AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 5

4 marks · Easy difficulty · Short Answer

Complete an equivalence table for fractions, decimals, and percentages, and find the percentage of a shaded grid.

Practise this question

Question

Part (a) presents a table with columns for Fraction, Decimal, and Percentage. The first row gives 0.5 and 50% with an empty fraction cell. The second row gives 1/10 and 10% with an empty decimal cell. The third row gives 2/5 and 0.4 with an empty percentage cell. Part (b) shows a rectangle divided into a 5-column by 4-row grid of 20 equal squares. The top 3 rows (15 squares) are shaded grey, and the bottom row (5 squares) is unshaded, asking what percentage of the grid is shaded.

Mark scheme

Show the mark scheme Mark scheme for question 5(a) lists the correct values: fraction 1/2 (or equivalent), decimal 0.1, and percentage 40(%). It awards B3 for all three values correct, B2 for two correct, and B1 for one correct, noting that equivalent answers must be in the correct form.

How to answer it

Fractions, Decimals, and Percentages (FDP)

📋 What this question tests
  • FDP Conversions: Converting fluently between common fractions, terminating decimals, and percentages.
  • Visual Representations: Expressing shaded portions of regular grids as fractions and converting them into percentages.
  • Place Value & Proportions: Recognising tenths, fifths, and quarters in various forms.

Question 5 (a)

Completing Equivalent Fractions, Decimals, and Percentages Table [3 Marks]

✅ Correct Answer

Fraction Decimal Percentage
1/2 0.5 50%
1/10 0.1 10%
2/5 0.4 40%

Any exact equivalent fraction like 5/10 or 50/100 is accepted for the first row, but fully simplified ( 1/2 ) is best practice.

📐 Step-by-Step Conversions

  1. Row 1: 50% means 50 out of 100 → 50/100 = 1/2 .
  2. Row 2: 1/10 means "one tenth" → Place value is 1 in the tenths column = 0.1 (or 1 ÷ 10 = 0.1).
  3. Row 3: Convert to an equivalent fraction with denominator 100:
    2/5 = 4/10 = 40/100 = 40% .
    Alternatively: 0.4 × 100 = 40% .

💡 Key Knowledge

  • "Per cent" means "out of 100": x% = x / 100 .
  • Decimal to Percentage: Multiply by 100 (shift digits two places to the left).
  • Common Benchmarks to Memorise:
    • 1/2 = 0.5 = 50%
    • 1/10 = 0.1 = 10%
    • 1/5 = 0.2 = 20% → so 2/5 = 0.4 = 40%

❌ Common Errors

  • Writing 0.01 for 1/10: Confusing one tenth (0.1) with one hundredth (0.01).
  • Writing 4% for 0.4: Forgetting that 0.4 is 4 tenths ( 40% ), whereas 4% is 0.04 .
  • Incorrect Form: Writing a decimal in the fraction column or a fraction in the percentage column.
Mark Scheme Breakdown:
• B3: All 3 values correct ( 1/2 , 0.1 , 40% ).
• B2: Any 2 values correct.
• B1: Any 1 value correct.

Question 5 (b)

Finding the Shaded Percentage of a Grid [1 Mark]

✅ Correct Answer

75%

The "%" symbol is already printed on the answer line, so simply writing 75 earns the mark.

📐 Step-by-Step Method

  1. Method 1 (Count Squares):
    • Count total squares: 5 columns × 4 rows = 20 squares .
    • Count shaded squares: 3 full rows = 3 × 5 = 15 squares .
    • Form the fraction: 15/20 .
    • Scale to /100: (15 × 5) / (20 × 5) = 75/100 = 75% .
  2. Method 2 (Row Proportions):
    • 3 complete rows out of 4 are shaded: 3/4 .
    • Convert known fraction to percentage: 3/4 = 75% .

🧠 Exam Technique

  • Look for rows or columns first: Rather than counting 20 individual squares, spot that exactly 3 out of 4 horizontal strips are fully shaded. This immediately gives 3/4 = 75% and saves time!
  • Check unshaded squares: 5 out of 20 squares are white ( 5/20 = 25% ). Check that 75% + 25% = 100% .

❌ Common Errors

  • Writing the fraction or count: Giving 15 or 15/20 instead of converting to a percentage. The question asks specifically: "What percentage..."
  • Miscounting the grid size: Assuming grids are always 10×10 (100 squares) and writing 15%. Always calculate the actual total!
Mark Scheme Breakdown:
• B1: 75 or 75% .

Topics

Number · 3.1.2 Fractions, decimals and percentages

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 3 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.