GCSE
MATHEMATICS
Higher Tier Paper 2 Calculator
Mark scheme for Predicted Paper
,Mark Scheme for AQA GCSE Mathematics Higher Paper 2
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 24%
• Recurring Patterns:
o Practical applications like calculating percentages, ratio-based problems, and bounds
estimation.
o Real-life contexts, such as financial and compound interest scenarios.
2. Algebra
• Percentage: 35%
• Recurring Patterns:
o Solving and rearranging equations, simplifying expressions, and working with quadratic
and nth term formulas.
o Logical reasoning and multi-step problem-solving in algebraic contexts.
3. Geometry
• Percentage: 25%
• Recurring Patterns:
o Calculations of angles, areas, and perimeters.
o Transformations (e.g., reflections, rotations), circle theorems, and similarity problems.
o Frequently integrated with arithmetic or algebra.
4. Probability and Statistics
• Percentage: 11%
• Recurring Patterns:
o Simple probability calculations and graphical data analysis.
o Probability trees and interpreting game probabilities.
5. Graphs
• Percentage: 5%
• Recurring Patterns:
o Focus on quadratic graphs, transformations, and gradient interpretation.
Page | 2
, o Minimal representation across all papers.
1. Most Tested Areas:
• Algebra dominates, consistently accounting for the largest share of questions and marks across
all three papers.
2. Least Tested Areas:
• Graph-related questions and probability/statistics receive less emphasis, with straightforward and
basic tasks.
3. Recurring Patterns Across Papers:
1. Practical Applications:
Many questions integrate real-world scenarios, such as financial calculations, measurements, and
population changes.
2. Stepwise Complexity:
Questions progress from simple calculations to multi-step, logic-based problems.
3. Integration Across Topics:
Some questions combine algebra with geometry or arithmetic with probability to assess
comprehensive understanding.
Page | 3
, Question 1
Work out (2.5 × 109 )3 .
Give the answer in standard form. (1 mark)
1. Strategies to Answer the Question
1. Expand the number:
(2.5 × 109 )3 = 2.53 × (109 )3 .
2. Calculate each component:
o 2.53 = 15.625.
o (109 )3 = 1027 .
3. Combine the results:
(2.5 × 109 )3 = 15.625 × 1027 .
4. Convert to standard form:
15.625 × 1027 = 1.5625 × 1028 .
2. Mark Scheme
• 1 mark for the correct answer in standard form: 1.5625 × 1028 .
3. Background Theory Needed for the Question
Standard Form and Laws of Exponents
5. Standard Form:
A number in standard form is written as a × 10n , where 1 ≤ a < 10 and n is an integer.
o Example: 45000 = 4.5 × 104 , 0.002 = 2 × 10−3.
6. Raising a Power to a Power:
Use the law of exponents:
Page | 4
MATHEMATICS
Higher Tier Paper 2 Calculator
Mark scheme for Predicted Paper
,Mark Scheme for AQA GCSE Mathematics Higher Paper 2
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 24%
• Recurring Patterns:
o Practical applications like calculating percentages, ratio-based problems, and bounds
estimation.
o Real-life contexts, such as financial and compound interest scenarios.
2. Algebra
• Percentage: 35%
• Recurring Patterns:
o Solving and rearranging equations, simplifying expressions, and working with quadratic
and nth term formulas.
o Logical reasoning and multi-step problem-solving in algebraic contexts.
3. Geometry
• Percentage: 25%
• Recurring Patterns:
o Calculations of angles, areas, and perimeters.
o Transformations (e.g., reflections, rotations), circle theorems, and similarity problems.
o Frequently integrated with arithmetic or algebra.
4. Probability and Statistics
• Percentage: 11%
• Recurring Patterns:
o Simple probability calculations and graphical data analysis.
o Probability trees and interpreting game probabilities.
5. Graphs
• Percentage: 5%
• Recurring Patterns:
o Focus on quadratic graphs, transformations, and gradient interpretation.
Page | 2
, o Minimal representation across all papers.
1. Most Tested Areas:
• Algebra dominates, consistently accounting for the largest share of questions and marks across
all three papers.
2. Least Tested Areas:
• Graph-related questions and probability/statistics receive less emphasis, with straightforward and
basic tasks.
3. Recurring Patterns Across Papers:
1. Practical Applications:
Many questions integrate real-world scenarios, such as financial calculations, measurements, and
population changes.
2. Stepwise Complexity:
Questions progress from simple calculations to multi-step, logic-based problems.
3. Integration Across Topics:
Some questions combine algebra with geometry or arithmetic with probability to assess
comprehensive understanding.
Page | 3
, Question 1
Work out (2.5 × 109 )3 .
Give the answer in standard form. (1 mark)
1. Strategies to Answer the Question
1. Expand the number:
(2.5 × 109 )3 = 2.53 × (109 )3 .
2. Calculate each component:
o 2.53 = 15.625.
o (109 )3 = 1027 .
3. Combine the results:
(2.5 × 109 )3 = 15.625 × 1027 .
4. Convert to standard form:
15.625 × 1027 = 1.5625 × 1028 .
2. Mark Scheme
• 1 mark for the correct answer in standard form: 1.5625 × 1028 .
3. Background Theory Needed for the Question
Standard Form and Laws of Exponents
5. Standard Form:
A number in standard form is written as a × 10n , where 1 ≤ a < 10 and n is an integer.
o Example: 45000 = 4.5 × 104 , 0.002 = 2 × 10−3.
6. Raising a Power to a Power:
Use the law of exponents:
Page | 4
