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Topic 7 Practice Paper: Equations and inequalities — question paper

QuizQuipPractice Series
QQ/IGCSE-MATHS/T7

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 7 Practice Paper

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.
  • 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 against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 7: linear equations with brackets and fractions, simultaneous pairs including word problems, quadratic equations by factorising and the formula, changing the subject, and linear inequalities on number lines.

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 5x − 4 = 16.

    1. A2
    2. B3
    3. C4
    4. D5
    ( )
  2. 2

    Solve 7 − x = 10.

    1. A−3
    2. B3
    3. C17
    4. D−17
    ( )
  3. 3

    Solve 3x⁄4 = 9.

    1. A6.75
    2. B3
    3. C9
    4. D12
    ( )
  4. 4

    For the pair x + y = 8 and x − y = 2, the value of x is

    1. A3
    2. B5
    3. C8
    4. D6.5
    ( )
  5. 5

    Solve (x − 3)⁄2 = 4.

    1. A11
    2. B5
    3. C5.5
    4. D2
    ( )
  6. 6

    Solve 2x + 1 > 7.

    1. Ax < 3
    2. Bx > 5
    3. Cx > 3
    4. Dx < 5
    ( )
  7. 7

    The smallest solution of x² + 3x − 10 = 0 is (Extended)

    1. A−2
    2. B5
    3. C2
    4. D−5
    ( )
  8. 8

    One root of x² − 6x + 3 = 0, correct to 3 significant figures, is (Extended)

    1. A5.449
    2. B5.45
    3. C0.551
    4. D3.00
    ( )
  9. 9

    Which description matches x ⩾ −2 on a number line?

    1. AAn open circle at −2 with the arrow pointing left
    2. BAn open circle at −2 with the arrow pointing right
    3. CA filled circle at 2 with the arrow pointing left
    4. DA filled circle at −2 with the arrow pointing right
    ( )
  10. 10

    Make h the subject of A = bh⁄2.

    1. Ah = 2A⁄b
    2. Bh = A⁄(2b)
    3. Ch = 2b⁄A
    4. Dh = b⁄(2A)
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show all your working.

  1. 11

    Linear work.

    1. (a)

      Solve 2x + 7 = 3(x − 1).

      [2]
    2. (b)

      Solve the pair x + 2y = 7 and 3x − 2y = 5.

      [3]
  2. 12

    Fractions and inequalities.

    1. (a)

      Solve 5⁄(2x) = 3⁄(x + 2). (Extended)

      [3]
    2. (b)

      Solve 3(2 − x) ⩾ 9.

      [2]
  3. 13

    Use the formula to solve x² + 2x − 9 = 0. Write both roots correct to 2 decimal places. (Extended)

    1. (a)

      Substitute a = 1, b = 2, c = −9 into the formula and simplify.

      [3]
    2. (b)

      Give both values of x to 2 decimal places.

      [2]
  4. 14

    Formulas and a word problem.

    1. (a)

      Make m the subject of F = ma.

      [1]
    2. (b)

      Two cinema tickets and three popcorns cost $23. One ticket and one popcorn cost $9. Form a pair of equations and find the price of a ticket and of a popcorn.

      [4]

— End of paper —