GCSE
MATHEMATICS
Higher Tier Paper 1 Non-Calculator
Mark scheme for Predicted Paper
,Mark Scheme for AQA GCSE Mathematics Higher Paper 3
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: 35%
• 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: 27%
• 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: 12%
• Recurring Patterns:
o Straightforward probability calculations using trees and Venn diagrams.
o Data interpretation and statistical measures, such as averages, are frequently
tested.
5. Graphs
Page | 2
, • Percentage: 5%
• 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.
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:
Many questions are set in practical scenarios, such as financial modeling, population
studies, and measurements.
2. Stepwise Progression:
Questions range from basic recall and calculation to multi-step reasoning and problem-
solving.
3. Cross-Topic Integration:
Some questions combine concepts, such as geometry with algebra or arithmetic with
probability, testing a holistic understanding.
Page | 3
, 1. y is 60% more than x. Circle the ratio x: y. (1 mark)
Strategies to Answer the Question
1. Recognize the meaning of "60% more" as y = x + 0.6x, simplifying to y = 1.6x.
2. Write the ratio as x: y = x: 1.6x.
3. Simplify x: 1.6x to 5: 8 by dividing both terms by 0.2.
Mark Scheme
• 1 mark for correctly circling 5: 8.
Background Theory Needed to Answer the Question
When a value is increased by a percentage, it becomes a fraction of the original value.
• For example, "60% more than x" means y = x + 0.6x, or y = 1.6x.
• Ratios simplify proportional relationships. In this case, x: y = x: 1.6x = 5: 8.
Example:
If x = 10, then y = 10 × 1.6 = 16.
The ratio is 10: 16, which simplifies to 5: 8.
Page | 4
MATHEMATICS
Higher Tier Paper 1 Non-Calculator
Mark scheme for Predicted Paper
,Mark Scheme for AQA GCSE Mathematics Higher Paper 3
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: 35%
• 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: 27%
• 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: 12%
• Recurring Patterns:
o Straightforward probability calculations using trees and Venn diagrams.
o Data interpretation and statistical measures, such as averages, are frequently
tested.
5. Graphs
Page | 2
, • Percentage: 5%
• 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.
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:
Many questions are set in practical scenarios, such as financial modeling, population
studies, and measurements.
2. Stepwise Progression:
Questions range from basic recall and calculation to multi-step reasoning and problem-
solving.
3. Cross-Topic Integration:
Some questions combine concepts, such as geometry with algebra or arithmetic with
probability, testing a holistic understanding.
Page | 3
, 1. y is 60% more than x. Circle the ratio x: y. (1 mark)
Strategies to Answer the Question
1. Recognize the meaning of "60% more" as y = x + 0.6x, simplifying to y = 1.6x.
2. Write the ratio as x: y = x: 1.6x.
3. Simplify x: 1.6x to 5: 8 by dividing both terms by 0.2.
Mark Scheme
• 1 mark for correctly circling 5: 8.
Background Theory Needed to Answer the Question
When a value is increased by a percentage, it becomes a fraction of the original value.
• For example, "60% more than x" means y = x + 0.6x, or y = 1.6x.
• Ratios simplify proportional relationships. In this case, x: y = x: 1.6x = 5: 8.
Example:
If x = 10, then y = 10 × 1.6 = 16.
The ratio is 10: 16, which simplifies to 5: 8.
Page | 4
