Your journey to excellence in
By Revision Genie
Understanding Number and Place Value
Unit 1
Reading Whole Numbers in Words
Writing Whole Numbers in Figures
Understanding Place Value
Identifying Decimal Places
Rounding Whole Numbers
Rounding Decimals to Whole Numbers
Rounding Decimals to Decimal Places
Rounding to Significant Figures
Converting Between Decimals and Fractions
Converting Between Fractions and Percentages
Converting Between Decimals and Percentages
Understanding and Using Ratios
Ordering Whole Numbers
Comparing Decimals
Ordering Fractions
Comparing Percentages
Understanding Directed Numbers
Ordering Directed Numbers
Expressing Numbers as Products of Primes
Finding the Highest Common Factor (HCF)
Finding the Lowest Common Multiple (LCM)
Using Square Numbers and Square Roots
Understanding Cubes and Cube Roots
Using Index Notation
Understanding Standard Form
Converting Numbers to Standard Form
Interpreting Standard Form on Calculators
Estimating Solutions to Calculations
Using Estimation in Multiplication and Division
Finding a Fraction of a Quantity
Finding a Percentage of a Quantity
Expressing One Number as a Fraction of Another
Expressing One Number as a Percentage of Another
Calculating Percentage Increases
Calculating Percentage Decreases
Using Percentage Multipliers
Understanding Recurring Decimals
Converting Recurring Decimals to Fractions
Identifying Rational and Irrational Numbers
Understanding and Simplifying Surds
Using Surds in Exact Calculations
Understanding Upper and Lower Bounds
Calculating Bounds in Addition and Subtraction
Calculating Bounds in Multiplication and Division
Understanding Proportional Division
Using Ratios in Real-Life Problems
Understanding Direct Proportion
Understanding Inverse Proportion
Solving Problems with Compound Percentages
Understanding Appreciation and Depreciation
Unit 2
Number Operations and Relationships
Understanding Odd and Even Numbers
Identifying Multiples of a Number
Finding Factors of a Number
Prime Numbers: Definition and Identification
Expressing Numbers as Products of Prime Factors
Square Numbers and Square Roots
Cube Numbers and Cube Roots
Introduction to Index Notation
Rules of Indices: Multiplication and Division
Rules of Indices: Power of a Power
Zero and Negative Indices
Fractional Indices and Their Meaning
Standard Form: Writing Large and Small Numbers
Calculations with Numbers in Standard Form
Understanding Rational and Irrational Numbers
Introduction to Surds
Simplifying Surds
Adding and Subtracting Surds
Multiplying and Dividing Surds
Direct Proportion: Concept and Examples
Inverse Proportion: Concept and Examples
Using Ratios in Real-Life Situations
Proportional Division Problems
Percentage Change: Increase and Decrease
Using Multipliers for Percentage Calculations
Repeated Percentage Change: Appreciation and Depreciation
Estimating Solutions to Numerical Problems
Upper and Lower Bounds in Calculations
Calculating Bounds for Addition and Subtraction
Calculating Bounds for Multiplication and Division
Using Venn Diagrams to Solve Number Problems
Efficient Use of a Calculator
Understanding Calculator Order of Operations
Interpreting Calculator Displays Correctly
Solving Real-Life Problems with Ratios and Proportions
Applying Simple Interest in Financial Calculations
Calculating Compound Interest Efficiently
Understanding Annual Rates: AER and APR
Foreign Currencies and Exchange Rate Calculations
Profit and Loss Calculations
Solving Problems Involving Appreciation and Depreciation
Understanding Recurring Decimals as Exact Fractions
Rounding Numbers to Significant Figures
Rounding Decimals to a Specified Number of Places
Converting Between Fractions, Decimals, and Percentages
Unit 3
Solving Numerical Problems
Understanding Numerical Problems
Interpreting Written and Visual Data
Using Timetables and Schedules
Solving Problems with Distance Charts
Holiday Booking Calculations
Principles of Personal Finance
Understanding Fuel and Utility Bills
Hire Purchase Calculations
Discount and VAT Applications
Taxation and Wages Problems
Loan Repayments and Mortgages
Budgeting Techniques
Exchange Rates and Commissions
Simple Interest Calculations
Compound Interest Calculations
Appreciation and Depreciation
Annual Rates: AER and APR
Finding Original Quantities
Real-World Ratio Problems
Proportional Division Applications
Estimation in Real-World Contexts
Rounding Solutions Appropriately
Accuracy in Problem Contexts
Understanding Measurement Error
Upper and Lower Bounds in Addition
Upper and Lower Bounds in Multiplication
Bounds in Division and Subtraction
Using Venn Diagrams in Problems
Interpreting Calculator Displays
Choosing Accuracy in Solutions
Foreign Currency Exchange Problems
Enterprise Calculations in Finance
Saving and Borrowing Calculations
Investing and Financial Growth Problems
Understanding Bounds in Error Analysis
Calculating Composite Financial Changes
Recognising and Applying Estimation Techniques
Solving Multi-Step Real-World Problems
Interpreting Financial Graphs and Tables
Common Errors in Financial Calculations
Using Compound Measures in Finance
Measurement Appropriateness in Contexts
Understanding Simple Enterprise Costs
Calculating Best Buys and Discounts
Handling Numerical Problems with Units
Unit 4
Basic Algebra and Expressions
Understanding Variables in Algebra
Definition of Terms and Coefficients
Simplifying Expressions with Addition
Simplifying Expressions with Subtraction
Combining Like Terms in Algebra
Simplifying Expressions with Multiplication
Simplifying Expressions with Division
Expanding Single Brackets
Expanding Double Brackets
Factorising Linear Expressions
Factorising Quadratic Expressions
Understanding Substitution in Algebra
Substituting Positive Numbers into Formulae
Substituting Negative Numbers into Formulae
Substituting Fractions into Formulae
Substituting Decimals into Formulae
Forming Expressions from Word Problems
Forming Equations from Word Problems
Solving Linear Equations with One Unknown
Solving Linear Equations with Two Unknowns
Solving Equations with Fractions
Solving Equations with Decimals
Understanding Sequences in Algebra
Identifying Patterns in Number Sequences
Finding the nth Term of a Linear Sequence
Finding the nth Term of a Quadratic Sequence
Generating Sequences from Formulae
Applying Algebra to Real-Life Problems
Common Errors in Simplifying Expressions
Common Errors in Substitution
Common Errors in Forming Equations
Common Errors in Solving Equations
Worked Examples: Simplifying Expressions
Worked Examples: Substitution Problems
Worked Examples: Forming Equations
Worked Examples: Solving Linear Equations
Worked Examples: nth Term Problems
Exam Tips for Algebra Questions
Recognising Misleading Patterns in Sequences
Using Algebra to Solve Geometry Problems
Using Algebra to Solve Financial Problems
Using Algebra to Solve Ratio Problems
Checking Solutions to Algebraic Problems
Understanding the Difference Between Expressions and Equations
Using Trial and Improvement to Solve Equations
Understanding Inequalities in Algebra
Solving Inequalities with One Variable
Solving Inequalities with Two Variables
Graphical Representation of Inequalities
Unit 5
Graphs and Functions
Introduction to Graphs and Functions
Understanding Cartesian Coordinates
Plotting Points on a Graph
The Equation of a Straight Line
Understanding the Gradient of a Line
Finding the Y-Intercept
Drawing Linear Graphs from Equations
Finding the Equation of a Line from a Graph
Parallel and Perpendicular Lines
Introduction to Quadratic Graphs
Plotting Quadratic Graphs from Tables
Key Features of Quadratic Graphs (Vertex, Axis of Symmetry)
Solving Quadratic Equations Using Graphs
Cubic Graphs: Key Features and Shapes
Plotting Cubic Graphs from Equations
Introduction to Reciprocal Graphs
Plotting Reciprocal Graphs
Understanding Asymptotes in Reciprocal Graphs
Introduction to Exponential Graphs
Plotting Exponential Graphs
Key Features of Exponential Graphs (Growth and Decay)
Transformations of Graphs: Introduction
Vertical Translations of Graphs
Horizontal Translations of Graphs
Reflections of Graphs (x-axis and y-axis)
Stretching Graphs Vertically
Stretching Graphs Horizontally
Combining Transformations on Graphs
Identifying Transformations from Graphs
Interpreting Real-Life Graphs
Distance-Time Graphs: Understanding and Plotting
Velocity-Time Graphs: Key Concepts
Finding Gradients on Real-Life Graphs
Finding Areas Under Graphs (Velocity-Time Context)
Sketching Linear Graphs Quickly
Sketching Quadratic Graphs Quickly
Sketching Cubic Graphs Quickly
Sketching Reciprocal Graphs Quickly
Sketching Exponential Graphs Quickly
Using Graphs to Solve Simultaneous Equations
Graphs of Inequalities: Shading Regions
Identifying Graph Types from Equations
Common Exam Traps in Graphs and Functions
Using Graphs to Model Real-World Situations
Comparing Different Types of Graphs
Using Technology to Plot Graphs
Exam Practice: Linear Graphs
Exam Practice: Quadratic Graphs
Exam Practice: Transformations of Graphs
Unit 6
Equations, Formulae, and Inequalities
Definition of an Equation
Definition of a Formula
Definition of an Inequality
Difference Between Equations, Formulae, and Inequalities
Solving One-Step Equations
Solving Two-Step Equations
Solving Multi-Step Equations
Solving Equations with Negative Numbers
Solving Equations with Brackets
Solving Equations with Variables on Both Sides
Solving Equations with Powers
Understanding Linear Equations
Understanding Quadratic Equations
Rearranging Formulae: Basic Techniques
Rearranging Formulae: Advanced Techniques
Rearranging Formulae with Fractions
Rearranging Formulae with Powers
Changing the Subject of a Formula
Introduction to Simultaneous Equations
Solving Simultaneous Equations by Substitution
Solving Simultaneous Equations by Elimination
Graphical Solutions to Simultaneous Equations
Solving Simultaneous Equations with Fractions
Introduction to Inequalities
Solving One-Step Inequalities
Solving Two-Step Inequalities
Solving Multi-Step Inequalities
Solving Inequalities with Fractions
Solving Inequalities with Decimals
Understanding Compound Inequalities
Solving Compound Inequalities
Solving Quadratic Inequalities
Common Errors in Rearranging Formulae
Common Errors in Solving Inequalities
Practical Applications of Equations
Practical Applications of Formulae
Practical Applications of Inequalities
Exam Tips for Equations
Exam Tips for Formulae
Exam Tips for Inequalities
Worked Examples: Solving Equations
Worked Examples: Rearranging Formulae
Worked Examples: Solving Inequalities
Using Equations, Formulae, and Inequalities in Word Problems
Interpreting Solutions in Context
Unit 7
Properties of Shape and Geometry
Basic Geometrical Terms
Types of Angles
Measuring Angles with a Protractor
Angles at a Point
Angles on a Straight Line
Opposite Angles at a Vertex
Parallel Lines and Angle Properties
Corresponding Angles
Alternate Angles
Interior Angles in Parallel Lines
Angle Sum of a Triangle
Exterior Angle of a Triangle
Properties of Equilateral Triangles
Properties of Isosceles Triangles
Properties of Right-Angled Triangles
Angle Sum of Quadrilaterals
Properties of Special Quadrilaterals
Regular and Irregular Polygons
Interior Angles of Polygons
Exterior Angles of Polygons
Congruence in Triangles
SSS, SAS, ASA, and RHS Congruence Rules
Similarity in Shapes
Ratios in Similar Shapes
Constructing Triangles
Constructing Quadrilaterals
Bisecting a Line Segment
Bisecting an Angle
Constructing Perpendiculars
Constructing Angles of 60°, 90°, and 45°
Drawing Nets of 3D Shapes
Plans and Elevations of 3D Shapes
Rotational Symmetry of Shapes
Reflection Symmetry of Shapes
Tiling Patterns and Tessellation
Transformations: Reflection
Transformations: Rotation
Transformations: Translation
Transformations: Enlargement
Column Vectors for Translation
Loci: Fixed Distance from a Point
Loci: Fixed Distance from a Line
Loci: Equidistant from Two Points
Loci: Equidistant from Two Lines
Intersecting Loci Problems
Using Bearings in Geometry
Scale Drawings and Maps
Unit 8
Trigonometry and Circle Theorems
Understanding Pythagoras' Theorem
Applying Pythagoras to Triangles
Reverse Problems with Pythagoras
Trigonometric Ratios: Sine
Trigonometric Ratios: Cosine
Trigonometric Ratios: Tangent
Using Trigonometric Ratios to Find Angles
Using Trigonometric Ratios to Find Sides
Angles of Elevation and Depression
Bearings and Trigonometry
Introduction to the Sine Rule
Solving Problems with the Sine Rule
Introduction to the Cosine Rule
Solving Problems with the Cosine Rule
Area of a Triangle Using Sine
Sketching Sine Graphs
Sketching Cosine Graphs
Sketching Tangent Graphs
Properties of Trigonometric Graphs
Circle Terminology: Radius, Diameter, Circumference
The Tangent to a Circle
Angles Subtended by Arcs at the Centre
Angles Subtended by Arcs at the Circumference
Angles in the Same Segment
Angles in a Semicircle
Opposite Angles of Cyclic Quadrilaterals
The Alternate Segment Theorem
Equal Tangents from an External Point
Constructing Geometrical Proofs for Circle Theorems
Identifying Circle Theorems in Problems
Using Circle Theorems in Calculations
Common Exam Traps in Circle Theorems
Combining Trigonometry and Circle Properties
Trigonometry in Real-Life Contexts
Using Pythagoras in 3D Problems
Trigonometry in 3D Problems
Proof of the Sine Rule
Proof of the Cosine Rule
Proofs Involving Circle Theorems
Exam Techniques for Trigonometry Questions
Exam Techniques for Circle Theorems Questions
Mixed Problems with Trigonometry and Circles
Using Exact Values in Trigonometry
Simplifying Problems with Diagrams
Understanding the Relationship Between Sine and Cosine
Understanding the Unit Circle
Using Trigonometry in Bearings Problems
Finding Unknowns Using Combined Rules
Understanding and Applying Compound Shapes in Circle Problems
Unit 9
Transformations and Coordinates
Introduction to Transformations
Understanding Coordinates in 4 Quadrants
Plotting Points on a Coordinate Grid
Identifying Midpoints of Line Segments
Reflection in a Vertical Line
Reflection in a Horizontal Line
Reflection in Diagonal Lines (e.g., y=x)
Describing Reflections
Rotation Through 90° Clockwise
Rotation Through 90° Anticlockwise
Rotation Through 180°
Finding the Centre of Rotation
Describing Rotations
Translation Using Column Vectors
Describing Translations
Enlargement with Positive Scale Factors
Enlargement with Fractional Scale Factors
Finding the Centre of Enlargement
Describing Enlargements
Combining Two Transformations
Understanding Tessellations
Solving Problems with Tiling Patterns
Interpreting Maps and Scale Drawings
Constructing Scale Drawings
Using Bearings in Geometry Problems
Constructing Loci Around a Point
Constructing Loci Around a Line
Constructing Loci Equidistant from Two Points
Constructing Loci Equidistant from Two Lines
Solving Problems Involving Intersecting Loci
Using Inequalities in Loci Questions
Transformations in Real-World Contexts
Examining Similarity in 2D Shapes
Examining Similarity in 3D Shapes
Understanding Ratios of Similar Shapes
Applying Transformations to Graphs
Common Mistakes in Transformations
Exam Techniques for Transformation Questions
Unit 10
Perimeter, Area, and Volume
Understanding Perimeter
Calculating Perimeter of Rectangles
Perimeter of Triangles
Perimeter of Regular Polygons
Perimeter of Irregular Shapes
Understanding Area
Area of Rectangles
Area of Triangles
Area of Parallelograms
Area of Trapeziums
Area of Circles
Area of Sectors
Area of Composite Shapes
Understanding Volume
Volume of Cubes and Cuboids
Volume of Prisms
Volume of Cylinders
Volume of Spheres
Volume of Cones
Volume of Pyramids
Volume of Composite Solids
Surface Area of Cubes and Cuboids
Surface Area of Prisms
Surface Area of Cylinders
Surface Area of Spheres
Surface Area of Cones
Surface Area of Pyramids
Surface Area of Composite Solids
Length of Arcs
Perimeter of Sectors
Understanding Units of Measurement
Converting Between Metric Units
Converting Between Metric and Imperial Units
Estimating Measurements
Using Formulae for Area and Volume
Problem Solving with Perimeter
Problem Solving with Area
Problem Solving with Volume
Problem Solving with Composite Shapes
Common Errors in Perimeter Calculations
Common Errors in Area Calculations
Common Errors in Volume Calculations
Exam Techniques for Perimeter Questions
Exam Techniques for Area Questions
Exam Techniques for Volume Questions
Worked Examples: Perimeter Problems
Worked Examples: Area Problems
Worked Examples: Volume Problems
Real-World Applications of Perimeter
Real-World Applications of Area
Real-World Applications of Volume
Unit 11
Statistics and Data Representation
Understanding the Statistical Problem-Solving Cycle
Specifying and Testing Hypotheses
Designing Effective Questionnaires
Avoiding Bias in Data Collection
Understanding Sampling Methods
Systematic Sampling Techniques
Stratified Sampling Techniques
Critiquing Sample Sizes and Reliability
Sorting and Classifying Data
Understanding Qualitative and Quantitative Data
Tallying Methods for Data Collection
Constructing Pictograms
Interpreting Pictograms
Constructing Bar Charts
Interpreting Bar Charts
Constructing Pie Charts
Interpreting Pie Charts
Constructing Vertical Line Diagrams
Interpreting Vertical Line Diagrams
Constructing Line Graphs for Time Data
Interpreting Line Graphs for Time Data
Constructing Grouped Frequency Diagrams
Interpreting Grouped Frequency Diagrams
Constructing Frequency Polygons
Interpreting Frequency Polygons
Constructing Scatter Diagrams
Interpreting Scatter Diagrams
Understanding Correlation Types
Drawing Lines of Best Fit on Scatter Diagrams
Understanding Causation vs Correlation
Constructing Cumulative Frequency Tables
Constructing Cumulative Frequency Diagrams
Interpreting Cumulative Frequency Diagrams
Estimating the Median from Cumulative Frequency
Understanding Measures of Central Tendency
Calculating the Mean for Discrete Data
Calculating the Median for Discrete Data
Calculating the Mode for Discrete Data
Identifying Modal Categories in Qualitative Data
Identifying Modal Classes in Grouped Data
Calculating the Mean for Grouped Data
Estimating the Median for Grouped Data
Understanding Measures of Spread
Calculating the Range for Data
Calculating the Interquartile Range
Constructing Box Plots
Interpreting Box Plots
Comparing Distributions Using Central Tendency
Comparing Distributions Using Spread
Constructing Histograms with Equal Class Widths
Constructing Histograms with Unequal Class Widths
Understanding Frequency Density in Histograms
Interpreting Shapes of Histograms
Identifying Patterns and Exceptions in Data
Recognizing Misleading Graphs and Charts
Drawing Conclusions from Data Representations
Unit 12
Probability and Risk
Understanding Probability Vocabulary
Probability Scale from 0 to 1
The Concept of Relative Frequency
Estimating Probability from Experiments
Theoretical Probability Basics
Equally Likely Outcomes
Experimental vs Theoretical Probability
Probability of an Event Not Occurring
Expressing Probability as Fractions, Decimals, Percentages
Using Venn Diagrams for Probability
Outcomes of Two Combined Experiments
Tabulating Outcomes of Compound Events
Tree Diagrams for Independent Events
Tree Diagrams for Dependent Events
Addition Rule for Mutually Exclusive Events
Multiplication Rule for Independent Events
Introduction to Conditional Probability
Understanding Dependent Events
Sampling Without Replacement
Calculating Probabilities Using Tree Diagrams
Using Graphs for Relative Frequency
Long-Term Stability of Relative Frequency
Total Probability of All Outcomes Equals 1
Common Probability Misconceptions
Risk and Probability in Real-Life Contexts
Interpreting Risk in Everyday Situations
Probability in Games and Gambling
Using Probability to Make Predictions
Worked Example: Rolling Two Dice
Worked Example: Probability with Cards
Worked Example: Probability in a Spinner
Worked Example: Marbles in a Bag
Worked Example: Conditional Probability
Common Exam Traps in Probability Questions
Interpreting Probability Questions Correctly
Strategies for Multi-Step Probability Problems
Using Probability in Decision Making
Understanding Fairness in Probability
Designing Experiments to Estimate Probability
Comparing Experimental and Theoretical Results
Probability and Risk in Health Contexts
Probability and Risk in Financial Contexts
Probability and Risk in Environmental Contexts
Interpreting Tree Diagrams in Context
Identifying Independent vs Dependent Events
Using Probability to Evaluate Outcomes
Let's master Mathematics together!Let's master Mathematics together!Let's master Mathematics together!