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Topic 6 Practice Paper: Algebraic manipulation — question paper

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QQ/IGCSE-MATHS/T6

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

Topic 6 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.
  • 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 6: substitution, expanding single, double and triple brackets, factorising with common factors, difference of two squares and quadratics, completing the square, and simplifying algebraic fractions.

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 8x − 3x + 2y.

    1. A7x + 2y
    2. B5xy
    3. C5x + 2y
    4. D11x + 2y
    ( )
  2. 2

    Expand 4(2x − 3).

    1. A8x − 12
    2. B8x − 3
    3. C2x − 12
    4. D8x + 12
    ( )
  3. 3

    Expand and simplify (y + 3)(y + 4).

    1. Ay² + 12y + 7
    2. By² + 7
    3. Cy² + 12
    4. Dy² + 7y + 12
    ( )
  4. 4

    Factorise 10x² − 15x fully.

    1. A5x(2x − 15)
    2. B5x(2x − 3)
    3. C10x(x − 15)
    4. D5(2x² − 3x)
    ( )
  5. 5

    Factorise x² − 16.

    1. A(x − 4)(x + 4)
    2. B(x − 4)²
    3. C(x − 8)(x + 2)
    4. D(x + 4)²
    ( )
  6. 6

    Factorise x² − 2x − 24.

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

    Write x² + 10x + 5 in completed-square form. (Extended)

    1. A(x + 5)² + 5
    2. B(x + 10)² − 95
    3. C(x + 5)² − 20
    4. D(x + 5)² − 5
    ( )
  8. 8

    Simplify (x² + 5x + 6) ÷ (x + 3).

    1. Ax − 2
    2. Bx + 2
    3. Cx + 3
    4. Dx² + 2
    ( )
  9. 9

    Find the value of 2t² + t when t = −3.

    1. A−15
    2. B−21
    3. C15
    4. D21
    ( )
  10. 10

    Expand and simplify (2x + 1)(x − 5).

    1. A2x² − 9x − 5
    2. B2x² − 5
    3. C2x² − 4x − 5
    4. D2x² + 9x − 5
    ( )

Section B: Structured questions[20 marks]

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

  1. 11

    Core algebra skills.

    1. (a)

      Expand 4(3x − 2).

      [1]
    2. (b)

      Expand and simplify (x + 7)(x − 2).

      [2]
    3. (c)

      Factorise 5x² − 20 completely.

      [2]
  2. 12

    Extended factorising.

    1. (a)

      Expand and simplify (2x − 1)(x + 3)(x − 2). Show your working. (Extended)

      [3]
    2. (b)

      Factorise 6x² + 7x − 3. (Extended)

      [2]
    3. (c)

      Factorise 4x² − 25.

      [1]
  3. 13

    Fractions and squares.

    1. (a)

      Simplify (x² − 4x + 3)/(x² − 9). (Extended)

      [3]
    2. (b)

      Write x² + 12x + 5 in the form (x + a)² + b. (Extended)

      [2]
  4. 14

    Substitution and simplification.

    1. (a)

      Work out the value of 3p² − 2q when p = −4 and q = 7.

      [2]
    2. (b)

      Expand and simplify 5(y + 3) − 2(2y − 1).

      [2]

— End of paper —