Topic Checklist

GCSE Maths

Last Updated on 11th Aug 2025

Grade 1 - 16 topics

Number

  • Place Value
  • Ordering Integers
  • Ordering Decimals
  • Reading Scales
  • Simple Mathematical Notation
  • Interpreting Real-Life Tables

Algebra

  • Introduction to Algebraic Conventions
  • Coordinates

Geometry & Measures

  • Simple Geometric Definitions
  • Polygons
  • Symmetries
  • Tessellations and Congruency
  • Names of Angles

Probability & Statistics

  • The Probability Scale
  • Tally Charts and Bar Charts
  • Pictograms

Grade 2 - 51 topics

Number

  • Adding Integers and Decimals
  • Subtracting Integers and Decimals
  • Four Rules of Negatives
  • Multiplying Integers
  • Dividing Integers
  • Inverse Operations
  • Money Questions
  • Negatives in Real Life
  • Introduction to Fractions
  • Equivalent Fractions
  • Simplifying Fractions
  • Half-Way Values
  • Factors, Multiples and Primes
  • Multiplying and Dividing by Powers of 10
  • Rounding to the Nearest 10, 100, 1000
  • Rounding to Decimal places
  • Index Notation

Algebra

  • Algebra - Addition and Subtraction
  • Index Notation (Algebra)
  • Algebra - Multiplication
  • Algebra - Division
  • Function Machines
  • Generating a Sequence - Term to Term

Ratio, Proportion, Rate of Change

  • Introduction to Ratio
  • Using Ratio for Recipe Questions
  • Introduction to Percentages
  • Value for Money
  • Introduction to Proportion

Geometry & Measures

  • Properties of Solids
  • Nets
  • Angles on a Line and at a Point
  • Measuring and drawing Angles
  • Drawing a Triangle Using a Protractor
  • Reflection
  • Rotations
  • Translations
  • Plans and Elevations
  • Perimeters
  • Area of a Rectangle
  • Area of a Triangle
  • Area of a Parallelogram
  • Area of a Trapezium

Probability & Statistics

  • Frequency Trees
  • Listing Outcomes
  • Calculating Probabilities
  • Mutually Exclusive Events
  • Two-Way Tables
  • Averages and the Range
  • Data - Discrete and Continuous
  • Vertical Line Charts
  • Frequency Tables and Diagrams

Grade 3 - 61 topics

Number

  • Multiplying Decimals
  • Dividing Decimals
  • Listing Strategies
  • Ordering Fractions
  • Adding and Subtracting Fractions
  • Finding a Fraction of an Amount
  • Multiplying Fractions
  • Dividing Fractions
  • BODMAS/BIDMAS
  • Reciprocals
  • Calculator Questions
  • Product of Primes
  • Highest Common Factor (HCF)
  • Lowest Common Multiple (LCM)
  • Squares, Cubes and Roots
  • Standard Form
  • FDP - Fractions, Decimals & Percentages
  • Percentage of an Amount
  • Change to a Percentage
  • Rounding to Significant Figures
  • Estimating Answers
  • Using Place Value

Algebra

  • Expanding Single Brackets
  • Expanding and Simplifying - Single Brackets
  • Expanding and Simplifying - Double Brackets
  • Simple Factorisation
  • Substitution
  • Drawing Straight Line Graphs
  • The Gradient of a Line
  • Drawing Quadratic Graphs
  • Sketching Functions
  • Solving Equations
  • Changing the subject of a formula
  • nth Term of a Sequence (Linear)
  • Special Sequences

Ratio, Proportion, Rate of Change

  • Exchanging Money
  • Sharing using Ratio
  • Ratios, Fractions and Graphs
  • Increase/Decrease by a Percentage
  • Percentage Change
  • Reverse Percentage Problems
  • Simple Interest

Geometry & Measures

  • Metric conversions
  • Problems on Coordinate Axes
  • Surface Area of a Prism
  • Circle Definitions
  • Area of a Circle
  • Circumference of a Circle
  • Volume of a Prism
  • Angles and Parallel Lines
  • Angles in a Triangle
  • Angles in Polygons
  • Bearings

Probability & Statistics

  • Experimental Probabilities
  • Possibility Spaces
  • Venn Diagrams - Introduction
  • Pie Charts
  • Stem and Leaf Diagrams
  • Scatter Diagrams
  • Averages from Frequency table
  • Estimate for the mean

Grade 4 - 27 topics

Number

  • Index Notation
  • Introduction to Bounds

Algebra

  • Index Notation (Algebra)
  • Midpoint of a Line
  • Expanding Single Brackets
  • Expanding and Simplifying - Single Brackets
  • Expanding and Simplifying - Double Brackets
  • Solving Equations
  • Changing the subject of a formula
  • Forming Formulae and Equations
  • Inequalities on a Number Line
  • Solve Linear Inequalities
  • Simultaneous Equations Graphically
  • Fibonacci Sequences

Ratio, Proportion, Rate of Change

  • Compound Measures
  • Distance-Time Graphs
  • Similar Shapes

Geometry & Measures

  • Constructing Perpendiculars
  • Bisecting an Angle
  • Loci
  • Draw a Triangle Using Compasses
  • Enlargements
  • Tangents, Arcs, Sectors and Segments
  • Pythagoras' Theorem

Probability & Statistics

  • Simple Tree Diagrams
  • Sampling Populations
  • Time Series

Grade 5 - 23 topics

Number

  • Negative Indices
  • Error Intervals
  • Mathematical Reasoning

Algebra

  • Factorising and Solving Quadratics
  • The Difference of Two Squares
  • Finding the Equation of a Straight Line
  • Roots and Turning Points of Quadratics
  • Cubic and Reciprocal Graphs
  • Simultaneous Equations Algebraically
  • Geometric Progressions

Ratio, Proportion, Rate of Change

  • Compound Interest and Depreciation
  • Ratio Questions

Geometry & Measures

  • Congruent triangles
  • Sectors of a Circle
  • Trigonometry
  • Spheres
  • Pyramids
  • Cones
  • Frustums
  • Exact Trigonometric Values
  • Introduction to Vectors

Probability & Statistics

  • Harder Tree Diagrams
  • Stratified sampling

Grade 6 - 11 topics

Number

  • Recurring Decimals to Fractions

Algebra

  • Expanding Triple Brackets
  • Iteration - Trial and Improvement
  • Iterative Processes

Geometry & Measures

  • Enlargement - Negative Scale Factor
  • Combinations of Transformations
  • Circle Theorems
  • Proof of Circle Theorems

Probability & Statistics

  • Probability using Venn Diagrams
  • Cumulative Frequency
  • Boxplots

Grade 7 - 19 topics

Number

  • Fractional Indices
  • Recurring Decimals - Proof

Algebra

  • Changing the subject of a formula (Hard)
  • Solving Quadratics with the Formula
  • Factorising Hard Quadratics
  • Algebraic Proof
  • Exponential Functions
  • Trigonometric Graphs
  • Transformation of Functions
  • Equation of a Circle

Ratio, Proportion, Rate of Change

  • Regions
  • Direct and Inverse Proportion
  • Ratio Questions

Geometry & Measures

  • Similarity - Area and Volume
  • The Sine Rule
  • The Cosine Rule
  • Area of a Triangle Using Sine

Probability & Statistics

  • And and Or Probability Questions
  • Histograms

Grade 8/9 - 14 topics

Number

  • Upper and Lower Bounds
  • Surds

Algebra

  • Perpendicular Lines
  • Completing the Square
  • Algebraic Fractions
  • Simultaneous Equations with a Quadratic
  • Solve Quadratic Inequalities
  • Finding the nth Term of a Quadratic
  • Inverse Functions
  • Composite Functions
  • Interpreting Graphs

Geometry & Measures

  • Pythagoras in 3D
  • Trigonometry in 3D
  • Vectors

Tutoring

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Elena Mirza

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Fas ensures that he has a clear understanding of my daughter’s knowledge gaps and then addresses these consistently. He provides timely feedback on every lesson which is very helpful. His explanations are clear and easy to follow. My daughter’s confidence improved significantly and her predicted grade increased by 2 grades.
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Abdur-Raheem

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C Owen

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Naz Siddiqi

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Fas provides weekly video reports detailing lesson content, progress, and assigned homework. My son, who previously lacked confidence, has developed a much stronger grasp of core concepts and now approaches maths with greater assurance. My daughter, already a capable mathematician, has continued to excel under his guidance.
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Lyndsay Glynn

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I would highly recommend Fas as a tutor, he has turned a 'dull and boring' (not to mention difficult) topic into something that both children feel confident with and are having a growing sense of confidence in. Fas is patient and encouraging, whilst setting clear targets for the children. I was rather expecting the children to complain about maths tutoring, however after lesson one, all complaints evaporated and they are already recognising the benefits. Fas is organised, punctual, professional and provides comprehensive feedback following every lesson. Highly recommend.
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Maaz Ahmed

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Six months of Fas’s 1-2-1 GCSE Maths tuition took me from Set 3 to Set 1—I’ve never felt more confident. I highly recommend Fas!
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Grant Jackson

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Since starting lessons with him, I've seen a real improvement not only in my daughter's maths skills but also in how positively she now approaches the subject. He makes lessons feel comfortable and productive, which has been so important in helping her ask questions without feeling worried about getting things wrong.
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🔥 Actively Maintained

We are always improving our content, adding new resources and adding features to enhance your learning experience.

  • 2 Aug, 2026New Roots & Turning Points of Quadratics Worksheet
  • 26 Jul, 2026New Equation of a Straight Line: Coorindates Worksheet
  • 20 Jul, 2026New Equation of a Straight Line: y=mx+c Worksheet
  • 10 Jul, 2026New Difference of Two Squares Worksheet
  • 7 Jul, 2026New Factorising & Solving Quadratics Worksheet
  • 5 Jul, 2026New Error Intervals Worksheet
  • 17 May, 2026New Negative Indices Worksheet
  • 9 May, 2026New Time Series Worksheet
  • 8 May, 2026New Capture-Recapture Worksheet
  • 20 Jan, 2026New Tree Diagrams Worksheet