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11+ · Algebra and Number

EP.M132 Substitution and Formulae in Words

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

The area A of a rectangle is given by A = l x w. Find the area when l = 6 m and w = 3 m.

A) 9 m²
B) 18 m²
C) 24 m²
D) 36 m²
E) 63 m²

(Total for Question 1 is 1 mark)

The total cost C (in pence) for a group is given by C = 120 + 35n, where n is the number of people. What is the cost in pounds for 4 people?

A) £2.20
B) £2.60
C) £3.60
D) £1.60
E) £0.60

(Total for Question 2 is 1 mark)

If S = 2(x + 3) and x = 4, what is S?

A) 11
B) 8
C) 14
D) 16
E) 10

(Total for Question 3 is 1 mark)

The perimeter P of a square with side s is P = 4s. Find P when s = 7 cm.

A) 14 cm
B) 21 cm
C) 28 cm
D) 49 cm
E) 35 cm

(Total for Question 4 is 1 mark)

A recipe says the number of scoops, S, needed is S = 3b - 1 where b is the number of bowls. How many scoops for b = 5?

A) 14
B) 15
C) 10
D) 13
E) 11

(Total for Question 5 is 1 mark)

From the formula M = 5 + 2n, where n is the number of items, find M when n = 0.

A) 0
B) 2
C) 5
D) 7
E) 10

(Total for Question 6 is 1 mark)

If T = (x + 2) x 3 and x = 2, what value of T is obtained?

A) 12
B) 9
C) 10
D) 6
E) 8

(Total for Question 7 is 1 mark)

The cooling time in minutes, C, is given by C = 10 + 2t where t is the temperature in degrees above 0. Find C when t = 6.

A) 12
B) 22
C) 18
D) 20
E) 16

(Total for Question 8 is 1 mark)

A car hire firm charges H = 25 + 15d where d is days hired. What is H for d = 3, in pounds?

A) £40
B) £55
C) £70
D) £45
E) £35

(Total for Question 9 is 1 mark)

For the formula F = 4p - (2 + p), find F when p = 3.

A) 6
B) 7
C) 8
D) 5
E) 9

(Total for Question 10 is 1 mark)

If G = 2(a + b) and a = 3, b = 4, what is G?

A) 10
B) 14
C) 24
D) 7
E) 12

(Total for Question 11 is 1 mark)

The number of tiles T needed is given by T = (length + width) x 2. If length = 5 and width = 2, find T.

A) 14
B) 15
C) 20
D) 10
E) 12

(Total for Question 12 is 1 mark)

The function t is defined by t = 4a - 5. Calculate t when a = 3, then find a when t = 11. Give both answers.

(Total for Question 13 is 2 marks)

A toy's price P in pence is given by P = 150 - 3x, where x is the number of stickers used. Find P when x = 10 and when x = 0. State both answers in pounds.

(Total for Question 14 is 2 marks)

The distance D in km between two towns is D = 3m + 2n where m = 4 and n = 5. Calculate D.

(Total for Question 15 is 2 marks)

Given Q = 2(x - 1) + 3y, find Q when x = 5 and y = 2.

(Total for Question 16 is 2 marks)

The volume V of a small box is V = l x w x h. Find V when l = 2 cm, w = 3 cm and h = 4 cm. Then find h when V = 36 cm³ and l = 3 cm, w = 3 cm.

(Total for Question 17 is 2 marks)

A gardener uses formula S = (p + q) x 4 where p is the number of pots and q is the number of seed trays. If p = 7 and q = 3, find S. Then find q if S = 40 and p = 5.

(Total for Question 18 is 2 marks)

A formula is given by R = 3(x + 2y) - 5. Calculate R when x = 4 and y = 3. Show your working.

(Total for Question 19 is 3 marks)

The time in minutes, Y, for a recipe is given by Y = 2(a + 3b) + 4 where a and b are whole numbers. Find Y when a = 2 and b = 3. Then if Y = 48 and a = 4, find b. Show your steps.

(Total for Question 20 is 3 marks)

Mark scheme · EP.M132 Substitution and Formulae in Words

Question 1

B1 correct option B (18 m²) cao
Answer: B) 18 m² (6 x 3 = 18).

Question 2

B1 correct option B (£2.60) cao
Answer: B) £2.60 (120 + 35 x 4 = 260 pence = £2.60).

Question 3

B1 correct option C (14) cao
Answer: C) 14 because 2(4 + 3) = 2 x 7 = 14.

Question 4

B1 correct option C (28 cm) cao
Answer: C) 28 cm (4 x 7 = 28).

Question 5

B1 correct option D (14) cao
Answer: D) 14 because 3 x 5 - 1 = 15 - 1 = 14.

Question 6

B1 correct option C (5) cao
Answer: C) 5 (5 + 2 x 0 = 5).

Question 7

B1 correct option A (12) cao
Answer: A) 12 because (2 + 2) x 3 = 4 x 3 = 12.

Question 8

B1 correct option B (22) cao
Answer: B) 22 (10 + 2 x 6 = 10 + 12 = 22).

Question 9

B1 correct option C (£70) cao
Answer: C) £70 because 25 + 15 x 3 = 25 + 45 = 70.

Question 10

B1 correct option B (7) cao
Answer: B) 7 because F = 4x3 - (2 + 3) = 12 - 5 = 7.

Question 11

B1 correct option B (14) cao
Answer: B) 14 because 2 x (3 + 4) = 2 x 7 = 14.

Question 12

B1 correct option A (14) cao
Answer: A) 14 because (5 + 2) x 2 = 7 x 2 = 14.

Question 13

M1 substitute a = 3 to get t = 4 x 3 - 5 (= 7) seen
A1 first answer t = 7 and second answer a = 4 cao
Answer: t = 7; when t = 11, 11 = 4a - 5 so 4a = 16 and a = 4.

Question 14

M1 substitutions P = 150 - 3 x 10 and P = 150 - 3 x 0 seen
A1 answers £1.20 and £1.50 cao
Answer: When x = 10: P = 150 - 30 = 120 pence = £1.20. When x = 0: P = 150 pence = £1.50.

Question 15

M1 substitution 3 x 4 + 2 x 5 (= 12 + 10) seen
A1 D = 22 km cao
Answer: D = 3 x 4 + 2 x 5 = 12 + 10 = 22 km.

Question 16

M1 substitute x = 5 and y = 2 to get 2(5 - 1) + 3 x 2 seen
A1 Q = 14 cao
Answer: Q = 2(5 - 1) + 3 x 2 = 2 x 4 + 6 = 8 + 6 = 14.

Question 17

M1 correct substitution for first part and rearrangement for second part seen
A1 first answer 24 cm³ and second answer h = 4 cm cao
Answer: First: V = 2 x 3 x 4 = 24 cm³. Second: 36 = 3 x 3 x h so h = 36 / 9 = 4 cm.

Question 18

M1 substitutions and rearrangement seen
A1 S = 40 and q = 5 cao
Answer: First: S = (7 + 3) x 4 = 10 x 4 = 40. Second: 40 = (5 + q) x 4 so 10 = 5 + q and q = 5.

Question 19

M1 substitution 3(4 + 2 x 3) - 5 or equivalent seen
M1 evaluation inside brackets 4 + 6 = 10 or 2 x 3 = 6 seen
A1 R = 25 cao
Answer: R = 3(4 + 2 x 3) - 5 = 3(4 + 6) - 5 = 3 x 10 - 5 = 30 - 5 = 25.

Question 20

M1 substitution and bracket expansion seen for first part: 2(2 + 3 x 3) + 4 or equivalent
M1 calculate first part to get Y = 26 or correct intermediate seen
A1 second part b = 6 cao
Answer: First: Y = 2(2 + 3 x 3) + 4 = 2(2 + 9) + 4 = 2 x 11 + 4 = 22 + 4 = 26. Second: 48 = 2(4 + 3b) + 4 so 44 = 2(4 + 3b) so 22 = 4 + 3b and 3b = 18 giving b = 6.

Substitution and Formulae in Words - Worksheets, Questions and Revision