KS2, KS3, KS4 (GCSE) & A-level Online Mathematics Tutoring
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Key Stage 4 (GCSE) Mathematics

Key Stage 4 (GCSE) Math Topics

Key Stage 4 (GCSE) Math Topics

We teach the complete Key Stage 4 (GCSE) 9-1 Mathematics Syllabus as set out by the UK Department of Education and as detailed by all the applicable exam boards - AQA, Edexcel and OCR. Our maths tutors will cover the following KS4 topics as required and will tailor each lesson plan to each student depending on the areas they need to improve on. We will continuously test our students’ learning progress by assigning them numerous practice questions to check their understanding and problem solving improvement on topics that are covered. We ensure thorough practice of past mock and GCSE exam papers takes place so our students are prepared to perform well in their actual exams.

  1. Understanding and Working with Numbers:

  • Factors and Multiples of whole numbers (integers) - LCM and HCF

  • Order of Operation (BODMAS)

  • Prime Numbers and Prime Factorisation

  • Square numbers, cubic numbers and Roots

  • Index Notation, Powers or 10 and Standard Form

  • Laws of Indices

2. Understanding and Working with Fractions, Decimals and Percentages:

  • Equivalent Fractions

  • Operations with Fractions (adding, subtracting, multiplying and dividing fractions)

  • Operations with Decimals (adding, subtracting, multiplying and dividing fractions)

  • Rounding and Place value of Decimals

  • Calculating percentages

  • Using Percentages in real life problems

3. Algebra

  • Algebraic Expressions and Indices

  • Simplifying Expressions

  • Substitution and Formulae

  • Expanding brackets and Factorising

  • Using Expressions and Formulae

  • Algebraic fractions

  • Surds

  • Solving algebraic fraction

4. Using and Working with Graphs

  • Linear Graphs

  • Rates of Change

  • Quadratic Graphs

  • Cubic and Reciprocal Graphs

5. Equations, Inequalities and Sequences

  • Rearranging simple linear equations

  • Solving linear equations

  • Solving equations with brackets

  • Solving Quadratic Equations

  • Completing the Square

  • Solving Simultaneous Equations (linear and quadratic)

  • Solving linear inequalities

  • Generating sequences and using the nth term

6. Angles and Trigonometry

  • Shapes and their properties

  • Angles (parallel lines and triangles)

  • Exterior and interior angles of a Polygon

  • Pythagoras Theorem

  • Trigonometry (using trigonometric ratios)

7. Understanding Averages and Ranges

  • Mean and Range

  • Mode, Median and Range

  • Types of averages

  • Solving problems relating to averages and ranges.

8. Perimeter, Area and Volume

  • Rectangles, Parallelograms and Triangles

  • Area of compound shapes

  • Surface area of 3D solids

  • Volume of prisms

  • Circumference and Area of a circle

  • Semicircles and sectors

  • Composite 2D shapes and cylinders

  • Pyramids and Cones

  • Spheres and composite solids

  • Solving Problems relating to perimeters, area and volumes

9. Understanding and Working with more complex Graphs

  • Coordinates, Linear Graphs and Gradients

  • Equation of straight line

  • Real life graphs

  • Distance-Time Graphs

  • Solving problems relating to graphs

10. Ratio and Proportion

  • Using ratios

  • Ratios and Measures

  • Using Proportions

  • Proportion and Graphs

  • Solving proportion problems

11. Trigonometry

  • Graphs of Sine, Cosine, Tangent functions

  • Sine Rule and Calculating Areas

  • Cosine Rule and 2D problems

  • Solving 3D problems

  • Transforming trigonometric graphs

12. Probability

  • Calculating probability

  • Venn Diagrams and set notation

  • Tree Diagrams

  • Combined events

  • Mutually Exclusive events

  • Independent events and Tree Diagrams

  • Conditional Probability

13. Construction, Loci and Bearings

  • Plans and Elevations

  • Accurate drawings

  • Scale drawings and maps

  • Constructions

  • Loci and Regions

  • Bearings

  • Reflect and Rotation

  • Transformation and combinations of transformations

14. Equations and Graphs

  • Expanding double brackets

  • Plotting and using quadratic graphs

  • Factorising quadratic expressions

  • Solving quadratic equations

  • Solving simultaneous equations graphically

  • Showing inequalities graphically

  • Solving quadratic equations graphically

  • Graphs of cubic functions

15. Circle Theorems

  • Radii and Chords

  • Tangents

  • Angles in Circles

  • Applying circle theorems

  16. Vectors and Geometric Proof

  • Vectors and vector notation

  • Vector arithmetic

  • Parallel Vectors

  • Solving Geometric problems

  17. Statistics

  • Sampling

  • Cumulative Frequency

  • Box Plots

  • Drawing Histograms

  • Interpreting histograms

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