AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 9

1 mark · Medium difficulty · Short Answer

Identify which given value of x results in the greatest value of y for the reciprocal equation y = 1/x.

Practise this question

Question

Question 9 states the equation y = 1/x and asks: 'Which of these values of x gives the greatest value of y? Circle your answer.' Four options are provided in a horizontal row: 9/20, 2/5, -80, and 95. The question is worth 1 mark.
Question text

9 y =

x

Which of these values of x gives the greatest value of y ?

Circle your answer.

[1 mark]

–80 95

20 5

Mark scheme

Show the mark scheme Mark scheme table for Question 9 showing Answer: '2/5', Mark: 'B1', with no additional comments.

Q Answer Mark Comments

9 B1

How to answer it

Reciprocals and Inverse Relationships

📋 What this question tests

This question assesses your understanding of the reciprocal function y = 1/x, operations with fractions, and how changing the value of x affects the value of y. Key skills include dividing by fractions, comparing values, and understanding positive vs negative numbers.

Question 9 • 1 Mark

Finding the Value of x Giving the Greatest y

Given equation: y = 1/x

✅ Correct Answer

2/5

Mark Scheme: B1 for circling or clearly indicating 2/5.

💡 Key Knowledge

  • Reciprocal: The reciprocal of a fraction a/b is b/a .
  • Inverse relationship: For positive numbers, as x gets smaller, 1/x gets larger.
  • Signs: A positive numerator divided by a negative denominator yields a negative number, which will always be less than positive values.

📐 Step-by-Step Calculation for Each Option

Substitute each given value of x into the formula y = 1/x :

  1. When x = 9/20:
    y = 1 ÷ (9/20) = 20/9 = 2.22...
  2. When x = 2/5:
    Convert to equivalent fraction: 2/5 = 8/20
    y = 1 ÷ (2/5) = 5/2 = 2.50
  3. When x = −80:
    y = 1 ÷ (−80) = −1/80 = −0.0125 (negative value)
  4. When x = 95:
    y = 1 ÷ 95 = 1/95 = 0.0105... (very small positive value)

Comparing all resulting values of y:
2.50 > 2.22... > 0.0105... > −0.0125
Therefore, the greatest value of y is 2.50, obtained when x = 2/5.

🧠 Exam Technique & Shortcuts

  • Eliminate immediately: Eliminate −80 because it gives a negative result. Eliminate 95 because dividing 1 by a large number gives a tiny decimal near zero.
  • Compare remaining fractions: You are left with 9/20 and 2/5 . Since you want the greatest value of 1/x , you need the smallest positive value of x .
  • Since 2/5 = 8/20 and 8/20 < 9/20 , 2/5 must give the largest reciprocal! No complex arithmetic is required.

❌ Common Traps & Misconceptions

  • Choosing the biggest x (95): Students often confuse finding the greatest value of x with finding the value of x that makes y greatest.
  • Misunderstanding reciprocals: Assuming that a larger denominator makes the reciprocal larger (e.g. thinking 9/20 gives a larger reciprocal than 2/5 because 9 and 20 are larger numbers).
  • Ignoring negative signs: Thinking −80 gives a very large magnitude without considering that it is negative.

Topics

Number · Algebra · 3.1.1 Structure and calculation · 3.1.2 Fractions, decimals and percentages · 3.2.1 Notation, vocabulary and manipulation

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.