Lesson B4

B4 Simultaneous equations: linear and quadratic Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson B4, Simultaneous equations: linear and quadratic: 20 multiple choice questions for the AQA Maths (7357), Unit 2: Algebra and functions, written with Revision Ninja.

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The 20 questions

  1. Solve x + y = 5 and x - y = 1 simultaneously.

    • x = 3, y = -2
    • x = 2, y = 3
    • x = 3, y = 2
    • x = 4, y = 1

  2. Solve y = x + 1 and y = x^2 - 1 simultaneously.

    • (2, 3) and (-1, 0)
    • (2, 3) and (1, 2)
    • (-2, -1) and (1, 2)
    • (2, 3) only

  3. Given x + y = 4 and xy = 3, find x^2 + y^2.

    • 16
    • 4
    • 7
    • 10

  4. Which method eliminates one variable by adding or subtracting the equations?

    • Completing the square
    • Substitution
    • Elimination
    • Factorisation

  5. What is the maximum number of real intersection points between a line and a parabola?

    • Infinitely many
    • Three
    • Two
    • One

  6. Find where the line y = x + 1 meets the circle x^2 + y^2 = 25.

    • (-3, -4) and (4, 3)
    • (3, 4) and (4, 3)
    • (3, 4) only
    • (3, 4) and (-4, -3)

  7. How many solutions exist for the linear system 2x + 3y = 6 and 4x + 6y = 10?

    • Two
    • Infinitely many
    • Zero
    • One

  8. How many solutions do 2x + 3y = 6 and 4x + 6y = 12 have?

    • Infinitely many
    • Exactly one
    • Exactly two
    • None

  9. What quadratic equation in x is formed by solving 2x - y = 1 and x^2 + y = 4 simultaneously?

    • x^2 - 2x - 5 = 0
    • x^2 - 2x - 3 = 0
    • x^2 + 2x - 5 = 0
    • x^2 + 2x - 3 = 0

  10. How many real intersection points do y = mx + 2 and y = x^2 + 1 have for any real m?

    • One
    • Two
    • Depends on m
    • Zero

  11. Solve x + 2y = 8 and 3x - y = 3.

    • x = 3, y = 2
    • x = 2, y = -3
    • x = -2, y = 3
    • x = 2, y = 3

  12. On a graph, what represents the solutions to a system of simultaneous equations?

    • y-intercepts
    • x-intercepts
    • Intersection points
    • Turning points

  13. Solve y = 3x and x^2 + y^2 = 40.

    • (2, 6) and (6, 2)
    • (4, 12) only
    • (3, 9) and (-3, -9)
    • (2, 6) and (-2, -6)

  14. Find where y = x - 2 meets y = x^2 - 4x + 2.

    • (1, -1) and (4, 2)
    • (0, -2) and (3, 1)
    • (2, 0) and (3, 1)
    • (1, -1) only

  15. Given x - y = 2 and x^2 - y^2 = 8, find x + y.

    • 2
    • 4
    • 16
    • 8

  16. Solve x^2 + y^2 = 13 and x + y = 5. Which pair of solutions is correct?

    • (1, 4) and (4, 1)
    • (2, 3) only
    • (2, 3) and (3, 2)
    • (-2, 7) and (7, -2)

  17. Which pair of equations has a unique solution?

    • x + y = 2 and 2x + 2y = 5
    • x + y = 2 and x - y = 0
    • x + y = 2 and 2x + 2y = 4
    • x = 1 and x = 2

  18. A line through (0, 1) with gradient 2 meets the line 3x + y = 11. Where do they meet?

    • (1, 3)
    • (3, 2)
    • (2, 3)
    • (2, 5)

  19. Solve x - 2y = 0 and xy = 8.

    • (2, 4) and (-2, -4)
    • (4, 2) and (-4, -2)
    • (4, -2) and (-4, 2)
    • (8, 1) only

  20. What geometrical relationship exists between a line and curve when their combined discriminant is zero?

    • Tangent
    • Perpendicular
    • Parallel
    • Secant

All AQA Maths quizzes