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Substitution into Expressions and Formulae - Worksheets, Questions and Revision

29 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 7)Substitution into Expressions and Formulae revision guide

This topic is chapter 3 of KS3 Maths: Algebra Practice Book 1.

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KS3 · Algebra

2.6 Substitution into Expressions and Formulae

AQA KS3.M-A6 · Calculators not allowed · about 85 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Use the formula P = 2(l + w) to find the perimeter of a rectangle with l = 4 and w = 2.
(2)
2
The formula for the cost of bus travel is C = 0.5n + 1, where n is the number of journeys. Work out C when n = 6.
(3)
3
A recipe uses 2c + 1 teaspoons of spice where c is the number of cups of flour. How many teaspoons are needed when c = 3?
(3)
4
Evaluate 2(x + 3) when x = 4. Show the substitution and give the final value.
(3)
5
Evaluate 3y - 2(x + 1) when x = 2 and y = 5. Show the steps.
(3)
6
The formula for the area of a triangle is A = 1/2 b h. Find A when b = 8 and h = 5.
(2)
7
Stretch question. The cooling formula for a cup of tea is T = 80 - 2n, where T is temperature in degrees Celsius after n minutes. A class drinks tea in pairs. Calculate the total temperature sum for 3 pairs if they drink after 5, 7 and 9 minutes. Show all substitution and addition steps.
(6)
8
Find the value of p + 5 when p = 7.
(1)
9
Evaluate 2a + 1 when a = 0.
(1)
10
Substitute x = 5 into x2 and give the value.
(1)
11
Evaluate 4b - 3 when b = 2.
(1)
12
Substitute t = 1/2 into 6t and give the answer as a fraction.
(1)
13
Evaluate 5x + 2 when x = -1.
(2)
14
The formula for the area of a rectangle is A = l w. Find A when l = 7 and w = 3.
(2)
15
Evaluate 5n when n = 3.
(1)
16
The formula for the cost of a taxi journey is C = 2n + 3, where n is the number of miles. Work out C when n = 8.
(2)
17
Evaluate 4(x + 2) when x = 3.
(2)
18
Substitute a = -3 into 2a2 and give the result.
(2)
19
Evaluate 5y - 3(x + 1) when x = 2 and y = 4. Show the steps.
(3)
20
A trapezium is split into two triangles. Triangle 1 has base 12 and height 7. Triangle 2 has base 8 and height 7. Using the formula A = 1/2 b h for each triangle, find the total area of the trapezium.
(3)
21
A theatre charges C = 8p + £3 for a group booking, where p is the number of people in the party. A group of 12 friends has a total budget of £100. Work out the cost for the group and state whether the budget is enough.
(4)
22
The cooling formula for a mug of tea is T = 90 - 3n, where T is the temperature in degrees Celsius after n minutes. Mug A is left to cool for 8 minutes and Mug B is left to cool for 15 minutes. Find the temperature of each mug, then work out the difference between them.
(4)
23
Stretch. A sequence rule is given by T = 2n2 - n. Work out T when n = 5, then work out T when n = -2, and state the sum of these two values.
(4)
24
Find the value of q + 8 when q = 6.
(1)
25
Evaluate 3a - 2 when a = 4.
(1)
26
Substitute x = 4 into x2 and give the value.
(1)
27
Substitute t = 1/3 into 9t and give the answer.
(1)
28
Evaluate 6 - y when y = 9.
(1)
29
The formula for the area of a rectangle is A = lw. Find A when l = 9 and w = 4.
(2)
Mark scheme · 2.6 Substitution into Expressions and Formulae

Question 1

  • M1 substitutes l and w and evaluates 2(4+2)
  • A1 12 cao
  • Answer: 12

Question 2

  • M1 substitutes 6 for n and shows 0.5 x 6 + 1 or equivalent
  • M1 evaluates 0.5 x 6 = 3 or shows intermediate step
  • A1 £4 cao
  • Answer: 4

Question 3

  • M1 substitutes 3 for c and writes 2 x 3 + 1 or equivalent
  • M1 evaluates 2 x 3 = 6
  • A1 7 teaspoons cao
  • Answer: 7

Question 4

  • M1 substitutes 4 into x + 3 to get (4 + 3) or shows step
  • M1 multiplies by 2 correctly to get 2 x 7
  • A1 14 cao
  • Answer: 14

Question 5

  • M1 substitutes x = 2 and y = 5 into expression and shows 3(5) - 2(2 + 1) or equivalent
  • M1 evaluates brackets and multiplication correctly, e.g. 15 - 2 x 3
  • A1 9 cao
  • Answer: 9

Question 6

  • M1 substitutes b = 8 and h = 5 into A = 1/2 b h or shows 1/2 x 8 x 5
  • A1 20 (square units) cao
  • Answer: 20

Question 7

  • M1 substitutes n = 5 correctly to get T = 80 - 2 x 5 = 70 for first pair
  • M1 substitutes n = 7 correctly to get T = 80 - 2 x 7 = 66 for second pair
  • M1 substitutes n = 9 correctly to get T = 80 - 2 x 9 = 62 for third pair
  • M1 adds the three temperatures to get 70 + 66 + 62
  • M1 evaluates the sum correctly to 198 or shows intermediate addition
  • A1 198 degrees Celsius cao
  • Answer: 198

Question 8

  • B1 12 cao
  • Answer: 12

Question 9

  • B1 1 cao
  • Answer: 1

Question 10

  • B1 25 cao
  • Answer: 25

Question 11

  • B1 5 cao
  • Answer: 5

Question 12

  • B1 3/1 or 3 cao (3) as fraction 3/1 acceptable
  • Answer: 3

Question 13

  • M1 substitutes -1 for x and evaluates 5(-1) + 2 or shows method
  • A1 -3 cao
  • Answer: -3

Question 14

  • M1 substitutes 7 and 3 into A = l w or shows multiplication 7 x 3
  • A1 21 (square units) cao
  • Answer: 21

Question 15

  • B1 15 cao
  • Answer: 15

Question 16

  • M1 substitutes n = 8 correctly, e.g. 2(8) + 3
  • A1 19 cao
  • Answer: 19

Question 17

  • M1 substitutes x = 3 into the bracket correctly, e.g. 4(5)
  • A1 20 cao
  • Answer: 20

Question 18

  • M1 squares -3 correctly to get 9 before multiplying by 2
  • A1 18 cao
  • Answer: 18

Question 19

  • M1 substitutes x = 2 and y = 4 correctly
  • M1 works out the bracket first, e.g. 3(3) = 9
  • A1 11 cao
  • Answer: 11

Question 20

  • M1 correct area for triangle 1, e.g. 1/2 x 12 x 7 = 42
  • M1 correct area for triangle 2, e.g. 1/2 x 8 x 7 = 28
  • A1 70 cao
  • Answer: 70

Question 21

  • M1 substitutes p = 12 correctly, e.g. 8(12) + 3
  • M1 correct multiplication, e.g. 8 x 12 = 96
  • A1 £99 cao
  • A1 correct conclusion: yes, the budget is enough, since 99 ≤ 100
  • Answer: £99; yes, the budget of £100 is enough

Question 22

  • M1 substitutes n = 8 correctly, e.g. 90 - 3(8) = 66
  • M1 substitutes n = 15 correctly, e.g. 90 - 3(15) = 45
  • M1 correctly subtracts the two temperatures
  • A1 21 degrees cao
  • Answer: Mug A: 66 degrees; Mug B: 45 degrees; difference: 21 degrees

Question 23

  • M1 correctly finds T when n = 5, e.g. 2(25) - 5 = 45
  • M1 correctly finds T when n = -2, keeping track of both negative signs, e.g. 2(4) - (-2) = 10
  • M1 correctly adds the two values
  • A1 55 cao
  • Answer: T(5) = 45, T(-2) = 10; the sum is 55

Question 24

  • B1 14 cao
  • Answer: 14

Question 25

  • B1 10 cao
  • Answer: 10

Question 26

  • B1 16 cao
  • Answer: 16

Question 27

  • B1 3 cao
  • Answer: 3

Question 28

  • B1 -3 cao
  • Answer: -3

Question 29

  • M1 substitutes l = 9 and w = 4 correctly
  • A1 36 cao
  • Answer: 36

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