GCSE Maths — Diagnostic Guide

Coverage Map

Grading Rubric

PASS Criteria

• Correctly solve at least 2 out of 3 Unit Tests with full working
• Correctly solve at least 2 out of 3 Integration Tests
• Show clear method marks even if final answer has arithmetic errors
• Correct use of mathematical notation and units

PARTIAL Criteria

• Correctly solve 1—2 Unit Tests and 1 Integration Test
• Shows correct method but with arithmetic errors
• Partially correct solutions with some steps missing
• Struggles with multi-step problems but handles single-step questions

FAIL Indicators

• Cannot convert between fractions, decimals, and percentages
• Cannot solve simple linear equations
• Cannot apply Pythagoras’ theorem correctly
• Does not show working for calculations
• Cannot interpret statistical diagrams (box plots, histograms)

Prerequisite Chains

Number (fractions, decimals, percentages, standard form)
  ├── Algebra (equations require number skills)
  │     └── Ratio and Proportion (proportional reasoning)
  └── Statistics (calculations require number skills)

Number (factors, multiples)
  └── Algebra (factorisation, simplification)

Algebra (solving equations)
  ├── Geometry (trigonometry, Pythagoras)
  └── Ratio and Proportion (formula rearrangement)

Geometry (area, perimeter)
  └── Statistics (histograms, frequency density)

Recommended order of diagnostic completion:

1. diag-number — foundational arithmetic skills
2. diag-algebra — core problem-solving toolkit
3. diag-geometry — requires algebra and number skills
4. diag-ratio-proportion — applied number skills
5. diag-statistics — integrates number and algebra skills

Timing Recommendations

Total recommended time: approximately 2.75 hours (spread across 2 sessions).

How to Use These Diagnostics

1. Complete each diagnostic without a calculator unless the question explicitly allows one.
2. Show ALL working — method marks are often worth more than the final answer in GCSE exams.
3. Pay attention to units — convert to consistent units before calculating.
4. Check solutions immediately, comparing both method and final answer.
5. If you score FAIL on a topic, review the source file and practise additional problems before retrying.
6. Integration Tests combine skills from multiple topics — these are essential for Paper 2 and Paper 3 preparation.
7. Common pitfalls to watch: percentage change vs percentage of, confusing median and mean, forgetting units in compound measures.

Summary

The key principles covered in this topic are linked in the sub-pages above. Focus on understanding the definitions, applying the formulas or frameworks, and evaluating strengths and limitations of each approach.

Worked Examples

Worked examples demonstrating the application of key concepts are covered in the detailed sub-pages linked above.

Common Pitfalls

• Confusing terminology or concepts that appear similar but have distinct meanings.
• Overlooking key assumptions or boundary conditions that limit applicability.