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Chapter 10 Practice Paper: Sequences — question paper

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QQ/GCSE-MATHS/CH10

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

Chapter 10 Practice Paper

Sequences

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.
  • Show how you test membership of a sequence.
  • 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 10: term-to-term and position-to-term rules, arithmetic nth terms and membership, triangular, square and cube numbers, Fibonacci-type and geometric sequences (Higher), and quadratic nth terms (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

    A sequence starts at 7 with rule “add 5”. The fourth term is

    1. A22
    2. B27
    3. C17
    4. D20
    ( )
  2. 2

    The rule nth = 3n + 1 builds a sequence. Which list are its first four terms?

    1. A3, 4, 5, 6
    2. B1, 4, 7, 10
    3. C4, 8, 12, 16
    4. D4, 7, 10, 13
    ( )
  3. 3

    The nth term of 6, 11, 16, 21, … is

    1. A5n
    2. B6n
    3. C5n + 1
    4. Dn + 5
    ( )
  4. 4

    The 12th term of 7n − 3 is

    1. A84
    2. B81
    3. C81 − 3 = 78
    4. D80
    ( )
  5. 5

    Is 50 a term of 6n + 2?

    1. Ayes, n = 7
    2. Bno, n = 8 is not whole
    3. Cyes, n = 8
    4. Dno, n = 48⁄6
    ( )
  6. 6

    The next square number after 1, 4, 9, 16, 25 is

    1. A30
    2. B36
    3. C49
    4. D35
    ( )
  7. 7

    The next term of 1, 3, 6, 10, 15 is

    1. A21
    2. B18
    3. C24
    4. D20
    ( )
  8. 8

    Stepping up by four each time, 3, 7, 11, 15, 19 continues with

    1. A23
    2. B24
    3. C22
    4. D21
    ( )
  9. 9

    The ratio of the geometric progression 81, 27, 9, 3 is (Higher)

    1. A×3
    2. B+27
    3. C×⅓ of 9
    4. D÷3
    ( )
  10. 10

    For 2, 5, 10, 17, 26, subtracting each first difference from the next gives (Higher)

    1. A3, 5, 7
    2. B4, 4, 4
    3. Cconstant 2
    4. D5, 7, 9
    ( )

Section B: Structured questions[20 marks]

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

  1. 11

    Rules and lists.

    1. (a)

      Substitute positions 1 to 4 into the rule nth = 8 − 2n, and list the terms.

      [2]
    2. (b)

      A sequence starts at −5 with term-to-term rule “add 6”. Write the first four terms and its nth term.

      [2]
  2. 12

    Membership tests.

    1. (a)

      Is 88 a term of 7n + 4?

      [2]
    2. (b)

      Is 90 a term of 7n + 4?

      [2]
  3. 13

    Famous number families.

    1. (a)

      These are cubes: continue 1, 8, 27, 64 with the next three terms, naming the sequence.

      [2]
    2. (b)

      A pattern of dots builds triangles with 1, 3, 6, 10 dots. How many dots does the 7th triangle have?

      [2]
  4. 14

    Higher sequences. (Higher)

    1. (a)

      Find the nth term of 6, 11, 18, 27, 38, …

      [3]
    2. (b)

      Write the next two terms of the geometric progression 4, 4√2, 8, …

      [2]
  5. 15

    Quadratic nth term in context. (Higher)

    1. (a)

      A fountain’s square layers hold 3, 6, 11, 18, 27 stones. Find the nth term.

      [3]

— End of paper —