Writing and Using Formulae - Worksheets, Questions and Revision

28 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 9)Writing and Using Formulae revision guide

This topic is chapter 9 of KS3 Maths: Algebra Practice Book 1.

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2.12 Writing and Using Formulae

AQA KS3.M-A12 · Calculators not allowed · about 90 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A mobile phone company charges a fixed monthly fee F plus 12 p per minute for calls. The cost in pence is C = F + 12m where m is minutes.

(a)If F = 350p, find C for m = 40 minutes.(2)

(b)If a customer pays 674p in total and F = 350p, how many minutes did they use? Give your answer as an integer.(1)

Compound operations and formulae. The formula M = 3(a - b) + 2b is used.

(a)Simplify the expression M in terms of a and b.(2)

(b)Find M when a = 4 and b = 1.(1)

Stretch 1: A small triangle and a similar big triangle have corresponding sides in ratio 1:n. Area of the small triangle is As and area of the big triangle is Ab. Let Ab = k As. Express k in terms of n and use it to find Ab when As = 6 and n = 3.

(a)Write k in terms of n, knowing area scales as the square of linear scale factor.(2)

(b)Find Ab when As = 6 and n = 3.(2)

Final fluency: Match each algebraic expression to its word description.

(a)Expression: 7m. Description choices: (i) m increased by 7, (ii) 7 times m, (iii) m divided by 7.(1)

(i) m increased by 7
(ii) 7 times m
(iii) m divided by 7

(b)Expression: n - 5. Description choices: (i) subtract n from 5, (ii) n minus 5, (iii) 5 minus n.(1)

(i) subtract n from 5
(ii) n minus 5
(iii) 5 minus n

Substitute and evaluate. Use the formula S = 2h + 5.

(a)Find S when h = 4.(1)

(b)Find S when h = 0.(1)

(c)Find S when h = -2.(1)

A car travels at a constant speed. Distance d in kilometres is given by d = 50t, where t is time in hours.

(a)How far does the car travel in 1.5 hours? Give your answer in km.(2)

(b)How long does it take to travel 125 km? Give your answer in hours.(1)

Rearrange the simple formula and solve. The formula is A = 3x + 7.

(a)Given A = 16, find x.(2)

(b)Given A = -2, find x.(1)

The area of a triangle is given by A = 1/2 b h. Rearrange to make h the subject.

(a)Rearrange A = 1/2 b h to make h the subject.(3)

(b)Use your rearranged formula to find h when A = 24 and b = 6.(1)

Write a formula from a worded rule. Each question uses the same letter for the unknown.

(a)Multiply a number n by 6, then subtract 4. Call the result R.(1)

(b)Add 9 to a number p, then divide the result by 3. Call the result S.(1)

(c)Double a number x, then square the result. Call the result T.(1)

Substitute negative and fractional values into formulae. Use C = 5t - 3.

(a)Find C when t = -1.(1)

(b)Find C when t = 1/2.(2)

Rearrange to make x the subject. Start from 4x + 9 = y.

(a)Rearrange 4x + 9 = y to make x the subject.(3)

(b)Use your formula to find x when y = 17.(1)

Write a formula for the perimeter P of a regular pentagon with side length s.

(1)

The formula A = 4x + 9 is used. Given A = 25, find x.

(1)

The volume of a prism is given by V = (1/2) b h l. Rearrange the formula to make l the subject.

(2)

Using l = 2V / (bh), find l when V = 60, b = 5 and h = 4.

(2)

Write a formula for this rule, using the same letter throughout: multiply a number n by 7, then add 5. Call the result R.

(1)

Substitute negative and fractional values into formulae. Use C = 4t - 5.

(a)Find C when t = -2.(1)

(b)Find C when t = 1/2.(1)

A parking garage charges a fixed entry fee of 200p plus 8p per minute parked, using the formula C = 200 + 8m. Find the cost of parking for 45 minutes, giving your final answer in pounds.

(3)

Using C = 200 + 8m, a customer pays 560p in total to park. Work out how many minutes they parked for.

(3)

Write a formula for the total cost C, in pounds, of buying n rulers at £0.65 each.

(1)

A gym charges a joining fee of £30 plus a monthly fee of m pounds, giving total cost after n months as T = 30 + mn.

(a)Given m = 22, find the total cost after 6 months.(2)

(b)A member has paid £250 in total after 10 months. Find m.(2)

Stretch: A large square and a similar small square have sides in ratio n:1. Area scales as the square of the linear scale factor, so the large square's area Al = k times the small square's area As.

(a)Write k in terms of n.(1)

(b)Find Al when As = 5 and n = 4.(3)

Write a formula for the area A of a triangle with base b and height h.

(1)

Use the formula S = 3h + 2. Find S when h = 5.

(1)

Use the formula S = 3h + 2. Find S when h = -3.

(1)

A train travels at a constant speed. Distance d in kilometres is given by d = 80t, where t is time in hours. How far does the train travel in 2.5 hours?

(2)

The formula for average speed v in m/s is v = s / t. A cyclist covers 300 m in 40 s. Find the average speed in m/s.

(2)

Using s = vt, a skater travels at 3 m/s for 25 s. Find the distance covered in metres.

(2)

Mark scheme · 2.12 Writing and Using Formulae

Question 1

(a) M1 substitution C = 350 + 12 x 40 or equivalent
(a) A1 830p cao
(a) Answer: 830
(b) B1 m = 27 cao
(b) Answer: 27

Question 2

(a) M1 expand 3(a - b) to 3a - 3b or equivalent
(a) A1 M = 3a - b cao
(a) Answer: M = 3a - b
(b) B1 M = 11 cao
(b) Answer: 11

Question 3

(a) M1 state area scale factor = n² or show k = n²
(a) A1 k = n² cao
(a) Answer: k = n²
(b) M1 substitute Ab = n² x As with n=3, As=6
(b) A1 54 cao
(b) Answer: 54

Question 4

(a) B1 choice (ii) 7 times m
(a) Answer: (ii)
(b) B1 choice (ii) n minus 5
(b) Answer: (ii)

Question 5

(a) B1 S = 13 cao
(a) Answer: 13
(b) B1 S = 5 cao
(b) Answer: 5
(c) B1 S = 1 cao
(c) Answer: 1

Question 6

(a) M1 substitution d = 50 x 1.5 or equivalent method
(a) A1 75 km cao
(a) Answer: 75 km
(b) B1 2.5 hours cao
(b) Answer: 2.5 hours

Question 7

(a) M1 form 3x + 7 = 16 and subtract 7 or equivalent method
(a) A1 x = 3 cao
(a) Answer: 3
(b) B1 x = -3 cao
(b) Answer: -3

Question 8

(a) M1 multiply both sides by 2 or show 2A = b h
(a) M1 divide both sides by b or show h = 2A / b
(a) A1 h = 2A / b cao
(a) Answer: h = 2A / b
(b) B1 h = 8 cm or units not required but value 8 cao
(b) Answer: 8

Question 9

(a) B1 R = 6n - 4 cao
(a) Answer: R = 6n - 4
(b) B1 S = (p + 9) / 3 or S = (p+9)/3 cao
(b) Answer: S = (p + 9) / 3
(c) B1 T = (2x)² or T = 4x² cao
(c) Answer: T = (2x)²

Question 10

(a) B1 C = -8 cao
(a) Answer: -8
(b) M1 substitution 5 x 1/2 - 3 or equivalent
(b) A1 -0.5 or -1/2 cao
(b) Answer: -0.5

Question 11

(a) M1 subtract 9 from both sides or show 4x = y - 9
(a) M1 divide both sides by 4 or show x = (y - 9) / 4
(a) A1 x = (y - 9) / 4 cao
(a) Answer: x = (y - 9) / 4
(b) B1 x = 2.0 or 2 cao
(b) Answer: 2

Question 12

B1 P = 5s oe
Answer: P = 5s

Question 13

B1 x = 4 cao
Answer: 4

Question 14

M1 multiplies both sides by 2, 2V = bhl
A1 l = 2V / (bh) cao
Answer: l = 2V / (bh)

Question 15

M1 substitutes V = 60, b = 5, h = 4
A1 6 cao
Answer: 6

Question 16

B1 R = 7n + 5 oe
Answer: R = 7n + 5

Question 17

(a) B1 -13 cao
(a) Answer: -13
(b) B1 -3 cao
(b) Answer: -3

Question 18

M1 substitutes m = 45
A1 560p
B1 converts to £5.60 (ft their pence value)
Answer: £5.60 (560p)

Question 19

M1 sets up 560 = 200 + 8m
M1 correct rearrangement, e.g. 8m = 360
A1 45 cao
Answer: 45 minutes

Question 20

B1 C = 0.65n oe
Answer: C = 0.65n

Question 21

(a) M1 substitutes m = 22, n = 6
(a) A1 162 cao
(a) Answer: £162
(b) M1 sets up 250 = 30 + 10m and subtracts 30
(b) A1 22 cao
(b) Answer: £22

Question 22

(a) B1 k = n² cao
(a) Answer: k = n²
(b) M1 substitutes n = 4 into k = n² to get k = 16
(b) M1 multiplies k by As
(b) A1 80 cao
(b) Answer: 80

Question 23

B1 A = (1/2)bh oe
Answer: A = (1/2)bh

Question 24

B1 17 cao
Answer: 17

Question 25

B1 -7 cao
Answer: -7

Question 26

M1 substitutes t = 2.5
A1 200 cao
Answer: 200 km

Question 27

M1 substitutes s = 300, t = 40
A1 7.5 cao
Answer: 7.5 m/s

Question 28

M1 substitutes v = 3, t = 25
A1 75 cao
Answer: 75 m

Writing and Using Formulae - Worksheets, Questions and Revision

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2.12 Writing and Using Formulae

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