Mark Scheme
Summer 2025
Pearson Edexcel GCSE
In Mathematics
Higher (Calculator) Paper 2
,Mark Scheme for Edexcel GCSE Mathematics Higher Paper 2
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 23%
• Recurring Patterns:
o Practical scenarios like percentage changes, proportional reasoning, and
bounds estimations.
o Foundational numerical operations integrated with real-world problem-
solving.
2. Algebra
• Percentage: 34%
• Recurring Patterns:
o A strong emphasis on solving equations, manipulating formulas, and working
with sequences.
o Frequent appearance of multi-step algebraic reasoning questions.
3. Geometry
• Percentage: 29%
• Recurring Patterns:
o Problems on area, volume, and angles.
o Application of circle theorems, transformations, and trigonometric
calculations.
o Often integrated with arithmetic in real-life contexts.
4. Probability and Statistics
• Percentage: 13%
• Recurring Patterns:
o Straightforward probability calculations using trees and Venn diagrams.
o Data interpretation and statistical measures, such as averages, are frequently
tested.
Page | 2
,5. Graphs
• Percentage: 10%
• Recurring Patterns:
o Graph-related questions focus on analyzing trends in quadratic and linear
graphs.
o Minimal focus across papers, with straightforward tasks involving graph
transformations.
Key Insights
1. Most Tested Areas:
• Algebra is consistently the most tested area, reflecting its central role in higher-tier
mathematical reasoning.
2. Least Tested Areas:
• Graphs and Probability/Statistics have limited representation, focusing on simpler,
foundational tasks.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
o Many questions are set in practical scenarios, such as financial modeling,
population studies, and measurements.
2. Stepwise Progression:
o Questions range from basic recall and calculation to multi-step reasoning and
problem-solving.
3. Cross-Topic Integration:
o Some questions combine concepts, such as geometry with algebra or
arithmetic with probability, testing a holistic understanding.
Page | 3
, Question 1: Sine and Angles
1. Strategies to answer the question
(a) Calculate the sine of the angle:
1. Use the formula for sine:
opposite
sin(𝜃) = hypotenuse.
2. Substitute opposite = 6 and hypotenuse = 10:
6
sin(𝜃) = 10 = 0.6.
(b) Find the angle:
3. Use the inverse sine function on your calculator:
𝜃 = sin−1 (0.6).
2. Mark Scheme
(a) Correct calculation of sin(𝜃) (1 mark).
(b) Correct angle value using sin−1 (1 mark).
3. Background Theory
• Trigonometric ratios: In a right-angled triangle, the sine of an angle is defined as the
ratio of the opposite side to the hypotenuse.
3
Example: For a triangle with sides 3, 4, and 5: sin(𝜃) = 5 = 0.6.
• Inverse sine: Use sin−1 on a calculator to find the angle when the sine value is
known.
Page | 4
Summer 2025
Pearson Edexcel GCSE
In Mathematics
Higher (Calculator) Paper 2
,Mark Scheme for Edexcel GCSE Mathematics Higher Paper 2
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 23%
• Recurring Patterns:
o Practical scenarios like percentage changes, proportional reasoning, and
bounds estimations.
o Foundational numerical operations integrated with real-world problem-
solving.
2. Algebra
• Percentage: 34%
• Recurring Patterns:
o A strong emphasis on solving equations, manipulating formulas, and working
with sequences.
o Frequent appearance of multi-step algebraic reasoning questions.
3. Geometry
• Percentage: 29%
• Recurring Patterns:
o Problems on area, volume, and angles.
o Application of circle theorems, transformations, and trigonometric
calculations.
o Often integrated with arithmetic in real-life contexts.
4. Probability and Statistics
• Percentage: 13%
• Recurring Patterns:
o Straightforward probability calculations using trees and Venn diagrams.
o Data interpretation and statistical measures, such as averages, are frequently
tested.
Page | 2
,5. Graphs
• Percentage: 10%
• Recurring Patterns:
o Graph-related questions focus on analyzing trends in quadratic and linear
graphs.
o Minimal focus across papers, with straightforward tasks involving graph
transformations.
Key Insights
1. Most Tested Areas:
• Algebra is consistently the most tested area, reflecting its central role in higher-tier
mathematical reasoning.
2. Least Tested Areas:
• Graphs and Probability/Statistics have limited representation, focusing on simpler,
foundational tasks.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
o Many questions are set in practical scenarios, such as financial modeling,
population studies, and measurements.
2. Stepwise Progression:
o Questions range from basic recall and calculation to multi-step reasoning and
problem-solving.
3. Cross-Topic Integration:
o Some questions combine concepts, such as geometry with algebra or
arithmetic with probability, testing a holistic understanding.
Page | 3
, Question 1: Sine and Angles
1. Strategies to answer the question
(a) Calculate the sine of the angle:
1. Use the formula for sine:
opposite
sin(𝜃) = hypotenuse.
2. Substitute opposite = 6 and hypotenuse = 10:
6
sin(𝜃) = 10 = 0.6.
(b) Find the angle:
3. Use the inverse sine function on your calculator:
𝜃 = sin−1 (0.6).
2. Mark Scheme
(a) Correct calculation of sin(𝜃) (1 mark).
(b) Correct angle value using sin−1 (1 mark).
3. Background Theory
• Trigonometric ratios: In a right-angled triangle, the sine of an angle is defined as the
ratio of the opposite side to the hypotenuse.
3
Example: For a triangle with sides 3, 4, and 5: sin(𝜃) = 5 = 0.6.
• Inverse sine: Use sin−1 on a calculator to find the angle when the sine value is
known.
Page | 4
