Lesson A12

A12 Sketching linear, quadratic, cubic and reciprocal graphs Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson A12, Sketching linear, quadratic, cubic and reciprocal graphs: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 2: Algebra, written with Revision Ninja.

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The 20 questions

  1. What is the shape of the graph of y = 1/x?

    • A straight line through the origin
    • A U-shaped curve in the first quadrant
    • Two curves in the second and fourth quadrants only
    • Two separate curves in the first and third quadrants

  2. What are the asymptotes of y = 1/x?

    • x = 1 and y = 1 only
    • The lines y = x and y = -x
    • The axes x = 0 and y = 0
    • x = 0 only, the y-axis

  3. Which statement describes the graph of y = x^3?

    • Passes through the origin, negative for negative x and positive for positive x
    • Always positive, touching the x-axis at the origin and turning back up on both sides
    • Never crosses the x-axis, with a turning point at (1, 1) and positive values for all x
    • Passes through the origin and is symmetric about the y-axis, with a turning point there

  4. Which is the graph of y = -x^2?

    • A U shape with its minimum at (0, -1)
    • A straight line through the origin with gradient -1
    • An inverted U shape with a maximum at the origin
    • A U shape with a minimum at the origin

  5. Which pair of points lies on the line y = -x + 3?

    • (0, 3) and (3, 0)
    • (0, 3) and (3, 3)
    • (-3, 0) and (0, 3)
    • (0, -3) and (3, 0)

  6. Where does y = x^2 - 4 cross the y-axis?

    • At (-4, 0)
    • At (2, 0)
    • At (0, 4)
    • At (0, -4)

  7. What is the value of y when x = 2 on the graph of y = 2/x?

    • 4
    • 2
    • 0.5
    • 1

  8. Which are the x-intercepts of y = x(x - 2)(x + 1)?

    • x = -1 and 2 only
    • x = 0 and 2 only
    • x = -1, 0 and 2
    • x = 1, 0 and -2

  9. Which equation gives a straight-line graph?

    • y = 4x^3 - 9
    • y = 4x^2 - 9
    • y = 4/x - 9
    • y = 4x - 9

  10. What is the turning point of y = (x - 3)^2?

    • (-3, 0)
    • (3, 0)
    • (3, 3)
    • (0, 3)

  11. Why does y = 1/x never cross the x-axis?

    • Because y = 1 when x = 1
    • Because x is never negative
    • Because 1 divided by any non-zero x is never zero
    • Because the graph is symmetric about the y-axis

  12. Where does the graph of y = x^3 + 2 cross the y-axis?

    • (0, -2)
    • (0, 2)
    • (2, 0)
    • (0, 8)

  13. What is the x-coordinate of the turning point of y = x^2 - x - 6?

    • x = 1
    • x = -0.5
    • x = 3
    • x = 0.5

  14. A hire company charges a fixed fee of 20 pounds plus 5 pounds per hour. Which graph shows the cost?

    • A curve through the origin
    • A straight line with intercept 5 and gradient 20
    • A straight line with intercept 20 and gradient 5
    • A reciprocal curve with an asymptote at 20

  15. Where does y = 2x - 4 cross the x-axis?

    • x = 2
    • x = -2
    • x = 4
    • x = -4

  16. Area 12 is fixed, and a rectangle has width x and length y = 12/x. What happens to y as x increases?

    • y increases without limit
    • y decreases towards zero
    • y stays the same
    • y becomes negative

  17. For y = -x^3, what is the sign and value of y when x = 2?

    • Positive, y = 8
    • Positive, y = 6
    • Negative, y = -6
    • Negative, y = -8

  18. (H) Which description fits y = 2^x?

    • Passes through (0, 0) as a straight line
    • Passes through (0, 1) and falls steeply
    • Passes through (0, 2) and falls steadily
    • Passes through (0, 1) and rises ever more steeply

  19. (H) What is the value of sin 90 degrees?

    • 1
    • 0.5
    • 0
    • -1

  20. (H) What is the maximum value of y = sin x for angles from 0 to 360 degrees?

    • 2
    • 1
    • 360
    • 0

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