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Chapter 8 Practice Paper: Quadratic equations and graphs — question paper

QuizQuipPractice Series
QQ/GCSE-MATHS/CH8

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 8 Practice Paper

Quadratic equations and graphs

Duration: 40 minutes
Total: 30 marks
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READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • The quadratic formula must be recalled — it will not be printed.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 8: solving quadratics by factorising, the quadratic formula and completing the square (Higher), roots, intercepts and turning points from graphs, symmetry, and approximate graphical solutions.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    Solve x² + 3x + 2 = 0.

    1. Ax = 1 or x = 2
    2. Bx = −1 or x = −2
    3. Cx = −1 or x = 2
    4. Dx = 1 or x = −2
    ( )
  2. 2

    Solve x² − 16 = 0.

    1. Ax = 4
    2. Bx = −4
    3. Cx = 4 or x = −4
    4. Dx = 8 or x = −2
    ( )
  3. 3

    Solve x² = 2x + 15.

    1. Ax = 5 or x = −3
    2. Bx = −5 or x = 3
    3. Cx = 5 or x = 3
    4. Dx = 15 or x = −1
    ( )
  4. 4

    The curve y = x² − 4x − 5 cuts the y-axis at

    1. A(0, 5)
    2. B(−5, 0)
    3. C(0, −4)
    4. D(0, −5)
    ( )
  5. 5

    Set each factor of y = (x − 6)(x + 2) to zero: the roots are

    1. A6 and −2
    2. B−6 and 2
    3. C6 and 2
    4. D−6 and −2
    ( )
  6. 6

    For 5x² − x − 3 = 0, the discriminant is (Higher)

    1. A61
    2. B−59
    3. C59
    4. D49
    ( )
  7. 7

    Complete the square for x² + 10x + 9. (Higher)

    1. A(x + 5)² + 9
    2. B(x + 5)² − 16
    3. C(x + 10)² − 91
    4. D(x − 5)² − 16
    ( )
  8. 8

    State where the curve y = (x − 7)² + 2 sits at its lowest. (Higher)

    1. A(−7, 2)
    2. B(7, −2)
    3. C(7, 2)
    4. D(2, 7)
    ( )
  9. 9

    Give the equation of the mirror line (axis of symmetry) for y = (x − 6)(x + 4).

    1. Ax = −1
    2. Bx = 6
    3. Cx = −4
    4. Dx = 1
    ( )
  10. 10

    A curve y = x² + x + 5 has b² − 4ac = −19, so its graph (Higher)

    1. Acrosses the x-axis twice
    2. Btouches the x-axis once
    3. Cnever reaches the x-axis
    4. Dis a straight line
    ( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for method as well as for the final answer.

  1. 11

    Quadratic solving.

    1. (a)

      Solve x² + 2x − 24 = 0.

      [2]
    2. (b)

      Solve x² − 5x = 36.

      [2]
  2. 12

    The formula. (Higher)

    1. (a)

      Solve x² − 4x + 1 = 0 using the formula, giving roots in exact surd form.

      [4]
  3. 13

    Square completion. (Higher)

    1. (a)

      Complete the square: express x² − 10x + 7 as (x − p)² + q.

      [2]
    2. (b)

      Hence write down the minimum point of y = x² − 10x + 7.

      [2]
  4. 14

    Graphs.

    1. (a)

      Factorise x² + x − 12 and hence state both x-intercepts of its graph.

      [3]
    2. (b)

      Write down the y-intercept of the graph.

      [1]
  5. 15

    Turning point from the completed square. (Higher)

    1. (a)

      For y = 3x² + 12x − 2, take the 3 out and complete the square, giving the form a(x − p)² + q.

      [3]
    2. (b)

      State the coordinates of the turning point.

      [1]

— End of paper —