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

2 marks · Easy difficulty · Short Answer

State the equation of a vertical straight line and the gradient of a horizontal straight line drawn on a coordinate grid.

Practise this question

Question

A Cartesian coordinate grid with x-axis from minus 1 to 5 and y-axis from 0 to 5. Line A is a vertical line passing through x equals 3. Line B is a horizontal line passing through y equals 2. Students are asked to complete two statements: 'The equation of line A is ______' and 'The gradient of line B is ______'.

Mark scheme

Show the mark scheme Mark scheme table for question 2 showing B2 for both correct answers: (first answer) x = 3 and (second answer) 0. A partial mark of B1 is given for either answer correct. Additional guidance states that 3 = x is equivalent to x = 3, 'zero' is allowed for 0, but unprocessed answers like 0/4 are not allowed.

How to answer it

Equations and Gradients of Straight Lines

AQA GCSE Mathematics • Coordinate Geometry • 2 Marks

What this question tests

  • Recognising and writing the equation of a vertical line parallel to the y-axis.
  • Understanding that horizontal lines have a gradient of zero.
  • Carefully distinguishing between what is asked: an equation vs a numerical gradient.

Part 1: The equation of line A

Identifying vertical lines parallel to the y-axis

✅ Correct Answer

x = 3 (or 3 = x )

1 Mark [B1]: Independent mark for the full equation including the letter x and the equals sign.

💡 Key Knowledge

  • A vertical line crosses the x-axis and has the same x-coordinate at every point.
  • Its equation is always written in the form x = k , where k is the x-intercept.
  • Here, line A crosses the x-axis at 3 , so all coordinates on this line have x = 3 (e.g. (3, 0), (3, 2), (3, 4)).

📐 Step-by-Step Method

  1. Look at line A: It is completely vertical.
  2. Trace where it cuts the axes: it crosses the x-axis at 3.
  3. Write the equation as: x = 3 .

❌ Common Errors

  • Writing y = 3 : Confusing the vertical line x = 3 with the horizontal line y = 3 .
  • Writing just 3 : An equation must contain an equals sign and a variable!
  • Writing coordinates such as (3, 0) instead of an equation.

Part 2: The gradient of line B

Finding the gradient of a horizontal line

✅ Correct Answer

0 (or written as word zero )

1 Mark [B1]: Independent mark for the single value 0.

💡 Key Knowledge

  • Gradient is the rate of change:
    Gradient = Change in y ÷ Change in x
  • A completely flat, horizontal line has zero vertical change (rise = 0).
  • Therefore, any horizontal line has a gradient of exactly 0.

📐 Step-by-Step Calculation

  1. Pick any two points on line B: for example, (0, 2) and (4, 2) .
  2. Calculate change in y: 2 − 2 = 0 .
  3. Calculate change in x: 4 − 0 = 4 .
  4. Divide: 0 ÷ 4 = 0 .

❌ Common Errors & Traps

  • The Question Trap: Writing y = 2 . Line B's equation is indeed y = 2 , but the question specifically asks for its gradient!
  • Leaving the answer unprocessed: The mark scheme explicitly states do not allow unprocessed answers such as 0/4 . You must evaluate it to 0 .
  • Writing "no gradient" or "infinite": A vertical line has an undefined/infinite gradient, but a flat horizontal line has a gradient of 0.

🧠 Exam Technique & Examiner Insight

Always re-read the bold words in the prompt. Notice that line A asks for the equation, while line B asks for the gradient. Many candidates lose an easy mark here simply because they rush and write equations for both lines.

Topics

Algebra · 3.2.2 Graphs

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.