Mark Scheme
Summer 2025
Pearson Edexcel GCSE
In Mathematics
Higher (Calculator) Paper 3H
,Mark Scheme for Edexcel GCSE Mathematics Higher Paper 3
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 23%
• Recurring Patterns:
o Problems focus on ratios, percentages, proportional reasoning, and bounds
estimations.
o Regular use of real-life contexts, such as financial modeling, scaling, and flow
rates.
o Multi-step numerical operations integrated with problem-solving.
2. Algebra
• Percentage: 35%
• Recurring Patterns:
o Consistently the most tested topic.
o Heavy focus on solving equations (quadratic, simultaneous), algebraic
manipulation, and graph transformations.
o Includes sequences, inequalities, and multi-step algebraic reasoning.
o Regular integration with other topics like graphs and geometry.
3. Geometry
• Percentage: 25%
• Recurring Patterns:
o Focus on trigonometry, circle theorems, transformations, and vector geometry.
o Problems involving areas, volumes, and spatial reasoning.
o Geometry often overlaps with algebra or arithmetic in complex questions.
4. Probability and Statistics
• Percentage: 11%
• Recurring Patterns:
o Standard probability calculations using tree diagrams and data interpretation.
o Frequent testing of cumulative frequency, box plots, and averages.
Page | 2
, o Often tied to real-world applications like population studies or surveys.
5. Graphs
• Percentage: 6%
• Recurring Patterns:
o Minimal focus but essential for foundational understanding.
o Tasks include plotting and interpreting linear and quadratic graphs.
o Regular questions on graph transformations and finding gradients or roots.
Key Insights
1. Most Tested Areas:
• Algebra is consistently the most tested topic, reflecting its importance in higher-tier
problem-solving.
2. Least Tested Areas:
• Graphs and Probability/Statistics have the lowest percentage, focusing on simpler,
foundational tasks.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
o Many problems are framed in practical scenarios, such as financial planning,
measurements, and motion.
2. Stepwise Progression:
o Questions range from basic recall/calculation to multi-step reasoning and
problem-solving.
3. Cross-Topic Integration:
o Frequent integration of concepts, such as geometry with algebra or arithmetic
with probability, to test holistic understanding.
Page | 3
, Question 1: Rearranging the Formula for the Volume of a Cone
1. Strategies to answer the question
1. Start with the formula for the volume of a cone:
1
𝑉 = 𝜋𝑟 2 ℎ.
3
2. Rearrange the formula to make ℎ the subject:
o Multiply both sides of the equation by 3 to get rid of the fraction:
3𝑉 = 𝜋𝑟 2 ℎ.
o Divide both sides
3𝑉
ℎ= .
𝜋𝑟 2
2. Mark Scheme
• Correct rearrangement of the formula (3 marks).
3. Background Theory
• Rearranging formulas: To solve for one variable in terms of others, perform inverse
operations to isolate the desired variable. For example, multiplying by the
denominator of a fraction or dividing by a coefficient.
Page | 4
Summer 2025
Pearson Edexcel GCSE
In Mathematics
Higher (Calculator) Paper 3H
,Mark Scheme for Edexcel GCSE Mathematics Higher Paper 3
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 23%
• Recurring Patterns:
o Problems focus on ratios, percentages, proportional reasoning, and bounds
estimations.
o Regular use of real-life contexts, such as financial modeling, scaling, and flow
rates.
o Multi-step numerical operations integrated with problem-solving.
2. Algebra
• Percentage: 35%
• Recurring Patterns:
o Consistently the most tested topic.
o Heavy focus on solving equations (quadratic, simultaneous), algebraic
manipulation, and graph transformations.
o Includes sequences, inequalities, and multi-step algebraic reasoning.
o Regular integration with other topics like graphs and geometry.
3. Geometry
• Percentage: 25%
• Recurring Patterns:
o Focus on trigonometry, circle theorems, transformations, and vector geometry.
o Problems involving areas, volumes, and spatial reasoning.
o Geometry often overlaps with algebra or arithmetic in complex questions.
4. Probability and Statistics
• Percentage: 11%
• Recurring Patterns:
o Standard probability calculations using tree diagrams and data interpretation.
o Frequent testing of cumulative frequency, box plots, and averages.
Page | 2
, o Often tied to real-world applications like population studies or surveys.
5. Graphs
• Percentage: 6%
• Recurring Patterns:
o Minimal focus but essential for foundational understanding.
o Tasks include plotting and interpreting linear and quadratic graphs.
o Regular questions on graph transformations and finding gradients or roots.
Key Insights
1. Most Tested Areas:
• Algebra is consistently the most tested topic, reflecting its importance in higher-tier
problem-solving.
2. Least Tested Areas:
• Graphs and Probability/Statistics have the lowest percentage, focusing on simpler,
foundational tasks.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
o Many problems are framed in practical scenarios, such as financial planning,
measurements, and motion.
2. Stepwise Progression:
o Questions range from basic recall/calculation to multi-step reasoning and
problem-solving.
3. Cross-Topic Integration:
o Frequent integration of concepts, such as geometry with algebra or arithmetic
with probability, to test holistic understanding.
Page | 3
, Question 1: Rearranging the Formula for the Volume of a Cone
1. Strategies to answer the question
1. Start with the formula for the volume of a cone:
1
𝑉 = 𝜋𝑟 2 ℎ.
3
2. Rearrange the formula to make ℎ the subject:
o Multiply both sides of the equation by 3 to get rid of the fraction:
3𝑉 = 𝜋𝑟 2 ℎ.
o Divide both sides
3𝑉
ℎ= .
𝜋𝑟 2
2. Mark Scheme
• Correct rearrangement of the formula (3 marks).
3. Background Theory
• Rearranging formulas: To solve for one variable in terms of others, perform inverse
operations to isolate the desired variable. For example, multiplying by the
denominator of a fraction or dividing by a coefficient.
Page | 4
