AQA GCSE Maths

Solving inequalities graphically

AQA GCSE Maths revision on Solving inequalities graphically. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.

Sample questions (3 of 16)

  1. Question 1

    When representing the inequality y > 2x + 1 on a Cartesian plane, what feature must the boundary line have to correctly show the inequality?

    • A) A dashed line
    • B) A solid line
    • C) A vertical line
    • D) A horizontal line
    Show answer

    Answer: A dashed line

    A dashed line indicates that the points lying exactly on the line do not satisfy the inequality, which is denoted by the 'greater than' or 'less than' symbols. If the inequality included 'or equal to', a solid line would be used to show inclusion of the boundary. This is a fundamental convention for graphical representation.

  2. Question 2

    If you are asked to shade the region representing y <= -x + 3, which side of the line should you shade?

    • A) The side containing the origin
    • B) The side above the line
    • C) The side furthest from the origin
    • D) The side containing the y-intercept only
    Show answer

    Answer: The side containing the origin

    By substituting the coordinate (0,0) into the inequality 0 <= -(0) + 3, we get 0 <= 3, which is a true statement. Since the origin satisfies the inequality, the region that includes the origin must be the correct side to shade. This method works for any line that does not pass through the origin.

  3. Question 3

    A student shades the region above the line y = x and labels it y < x. What is the fundamental error in their reasoning?

    • A) They have incorrectly identified the region for the inequality
    • B) They have used a solid line instead of a dashed one
    • C) They should have shaded below the y-axis
    • D) They have ignored the intercept value
    Show answer

    Answer: They have incorrectly identified the region for the inequality

    For any point above the line y = x, the y-coordinate is greater than the x-coordinate. Therefore, shading above the line represents the inequality y > x. The student likely confused the direction of the inequality sign with the physical position of the shading.

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13 more questions on Solving inequalities graphically — plus mistakes tracking and spaced repetition across the whole Maths spec.

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