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Grade 3 · Foundation · free GCSE maths worksheet

Substituting into expressions and formulae

Including negative numbers and squares.

17 original questions, 58 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

T = 4x + 3y

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

2 marks
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26
2

v = 5t − 8

Work out the value of v when t = 3.4

2 marks
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9
3

The perimeter of a rectangle is given by the formula P = 2l + 2w

Work out the value of P when l = 7.5 and w = 4.2

2 marks
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23.4
4

E = 3a − 2b

Work out the value of E when a = −4 and b = 5.

2 marks
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-22
5

Work out the value of  x2 + 7x  when x = 6.

2 marks
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78
6

5y = 35

  1. Work out the value of y.
  2. Work out the value of  2y2
3 marks
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a) 7 b) 98
7
  1. Simplify  4c × 2d
  2. Work out the value of  4c × 2d  when c = 3 and d = 1.5
3 marks
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a) 8cd b) 36
8

Here is a table of values for 4n − 5

n25??
4n − 5??1935

Work out the four missing numbers in the table (the two n values and the two values of 4n − 5 marked ?).

4 marks
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3, 15, 6, 10
9

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
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a) 50 b) 15
10

A tool hire company uses this rule to work out the cost of hiring a floor sander.

Total cost = £45 × number of days + £60 deposit

  1. Meera hires the sander for 7 days.
    Work out her total cost.
  2. Liam's total cost is £555.
    Work out the number of days Liam hires the sander for.
4 marks
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a) £375 b) 11
11
  1. Work out the value of  2a − 3b  when a = −1 and b = 4.
  2. Work out the value of  4a2 + b  when a = −3 and b = −7.
4 marks
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a) -14 b) 29
12

The speed, S, in metres per second of a runner is given by the formula

S = 60t

where t is the time in seconds taken to run 60 metres.

  1. Work out the value of S when t = 4 and when t = 12.
  2. Zara says, “When t gets bigger, S gets bigger.” Use your answers to part (a) to show that Zara is wrong.
  3. Work out the value of t when S = 7.5
4 marks
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a) 15 and 5 b) t = 4 gives S = 15 but t = 12 gives S = 5, which is smaller c) 8
13

v = u + at

  1. Work out the value of v when u = 7, a = 9.8 and t = 5.
  2. Work out the value of t when v = 87, u = 12 and a = 5.
4 marks
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a) 56 b) 15
14

y = 3(x + 4)

  1. Work out the value of y when x = 5
  2. Work out the value of x when y = 27
4 marks
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a) 27 b) 5
15

m = 3n − 2p

  1. Work out the value of m when n = −5 and p = 4.
  2. Work out the value of n when m = 19 and p = −2.
4 marks
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a) -23 b) 5
16
  1. Work out the value of  5x + 2y  when x = 4 and y = −3.
  2. Work out the value of  x2 − 4x  when x = −2.
  3. D = (h + 3k) ÷ 2
    Work out the value of h when D = 10 and k = 4.
6 marks
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a) 14 b) 12 c) 8
17

A builder uses the formula C = 8n + 45 to work out the cost, in pounds, of a job that takes n hours.

Priya estimates the cost of a 16 hour job as £150.

An estimate is acceptable if it is within 10% of the cost given by the formula.

Is Priya's estimate acceptable? You must show your working.

4 marks
Show answer
No

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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