Mathematics for GCSE/IGCSE

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Here is a comprehensive outline for a GCSE/IGCSE Mathematics course, covering both the Foundation and Higher tiers:

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Grade 1–3 (Basic Level):

Number 7 Topics

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Place Value

Basic Operations (addition, subtraction, multiplication, division)

Fractions, Decimals, Percentages (basic operations, conversions)

Rounding, Estimation, and Approximations

Negative Numbers

Factors, Multiples, and Prime Numbers

Powers and Roots (square roots, cube roots)

Algebra 5 Topics

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Introduction to Algebraic Expressions

Simplifying Algebraic Expressions

Solving Simple Linear Equations (one-step and two-step)

Substitution into Expressions

Basic Sequences (arithmetic sequences)

Ratio, Proportion, and Rates of Change 4 Topics

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Simple Ratios (e.g., sharing in a ratio)

Proportional Relationships (e.g., scale factors)

Percentage Change

Direct and Inverse Proportions

Geometry and Measures 5 Topics

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Perimeter and Area of 2D Shapes

Volume of Simple 3D Shapes (prisms, cubes, cuboids)

Properties of 2D and 3D Shapes (triangles, squares, circles, cuboids)

Basic Symmetry and Transformations (reflection, rotation, translation)

Angle Sum of Triangles and Quadrilaterals

Statistics 4 Topics

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Tally Charts and Frequency Tables

Bar Charts and Pictograms

Mean, Median, Mode

Probability (simple events and outcomes)

Probability 2 Topics

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Probability as a Fraction (with outcomes to 1)

Understanding Basic Probability Terms (certain, likely, unlikely)

Grade 4–5 (Intermediate Level)

Number 4 Topics

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Fractions, Decimals, Percentages (operations with fractions, percentage increase/decrease)

Decimal Operations

Powers and Indices (squares, cubes, square roots)

Standard Form and Scientific Notation

Algebra 5 Topics

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Expanding and Factorizing Linear Expressions

Solving Linear Equations (including equations with unknowns on both sides)

Solving Simple Quadratic Equations by Factorisation

Linear Graphs (equations of straight lines)

Solving Simple Simultaneous Equations (graphically and algebraically)

Ratio, Proportion, and Rates of Change 3 Topics

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Using Proportions in Word Problems

Direct and Inverse Proportions (word problems)

Compound Proportions (simple mixtures, recipes)

Geometry and Measures 5 Topics

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Area and Volume of Composite Shapes

Pythagoras’ Theorem (right-angled triangles)

Basic Trigonometry (using sine, cosine, and tangent)

Angles in Parallel Lines and Polygons

3D Shapes (surface area and volume calculations)

Statistics 4 Topics

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Interpreting Bar Charts, Pie Charts, and Histograms

Cumulative Frequency and Box Plots

Averages (mean, median, mode, and range)

Probability (calculating probability of simple events)

Probability 2 Topics

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Probability of Two Events (using and/or)

Tree Diagrams

Higher Tier (Grades 4–9)

Number 4 Topics

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More Complex Operations with Fractions and Decimals

Integer and Decimal Powers (rules of indices)

Standard Form (multiplying and dividing numbers in standard form)

Ratios and Proportions (more complex problems involving ratios, scale factors)

Algebra 6 Topics

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Solving Quadratic Equations (factorizing, using the quadratic formula)

Algebraic Manipulation (simplifying and expanding expressions)

Simultaneous Linear Equations (substitution, elimination)

Linear Graphs and their Equations (y = mx + c, gradient, intercepts)

Rearranging Formulas

Solving Inequalities (graphical and algebraic)

Ratio, Proportion, and Rates of Change 2 Topics

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Direct and Inverse Proportions in Context

Percentages in Real-World Contexts (interest, growth/decay)

Geometry and Measures 5 Topics

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Trigonometry (sin, cos, tan in right-angled triangles)

Pythagoras’ Theorem (applications to non-right-angled triangles)

3D Geometry (volume and surface area of cylinders, cones, spheres)

Circle Theorems and Proofs

Transformations (rotation, reflection, enlargement, and translation in detail)

Statistics 4 Topics

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Constructing and Interpreting Cumulative Frequency Graphs

Box Plots and Outliers

Averages and Range (comparison between data sets)

Sampling Methods (random, stratified, and systematic sampling)

Probability 3 Topics

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Venn Diagrams and Probability Calculations

Tree Diagrams for Conditional Probability

Combining Probabilities (independent and dependent events)

Grade 7–9 (Advanced Level)

Number 4 Topics

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Advanced Indices and Surds (simplifying, rationalizing denominators)

Complex Decimal and Fraction Operations (proportions, ratios)

Exact Values in Standard Form

Arithmetic and Geometric Sequences

Algebra 5 Topics

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Solving Quadratic Equations (completing the square, quadratic formula)

Solving Simultaneous Equations (one linear, one quadratic)

Algebraic Fractions (simplifying, multiplying/dividing)

Inequalities (including quadratic inequalities)

Functions and Graphs (domain, range, inverse functions)

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Mathematics for GCSE/IGCSE

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