Writing and Using Formulae - Worksheets, Questions and Revision

14 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Algebra

KS3.M-A12 Writing and Using Formulae

AQA KS3.M-A12 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write a formula for each description. Use a single letter for the variable.
(a)The perimeter P of a square with side length s.(1)
(b)The total cost C in pounds for buying n notebooks at 1.75 pounds each.(1)
(c)The area A of a rectangle with width w and length l.(1)
(d)Total marks T when a test has q questions worth 2 marks each and m questions worth 3 marks each.(1)
2
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)
3
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)
4
Use formulae with units. The formula for average speed v in m/s is v = s / t, where s is distance in metres and t is time in seconds.
(a)A runner covers 400 m in 50 s. Find the average speed in m/s. Give your answer as a decimal to two decimal places.(2)
(b)A skateboarder travels at 2 m/s for 45 s. Find the distance covered in metres.(2)
5
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)
6
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)
7
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)
8
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)
9
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)
10
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 = 350 pence, find C for m = 40 minutes.(2)
(b)If a customer pays 674 pence in total and F = 350 pence, how many minutes did they use? Give your answer as an integer.(1)
11
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)
12
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)
13
Stretch 2: A formula for the temperature T in degrees C after t hours is T = 20 - 3t. Two students disagree about when T reaches 2 degrees C. Use the formula to find t and state if t is positive.
(a)Solve 20 - 3t = 2 for t.(1)
(b)Is t positive? Give a brief reason.(1)
14
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
Mark scheme · KS3.M-A12 Writing and Using Formulae

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14