GCSE
MATHEMATICS
Higher Tier Paper 1 Non-Calculator
Mark scheme for Predicted Paper
,Mark Scheme for AQA GCSE Mathematics Higher Paper 1
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 25%
• Recurring Patterns:
o Calculations involving fractions, decimals, percentages, and ratios.
o Estimation and numerical problem-solving in practical contexts.
o Frequently integrated into multi-step questions requiring logical reasoning.
2. Algebra
• Percentage: 35%
• Recurring Patterns:
o Simplifying and solving linear and quadratic equations.
o Rearranging formulas and working with nth term sequences.
o Logical reasoning applied in algebraic contexts, such as completing the square.
3. Geometry
• Percentage: 24%
• Recurring Patterns:
o Calculation of areas, perimeters, and volumes of 2D and 3D shapes.
o Angle properties, transformations, and symmetry are regularly tested.
o Application of circle theorems and geometry rules in diagrams.
4. Probability and Statistics
• Percentage: 11%
• Recurring Patterns:
o Simple probability problems involving trees and Venn diagrams.
o Questions often emphasize interpreting and analyzing given data.
5. Graphs
Page | 2
, • Percentage: 5%
• Recurring Patterns:
o Plotting and interpreting quadratic and linear graphs.
o Limited focus, with straightforward tasks assessing trends and key points.
1. Most Tested Areas:
• Algebra dominates, forming the largest proportion of questions, reflecting its
importance in higher-tier mathematical reasoning.
2. Least Tested Areas:
• Probability and graphs appear less frequently, focusing on simpler interpretation and
problem-solving tasks.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
Many arithmetic and geometry questions are set in practical scenarios, such as cost
analysis, measurements, or angles in real-world shapes.
2. Stepwise Complexity:
Questions progress from foundational calculations to multi-step reasoning, ensuring
diverse skill assessment.
3. Cross-Topic Integration:
Some questions combine arithmetic with geometry or algebra, testing the ability to apply
concepts cohesively.
Page | 3
, Question 1
(a) Work out ∛(729×1000). (1 mark)
1. Strategies to Answer the Question
1. Compute 729 × 1000 = 729,000.
2. Break 729,000 into components for easier calculation:
∛(729 × 1000) = ∛(729) × ∛(1000).
3. Evaluate ∛729 = 9 and ∛1000 = 10.
4. Multiply 9 × 10 = 90.
2. Mark Scheme
• 1 mark for the correct answer: 90.
3. Background Theory Needed for the Question
The cube root of a number x, written as ∛x, is the number that, when multiplied by itself three
times, gives x.
For example:
• ∛8 = 2 because 2 × 2 × 2 = 8.
• ∛27 = 3 because 3 × 3 × 3 = 27.
Here, cube roots are calculated for 729 and 1000:
• ∛729 = 9 because 93 = 729.
• ∛1000 = 10 because 103 = 1000.
Using the property of cube roots:
∛(a × b) = ∛a × ∛b.
Page | 4
MATHEMATICS
Higher Tier Paper 1 Non-Calculator
Mark scheme for Predicted Paper
,Mark Scheme for AQA GCSE Mathematics Higher Paper 1
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 25%
• Recurring Patterns:
o Calculations involving fractions, decimals, percentages, and ratios.
o Estimation and numerical problem-solving in practical contexts.
o Frequently integrated into multi-step questions requiring logical reasoning.
2. Algebra
• Percentage: 35%
• Recurring Patterns:
o Simplifying and solving linear and quadratic equations.
o Rearranging formulas and working with nth term sequences.
o Logical reasoning applied in algebraic contexts, such as completing the square.
3. Geometry
• Percentage: 24%
• Recurring Patterns:
o Calculation of areas, perimeters, and volumes of 2D and 3D shapes.
o Angle properties, transformations, and symmetry are regularly tested.
o Application of circle theorems and geometry rules in diagrams.
4. Probability and Statistics
• Percentage: 11%
• Recurring Patterns:
o Simple probability problems involving trees and Venn diagrams.
o Questions often emphasize interpreting and analyzing given data.
5. Graphs
Page | 2
, • Percentage: 5%
• Recurring Patterns:
o Plotting and interpreting quadratic and linear graphs.
o Limited focus, with straightforward tasks assessing trends and key points.
1. Most Tested Areas:
• Algebra dominates, forming the largest proportion of questions, reflecting its
importance in higher-tier mathematical reasoning.
2. Least Tested Areas:
• Probability and graphs appear less frequently, focusing on simpler interpretation and
problem-solving tasks.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
Many arithmetic and geometry questions are set in practical scenarios, such as cost
analysis, measurements, or angles in real-world shapes.
2. Stepwise Complexity:
Questions progress from foundational calculations to multi-step reasoning, ensuring
diverse skill assessment.
3. Cross-Topic Integration:
Some questions combine arithmetic with geometry or algebra, testing the ability to apply
concepts cohesively.
Page | 3
, Question 1
(a) Work out ∛(729×1000). (1 mark)
1. Strategies to Answer the Question
1. Compute 729 × 1000 = 729,000.
2. Break 729,000 into components for easier calculation:
∛(729 × 1000) = ∛(729) × ∛(1000).
3. Evaluate ∛729 = 9 and ∛1000 = 10.
4. Multiply 9 × 10 = 90.
2. Mark Scheme
• 1 mark for the correct answer: 90.
3. Background Theory Needed for the Question
The cube root of a number x, written as ∛x, is the number that, when multiplied by itself three
times, gives x.
For example:
• ∛8 = 2 because 2 × 2 × 2 = 8.
• ∛27 = 3 because 3 × 3 × 3 = 27.
Here, cube roots are calculated for 729 and 1000:
• ∛729 = 9 because 93 = 729.
• ∛1000 = 10 because 103 = 1000.
Using the property of cube roots:
∛(a × b) = ∛a × ∛b.
Page | 4
