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Chapter 5 Practice Paper: Algebraic manipulation — question paper

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QQ/GCSE-MATHS/CH5

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

Chapter 5 Practice Paper

Algebraic manipulation

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 answers in their simplest form.
  • 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 5: notation and vocabulary, collecting like terms, expanding single and double brackets, factorising common factors and quadratics, the difference of two squares, ax² + bx + c (Higher), algebraic fractions (Higher), and indices and surds in algebra (Higher).

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

    Simplify 8m + 3n − 5m + n.

    1. A3m + 4n
    2. B11m + 4n
    3. C3m + 2n
    4. D6mn
    ( )
  2. 2

    Expand 2(4x − 7).

    1. A8x − 7
    2. B6x − 9
    3. C8x − 14
    4. D8x + 14
    ( )
  3. 3

    Expand −4(2 − y).

    1. A−8 − 4y
    2. B−8 + 4y
    3. C8 − 4y
    4. D8 + 4y
    ( )
  4. 4

    Expand (x + 1)(x + 7).

    1. Ax² + 7x + 7
    2. Bx² + 8x + 8
    3. Cx² + 6x + 7
    4. Dx² + 8x + 7
    ( )
  5. 5

    Factorise x² + 9x + 20.

    1. A(x + 2)(x + 10)
    2. B(x + 4)(x + 5)
    3. C(x + 20)(x + 1)
    4. D(x − 4)(x − 5)
    ( )
  6. 6

    Factorise x² − 36.

    1. A(x − 6)²
    2. B(x + 6)(x − 6)
    3. C(x + 36)(x − 1)
    4. D(x − 18)(x + 2)
    ( )
  7. 7

    Factorise 3x² − 12x.

    1. A3x(x − 4)
    2. B3(x² − 4x)
    3. C3x(x − 12)
    4. Dx(3x − 12)
    ( )
  8. 8

    Simplify (x² + 7x + 10) ÷ (x + 2). (Higher)

    1. Ax − 5
    2. Bx + 10
    3. Cx + 5
    4. Dcannot be simplified
    ( )
  9. 9

    Simplify (5x²)². (Higher)

    1. A5x⁴
    2. B10x⁴
    3. C25x²
    4. D25x⁴
    ( )
  10. 10

    Expand (x + 2)(x − 2)(x + 3) as far as (x² − 4)(x + 3) and choose the fully expanded form.

    1. Ax³ + 3x² − 4x − 12
    2. Bx³ + 3x² + 4x − 12
    3. Cx³ − 3x² − 4x − 12
    4. Dx³ − 12
    ( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for method as well as for the final answer. Give answers in their simplest form.

  1. 11

    Expanding skills.

    1. (a)

      Take away 2(x − 4) from 5(2x − 3), expanding both brackets and simplifying the result.

      [3]
    2. (b)

      Expand 3x(2x² − 5x).

      [1]
  2. 12

    Quadratic work.

    1. (a)

      Expand (2x − 3)(x + 4).

      [2]
    2. (b)

      Factorise x² − 2x − 24.

      [2]
  3. 13

    Factorising in shapes.

    1. (a)

      A rectangle has area (x² + 9x + 18) cm² and one side (x + 3) cm. Write an expression for the other side.

      [3]
    2. (b)

      State the value of x that would make the rectangle a square.

      [1]
  4. 14

    Higher factorising. (Higher)

    1. (a)

      Factorise 4x² + 5x − 6.

      [2]
    2. (b)

      Factorise fully 2x³ − 8x.

      [3]
  5. 15

    Cancelling common factors. (Higher)

    1. (a)

      Simplify (x² − 4x − 21) ÷ (x² − 49).

      [3]

— End of paper —