AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 2

2 marks · Easy difficulty · Short Answer

Work out the integer value of x that satisfies the double inequality 1.07 < x/9 < 1.17.

Practise this question

Question

Question 2 gives the inequality 1.07 < x/9 < 1.17, stating that x is an integer. It asks the student to 'Work out the value of x' with an answer line 'x = ' and is worth 2 marks.
Question text

x

21.07 < < 1.17 where x is an integer.

Work out the value of x.

[2 marks]

x =

Mark scheme

Show the mark scheme Mark scheme for Question 2: M1 for finding 1.07 * 9 or 9.6(3), or 1.17 * 9 or 10.5(3). A1 for the final answer 10. Special case SC1 for an answer of 10/9 or embedded answer 1.07 < 10/9 < 1.17 oe.

Q Answer Mark Comments

1.07 × 9 or 9.6(3)

or M1

1.17 × 9 or 10.5(3)

10 10

A1 SC1 oe

Additional Guidance

Answer 10 M1A1

10 10

Answer or embedded answer eg 1.07 < < 1.17 oe SC1

How to answer it

Solving Double Inequalities with Integer Values

📌 What This Question Tests

This question tests your ability to solve a compound (double) inequality involving a fraction, multiply through by a positive number to clear the denominator, and correctly identify a single integer (whole number) lying strictly between two decimal limits.

Question 2   [2 marks]

1.07 < x/9 < 1.17 where x is an integer. Work out the value of x.

📐 Step-by-Step Solution

1 Clear the fraction: Multiply all three parts of the inequality by 9.
1.07 × 9 < x < 1.17 × 9
2 Calculate the decimal boundaries:
1.07 × 9 = 9.63
1.17 × 9 = 10.53
Inequality becomes: 9.63 < x < 10.53
3 Find the unique integer:
An integer is a whole number.
The whole numbers around this range are 9, 10, and 11.
• 9 is too small (9 < 9.63)
• 11 is too large (11 > 10.53)
The only whole number strictly between 9.63 and 10.53 is 10.

✅ Correct Answer & Marks

x = 10

Mark Breakdown:
• [M1] Method mark for calculating 1.07 × 9 (giving 9.63) OR 1.17 × 9 (giving 10.53).
• [A1] Accuracy mark for concluding with exactly 10 .

💡 Key Knowledge

  • Integer: A whole number (can be positive, negative, or zero; no decimal or fractional part).
  • Double Inequalities: Whatever operation you apply to the middle, you must apply to both the left and right sides.
  • Multiplying or dividing by a positive number does not change the inequality direction.

🧠 Exam Technique & Examiner Insight

  • Show intermediate values: Always write down at least one calculated boundary ( 9.63 or 10.53 ). If you make a slip writing the final answer, this secures the M1 mark.
  • Special Case (SC1): If a student writes 10/9 on the answer line, or leaves their final answer embedded as 1.07 < 10/9 < 1.17 , only 1 mark out of 2 is awarded (SC1) because x itself was not explicitly stated as an integer.

❌ Common Errors to Avoid

  • Giving a fraction: Writing x = 10/9 instead of x = 10 . The question asks for the integer x, not the fraction x/9.
  • One-sided multiplication: Multiplying only the right-hand boundary by 9 and guessing from there.
  • Rounding incorrectly: Rounding 9.63 down to 9 and writing 9, but 9 is not greater than 9.63.

Topics

Algebra · Number · 3.1.1 Structure and calculation · 3.2.3 Solving equations and inequalities

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.