Lesson B4

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

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

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.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

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. How many real intersection points can a line and a parabola have?

    • Zero, one or two
    • Infinitely many
    • Exactly two
    • Exactly four

  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 do 2x + 3y = 6 and 4x + 6y = 10 have?

    • None, since the lines are parallel
    • Infinitely many
    • Exactly two
    • Exactly one

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

    • Infinitely many
    • Exactly one
    • Exactly two
    • None

  9. Solve 2x - y = 1 and x^2 + y = 4 exactly.

    • x = -1 + sqrt(6), y = -3 + 2 sqrt(6); and x = -1 - sqrt(6), y = -3 - 2 sqrt(6)
    • x = -1 + sqrt(5), y = -3 + 2 sqrt(5); and x = -1 - sqrt(5), y = -3 - 2 sqrt(5)
    • x = 1 + sqrt(6), y = 1 + 2 sqrt(6); and x = 1 - sqrt(6), y = 1 - 2 sqrt(6)
    • x = 2 and y = 3 only

  10. For the line y = mx + 2 and the curve y = x^2 + 1, which statement is correct?

    • They never meet for any real m
    • They touch for exactly one value of m
    • They meet only when m = 2
    • They meet at two distinct points for every real m

  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. Which graphical fact is the basis for solving simultaneous equations?

    • The solutions are the coordinates of the points where the two graphs intersect
    • The solutions are the gradients of both graphs
    • The solutions are the turning points of both graphs
    • The solutions are the points where either graph crosses the y-axis

  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. When the substitution of a line into a quadratic curve gives a quadratic with discriminant 0, what does this mean?

    • The system has infinitely many solutions
    • The line is a tangent, meeting the curve at exactly one point
    • The line and the curve meet at two distinct points
    • The line and the curve never meet

All AQA Maths quizzes