Lesson 1.02c

1.02c Equations and inequalities Quiz: OCR Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.02c, Equations and inequalities: 20 multiple choice questions for the OCR Maths (H240), Unit 2: Algebra and Functions, written with Revision Ninja.

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The 20 questions

  1. A line and a parabola are given as y = 4 - 3x and y = x^2 + 2x - 2. How many intersection points are there?

    • 0
    • 2
    • 4
    • 1

  2. Solve 2x + 3y = 9 and x - y = 1 simultaneously.

    • x = 7/5, y = 12/5
    • x = 2, y = 1
    • x = 12/5, y = 7/5
    • x = 3, y = 2

  3. Which method eliminates a variable by adding or subtracting the equations?

    • Differentiation
    • Elimination
    • Factorising
    • Completing the square

  4. When solving y = 2x - 1 and x + y = 5 by substitution, what expression replaces y?

    • x + 5
    • 2x + 1
    • 2x - 1
    • 5 - x

  5. Solve x + y = 3 and x - y = 1.

    • x = 2, y = 1
    • x = 3, y = 0
    • x = 1, y = 2
    • x = 2, y = -1

  6. A line meets a parabola at two distinct points. What is the sign of the discriminant of the quadratic formed by substitution?

    • Undefined
    • Positive
    • Zero
    • Negative

  7. Solve 4x - 2y = 10 and y = x - 4.

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

  8. Which pair is a solution of y = x + 1 together with xy = 6?

    • (3, 2)
    • (2, 3)
    • (-2, 3)
    • (2, -3)

  9. Solve 1/(x - 1) + 1/(x + 1) = 1.

    • x = 1 +/- 2
    • x = 1 +/- sqrt(2)
    • x = -1 +/- sqrt(2)
    • x = 2 +/- sqrt(2)

  10. Which set contains all real solutions of x^3 - 2x^2 - 5x + 6 = 0?

    • {-2, 1, 3}
    • {1, 3}
    • {-2, 1, 2, 3}
    • {-3, -2, 1}

  11. Solve x^2 + 3x - 4 = 0.

    • x = 2 or x = -2
    • x = -1 or x = 4
    • x = 1 or x = 4
    • x = 1 or x = -4

  12. Solve x/2 + y/3 = 4 and x - y = 3 simultaneously.

    • x = 9, y = 6
    • x = 4, y = 1
    • x = 6, y = 3
    • x = 3, y = 0

  13. How many real solutions does the system y = x^2 and y = 2x - 1 have?

    • One
    • None
    • Three
    • Two

  14. Two numbers have sum 20 and product 96. What are they?

    • 10 and 10
    • 4 and 24
    • 6 and 16
    • 8 and 12

  15. A rectangle has perimeter 30 and area 50. What are its side lengths?

    • 4 and 11
    • 6 and 9
    • 5 and 10
    • 3 and 12

  16. What are the x-values solving 2x + y = 7 and x^2 + y^2 = 13 simultaneously?

    • x = 2 and x = 3
    • x = 1 and x = 3.6
    • x = -2 and x = 3.6
    • x = 2 and x = 3.6

  17. For what values of k does x^2 - 2kx + (k + 3) = 0 have equal roots?

    • k = 3 or k = -1
    • k = 1 or k = -3
    • k = (1 +/- sqrt(13))/2
    • k = (1 +/- sqrt(5))/2

  18. Which set gives the solutions of (x - 2)^2 - 4 = 0?

    • x = 4 only
    • x = 0 or x = 4
    • x = 2 or x = -2
    • x = -2 or x = 0

  19. For x^2 + bx + 9 = 0 to have a repeated root, what must b be?

    • b = 9 or b = -9
    • b = 6 or b = -6
    • b = 18 only
    • b = 3 or b = -3

  20. Solve x - y = 1 and x^2 - y^2 = 7 simultaneously.

    • x = 3, y = 4
    • x = 5, y = 4
    • x = 4, y = 2
    • x = 4, y = 3

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