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Chapter 9 Practice Paper: Simultaneous equations and inequalities — question paper

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QQ/GCSE-MATHS/CH9

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

Chapter 9 Practice Paper

Simultaneous equations and inequalities

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.
  • Give simultaneous answers as pairs of values, checked where asked.
  • 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 9: simultaneous equations by elimination and substitution, linear–quadratic pairs (Higher), linear inequalities on number lines, quadratic inequalities and graph regions with set notation (Higher), and approximate solutions from graphs.

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

    Adding x + y = 6 and x − y = 2 gives

    1. A2y = 4
    2. B2x = 4
    3. C2x = 8
    4. Dx = 8
    ( )
  2. 2

    The pair satisfying both x + y = 6 and x − y = 2 at once is

    1. Ax = 2, y = 4
    2. Bx = 8, y = 2
    3. Cx = 3, y = 3
    4. Dx = 4, y = 2
    ( )
  3. 3

    Replacing y by 3x in the equation x + y = 8 produces

    1. Ax + 3 = 8
    2. B4x = 8
    3. Cx + 3x = 8
    4. D3x + y = 8
    ( )
  4. 4

    Solve x > −2 and x ≤ 1. The integers satisfying both are

    1. A−2, −1, 0, 1
    2. B−1, 0, 1
    3. C−1 and 1
    4. Dall integers
    ( )
  5. 5

    Solve 5 − x < 3.

    1. Ax < 2
    2. Bx < 8
    3. Cx > −2
    4. Dx > 2
    ( )
  6. 6

    For 5x + 2y = 20 and 5x − y = 5, subtracting gives

    1. A3y = 15
    2. B10x = 25
    3. Cy = 15
    4. D3y = −15
    ( )
  7. 7

    Solving that pair gives

    1. Ay = 5, x = 2
    2. By = 3, x = 2.8
    3. Cx = 5, y = −1
    4. Dy = 15, x = −2
    ( )
  8. 8

    For which x is x² − 1 positive? (Higher)

    1. A−1 < x < 1
    2. Bx > 1 only
    3. Cx < −1 or x > 1
    4. Dno solutions
    ( )
  9. 9

    A dashed boundary line is used for (Higher)

    1. Ay ≤ x
    2. By < x
    3. Cy ≥ x
    4. Dy = x
    ( )
  10. 10

    Two plotted lines cross at (2.5, 4). The simultaneous solution is approximately

    1. Ax ≈ 2.5, y ≈ 4
    2. Bx = 2.5, y = 4 exactly
    3. Cx = 4, y = 2.5
    4. Dno solution
    ( )

Section B: Structured questions[20 marks]

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

  1. 11

    Simultaneous equations.

    1. (a)

      Solve 3x + 2y = 19 and x − 2y = −5.

      [3]
    2. (b)

      Check the solution in the first equation.

      [1]
  2. 12

    Scaling then solving.

    1. (a)

      Solve 4x + y = 14 and 6x − 2y = 6.

      [4]
  3. 13

    Inequalities.

    1. (a)

      Solve 7 − 2x ≥ 1 and show the solution on a number line.

      [3]
    2. (b)

      Write the solution set using set notation.

      [1]
  4. 14

    Linear–quadratic pair. (Higher)

    1. (a)

      A circle has equation x² + y² = 25 and a chord of the circle lies along the line y = x − 1. Solve the pair to find where the chord meets the circle.

      [4]
    2. (b)

      State the number of crossing points of the line and the circle.

      [1]
  5. 15

    Quadratic inequality. (Higher)

    1. (a)

      Solve x² + 2x − 15 ≥ 0, giving the answer in set notation.

      [3]

— End of paper —