in Words
Rotation About the Origin
Rotation About a Vertex
Rotation About Midpoints of Edges
Describing Rotations in Words
Enlargement with Positive Scale Factors
Enlargement with Fractional Scale Factors
Describing Enlargements in Words
Translation by Vectors
Combining Transformations
Identifying Transformations from Diagrams
Drawing Transformations Step-by-Step
Properties of Transformations
Recognizing Symmetry in Transformations
Introduction to Vectors
Vector Notation and Representation
Adding Vectors Graphically
Adding Vectors Algebraically
Subtracting Vectors Graphically
Subtracting Vectors Algebraically
Multiplying Vectors by Scalars
Magnitude of a Vector
Using the Magnitude Formula
Position Vectors and Coordinates
Expressing Vectors in Terms of Two Others
Proving Parallel Vectors
Proving Collinearity of Points
Vectors in Geometric Proofs
Solving Ratio Problems with Vectors
Vector Applications in Similarity
Common Errors in Transformations
Common Errors in Vector Arithmetic
Examining Combined Transformations
Examining Vector Problems in Context
Unit 8
Probability
Understanding the Probability Scale
Calculating Probability of a Single Event
Complementary Events in Probability
Expressing Probability as Fractions, Decimals, and Percentages
Interpreting Probability from Tables
Using Venn Diagrams for Probability Problems
Understanding Relative Frequency
Estimating Probability Using Relative Frequency
Expected Frequency from Probability
Identifying Fairness, Bias, and Randomness
Introduction to Combined Events
Using Sample Space Diagrams for Combined Events
Using Venn Diagrams for Combined Events
Using Tree Diagrams for Combined Events
Calculating Probability with Replacement
Calculating Probability without Replacement
Understanding Mutually Exclusive Events
Understanding Independent Events
Probability of A and B (Intersection)
Probability of A or B (Union)
Conditional Probability Basics
Using Venn Diagrams for Conditional Probability
Using Tree Diagrams for Conditional Probability
Using Tables for Conditional Probability
Common Misconceptions in Probability Calculations
Interpreting Real-Life Probability Scenarios
Examining Probability in Games of Chance
Understanding Probability in Experimental Contexts
Avoiding Errors in Tree Diagram Calculations
Interpreting Overlapping Events in Venn Diagrams
Identifying Errors in Complementary Events
Linking Relative Frequency to Theoretical Probability
Unit 9
Statistics
Classifying Data: Qualitative vs Quantitative
Discrete and Continuous Data
Organising Data into Frequency Tables
Tally Charts and Two-Way Tables
Mean of a Data Set
Median of a Data Set
Mode of a Data Set
Range as a Measure of Spread
Choosing Between Mean, Median, and Mode
Grouped Frequency Tables: Estimating the Mean
Identifying the Modal Class
Calculating the Range and Interquartile Range
Bar Charts: Drawing and Interpreting
Composite and Dual Bar Charts
Pie Charts: Constructing and Interpreting
Pictograms: Representation and Analysis
Stem-and-Leaf Diagrams with Keys
Scatter Diagrams: Plotting Data Points
Correlation: Positive, Negative, and None
Drawing a Line of Best Fit by Eye
Using a Line of Best Fit to Make Predictions
Cumulative Frequency Tables
Drawing Cumulative Frequency Diagrams
Estimating the Median from Cumulative Frequency
Interquartile Range from Cumulative Frequency
Percentiles from Cumulative Frequency Diagrams
Histograms: Frequency Density and Class Width
Drawing Histograms with Unequal Class Intervals
Interpreting Histograms to Find Frequencies
Comparing Data Sets Using Averages
Comparing Data Sets Using Measures of Spread
Limitations of Statistical Conclusions
Common Errors in Data Representation