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Year 7 · Key Stage 3 · free KS3 maths worksheet

Substitution and sequences

12 original questions, 35 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Here is the sequence of odd numbers.

1    3    5    7    9    ...

  1. Write down the two odd numbers that come after 23.
  2. Write down the 10th even number.
  3. Kai says, "The 20th odd number is 40." Explain why Kai is wrong.
3 marks
Show answer
a) 25 and 27 b) 20 c) 40 is even, the 20th odd number is 39
2

T = 4x + 3y

Work out the value of T when x = 5 and y = 2.

2 marks
Show answer
26
3

Fill in the missing numbers in each sequence.

  1. 4,  9,  ___,  19,  ___
  2. 50,  ___,  36,  29,  ___
  3. 3,  6,  12,  ___,  48
3 marks
Show answer
a) 14 and 24 b) 43 and 22 c) 24
4

The nth term of a sequence is 6n − 1

Write down the first three terms of the sequence.

2 marks
Show answer
5, 11, 17
5

The nth term of a sequence is 20 − 4n

  1. Write down the first four terms of the sequence.
  2. Work out the 10th term of the sequence.
2 marks
Show answer
a) 16, 12, 8, 4 b) -20
6
  1. Work out the value of 3x2 + 4 when x = −2
  2. Work out the value of 2x3 when x = 3
  3. Work out the value of 2x3 when x = −1
3 marks
Show answer
a) 16 b) 54 c) -2
7

Here are the first four terms of an arithmetic sequence.

5   9   13   17

Find an expression, in terms of n, for the nth term of the sequence.

2 marks
Show answer
4n + 1
8

F = 5v + 20

  1. Work out the value of F when v = 6.
  2. Work out the value of v when F = 95.
4 marks
Show answer
a) 50 b) 15
9

The nth term of a sequence is 5n − 3

  1. Work out the 12th term of the sequence.
  2. Is 122 a term of the sequence? You must show how you get your answer.
3 marks
Show answer
a) 57 b) Yes, 5n - 3 = 122 gives n = 25, a whole number
10

Here are the first three patterns in a sequence made from matchsticks.

  1. How many matchsticks are needed for Pattern 4?
  2. Find an expression, in terms of n, for the number of matchsticks in Pattern n.
  3. Which pattern uses 31 matchsticks?
Pattern 1Pattern 2Pattern 3
4 marks
Show answer
a) 13 b) 3n + 1 c) Pattern 10
11

The perimeter, P, of a rectangle is given by the formula

P = 2(l + w)

A rectangular football pitch for Year 7 has a perimeter of 34 m and a length of 11 m.

Work out the width of the pitch.

3 marks
Show answer
6 m
12

Here are the first four terms of an arithmetic sequence.

8   15   22   29

  1. Find an expression, in terms of n, for the nth term of the sequence.
  2. Explain why 150 is not a term of the sequence.
4 marks
Show answer
a) 7n + 1 b) 7n + 1 = 150 gives 7n = 149, and 149 is not divisible by 7

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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