Skip to content

Maths Practice (Interactive) | GCSE

Intuition

Learning through practice: Practice problems are like training drills — they help you apply knowledge under exam conditions and identify areas that need more study.

Why it matters: Regular practice builds confidence and reveals patterns in how questions are asked. Each problem reinforces key concepts and exam techniques.

The key insight: Making mistakes during practice is valuable — each error points to a concept that needs clarification before the real exam.

GCSE — Maths Practice

10 auto-graded practice problems. Select an answer, submit, and review the explanation.

Worked Examples

Example 1: Percentage Change

Problem: A house price increases from £120,000 to £135,000. What is the percentage increase?

Solution: Step 1: Find the increase: £135,000−£120,000=£15,000£135,000 - £120,000 = £15,000

Step 2: Divide by the original value: 15,000120,000=0.125\frac{15,000}{120,000} = 0.125

Step 3: Convert to percentage: 0.125×100=12.5%0.125 \times 100 = 12.5\%

Key insight: Percentage change always uses the ORIGINAL value as the denominator.

Example 2: Simultaneous Equations

Problem: Solve 2x+y=72x + y = 7 and x−y=2x - y = 2.

Solution: Step 1: Add the equations: (2x+y)+(x−y)=7+2(2x + y) + (x - y) = 7 + 2

Step 2: Simplify: 3x=9⇒x=33x = 9 \Rightarrow x = 3

Step 3: Substitute into equation 2: 3−y=2⇒y=13 - y = 2 \Rightarrow y = 1

Step 4: Check in equation 1: 2(3)+1=72(3) + 1 = 7 ✓

Key insight: Adding equations works well when one variable has opposite coefficients (here, +y+y and −y-y cancel).

Example 3: Circle Theorems

Problem: In a circle, angle ABC = 40° where A, B, C are on the circumference. Find the angle at the centre, AOC.

Solution: Step 1: Angle at centre = 2 × angle at circumference (both subtended by the same arc AC)

Step 2: ∠AOC=2×40°=80°\angle AOC = 2 \times 40° = 80°

Key insight: The angle at the centre is always double the angle at the circumference when both subtend the same arc. This is one of the most tested circle theorems.

Number

Algebra

Geometry

Statistics

Ratio and Proportion

Cross-References

  • Maths: Detailed notes on number, algebra, geometry, and statistics topics.
  • Maths Question Bank: Additional practice questions organized by topic.
  • Practice Physics: Interactive practice problems covering physics topics that use mathematical skills.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.