The formula for the area of a rectangle is A = lw. Find A when l = 9 and w = 4.
(2)
9
Use the formula P = 2(l + w) to find the perimeter of a rectangle with l = 6 and w = 5.
(2)
10
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)
11
A recipe uses 3c + 2 grams of salt, where c is the number of portions. Work out the amount of salt needed for c = 5 portions.
(2)
12
Evaluate 4(x + 2) when x = 3.
(2)
13
Substitute a = -3 into 2a2 and give the result.
(2)
14
Evaluate 5y - 3(x + 1) when x = 2 and y = 4. Show the steps.
(3)
15
A petrol pump formula for cost is P = 1.4n, where n is the number of litres bought and P is the cost in pounds. Priya buys 15 litres of petrol and pays with a 25 pound note. Work out how much change she receives.
(3)
16
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)
17
A theatre charges C = 8p + 3 pounds 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 pounds. Work out the cost for the group and state whether the budget is enough.
(4)
18
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)
19
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)
Mark scheme · KS3.M-A6D Substitution into Expressions and Formulae: Fluency and Exam Drill
Question 1
B1 15 cao
Answer: 15
Question 2
B1 14 cao
Answer: 14
Question 3
B1 10 cao
Answer: 10
Question 4
B1 16 cao
Answer: 16
Question 5
B1 1 cao
Answer: 1
Question 6
B1 3 cao
Answer: 3
Question 7
B1 -3 cao
Answer: -3
Question 8
M1 substitutes l = 9 and w = 4 correctly
A1 36 cao
Answer: 36
Question 9
M1 substitutes l = 6 and w = 5 correctly, e.g. 2(6 + 5)
A1 22 cao
Answer: 22
Question 10
M1 substitutes n = 8 correctly, e.g. 2(8) + 3
A1 19 cao
Answer: 19
Question 11
M1 substitutes c = 5 correctly, e.g. 3(5) + 2
A1 17 grams cao
Answer: 17 grams
Question 12
M1 substitutes x = 3 into the bracket correctly, e.g. 4(5)
A1 20 cao
Answer: 20
Question 13
M1 squares -3 correctly to get 9 before multiplying by 2
A1 18 cao
Answer: 18
Question 14
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 15
M1 substitutes n = 15 correctly, e.g. 1.4 x 15
M1 correct cost of 21 pounds found and subtracted from 25
A1 4 pounds cao
Answer: 4 pounds
Question 16
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 17
M1 substitutes p = 12 correctly, e.g. 8(12) + 3
M1 correct multiplication, e.g. 8 x 12 = 96
A1 99 pounds cao
A1 correct conclusion: yes, the budget is enough, since 99 ≤ 100
Answer: 99 pounds; yes, the budget of 100 pounds is enough
Question 18
M1 substitutes n = 8 correctly, e.g. 90 - 3(8) = 66
M1 substitutes n = 15 correctly, e.g. 90 - 3(15) = 45