GCSE MATHEMATICS KEY TOPIC PRACTICE SHEETS EXPRESSIONS, FORMULAE AND SUBSTITUTION (EDEXCEL FOUNDATION) These questions are suitable for Foundation Tier students. All questions should be done without a calculator. www.tutor2u.net/maths
1 The formula for the equation of a line is y = 2x 1. Use this formula to complete the table of coordinate values below. x -3-1 1 3 5 y -3 9 (Total for Question 1 is 2 marks) 2 Phil uses this formula to work out the perimeter of this shape: x P = 3x + y + z Calculate P when x = 4.1, y = 7.7 and z = 7. z y P =.. (Total for Question 2 is 3 marks) x x Copyright tutor2u 2017 2
3 f = uv + w u = 3 v = 5 w = 24 Work out the value of f. (Total for Question 3 is 2 marks) 4 Alex made m mobile phone calls last month. Ryan made 20 fewer calls than Alex last month. (a) Write an expression for the number of phone calls made by Ryan last month. (1) The following formula is used to calculate the cost of Alex s mobile phone bill: 20m + 3000 C = 100 C = Cost in pounds, m = The number of calls Alex made 50 phone calls last month. (b) How much was Alex s mobile phone bill last month?... (3) (Total for Question 4 is 4 marks) Copyright tutor2u 2017 3
5 A newsagents sells bars of chocolate for 70 pence and cans of fizzy drinks for 40 pence. Hayley buys b bars of chocolate and c cans of fizzy drinks. Write an expression for the amount, in pence, that she spends. 6 u = v at (Total for Question 5 is 2 marks) When v = 8, a = 2 and t = 12, work out u. (Total for Question 6 is 2 marks) 7 This formula is used to work out the height, h, of a trapezium when given the lengths of the parallel sides, a and b, and the area, A. h = 2A a + b Evaluate h when A = 48, a = 4 and b = 8. (Total for Question 7 is 2 marks) Copyright tutor2u 2017 4
8 A physical training session involves running around the perimeter of a tennis court and running around the perimeter of a football pitch. The perimeter of the tennis court is c metres. The perimeter of the football pitch is p metres. I ran 5 times around the tennis court and 3 times around the football pitch. (a) Find an expression in terms of c and p for the total number of metres I ran in total. You are now given that c = 64 and p = 300. (b) Using your answer to part (a) or otherwise, find the total distance I ran in metres. (1) (2) (Total for Question 8 is 3 marks) Copyright tutor2u 2017 5
9 In a rectangle, the length of the longer sides is x centimetres. The length of the shorter sides is 5 centimetres less. (a) Write down, in terms of x, the length of each shorter side. (1) (b) Write down, in terms of x, the length of the perimeter of the rectangle. Give your answer as simply as possible. (2) (c) Given that the perimeter of the rectangle is 50 centimetres, find the lengths of the sides of the rectangle. (3) (Total for Question 9 is 6 marks) Copyright tutor2u 2017 6
10 Pressure = Force Area 1 kilonewton = 1000 newtons Find the pressure exerted by a force of 0.35 kilonewtons on an area of 7 m ]. 11 x = y c m Find x when y =6.2, c = 5.9 and m = 10. newtons/m ] (Total for Question 10 is 2 marks) (Total for Question 11 is 3 marks) Copyright tutor2u 2017 7
12 A car rental company, ABC Cars, hires out cars at a rate of 70 per day, plus a payment of 30 regardless of the number of days of hire. (a) Using C for the cost of hire in pounds ( ), and d for the number of days that the car is hired, write a formula for calculating the cost of hire. (2) Another car rental company, XYZ Cars, uses the following formula for calculating the cost of hire: A = 50d + 100 where A = the amount of the cost of hire in pounds ( ) and d = the number of days that the car is hired. The Smith family need to hire a car for 3 days. (b) Which rental company should the Smith family use? Show your working clearly and justify your answer. (3) (Total for Question 12 is 5 marks) Copyright tutor2u 2017 8
13 Sophie has one younger brother and one older sister. She was born 2 years before her brother and 5 years after her sister. Sophie s age is x years old. Find an expression for the mean age of Sophie, her brother and her sister. Write your answer as simply as possible. 14 A coffee shop sells tea, coffee and orange juice in the ratio 1 c 5. (Total for Question 13 is 3 marks) (a) Write an expression, as a fraction, for the proportion of drinks sold that were coffee. (2) (b) Given that c = 3, evaluate the proportion of drinks sold that were coffee, giving your answers as a simplified fraction. (2) (Total for Question 14 is 4 marks) Copyright tutor2u 2017 9
15 Toby is impressing his friends with a number puzzle. He gets his friend to think of a number, add 5 to it, then double their answer. His friend then tells Toby their final answer and Toby tells them what number they thought of. (a) If n is the number that Toby s friend thinks of and A is their final answer, write a formula for A in terms of n. (b) Toby s friend, Annabel, thinks of a number. Her final answer is 76. What number was Annabel first thinking of? (3) (3) (Total for Question 15 is 6 marks) Copyright tutor2u 2017 10
GCSE MATHEMATICS KEY TOPIC PRACTICE SHEETS EXPRESSIONS, FORMULAE AND SUBSTITUTION (EDEXCEL FOUNDATION) These questions are suitable for Foundation Tier students. All questions should be done without a calculator. MODEL ANSWERS www.tutor2u.net/maths
1 The formula for the equation of a line is! = 2$ 1. Use this formula to complete the table of coordinate values below. x -3-1 1 3 5 y -3 9 (Total for Question 1 is 2 marks) 2 Phil uses this formula to work out the perimeter of this shape: x ' = 3$ +! + * Calculate ' when $ = 4.1,! = 7.7 and * = 7. z y P =.. (Total for Question 2 is 3 marks) x x Copyright tutor2u 2017 2
3. = /0 + 1 / = 3 0 = 5 1 = 24 Work out the value of.. (Total for Question 3 is 2 marks) 4 Alex made 3 mobile phone calls last month. Ryan made 20 fewer calls than Alex last month. (a) Write an expression for the number of phone calls made by Ryan last month. (1) The following formula is used to calculate the cost of Alex s mobile phone bill: 206 + 3000 4 = 100 4 = 4789 ;< =7/<>8, 6 = AhC </6DCE 7. FGHH8 Alex made 50 phone calls last month. (b) How much was Alex s mobile phone bill last month?... (3) (Total for Question 4 is 4 marks) Copyright tutor2u 2017 3
5 A newsagents sells bars of chocolate for 70 pence and cans of fizzy drinks for 40 pence. Hayley buys b bars of chocolate and c cans of fizzy drinks. Write an expression for the amount, in pence, that she spends. 6 / = 0 G9 (Total for Question 5 is 2 marks) When 0 = 8, G = 2 and 9 = 12, work out /. (Total for Question 6 is 2 marks) 7 This formula is used to work out the height, J, of a trapezium when given the lengths of the parallel sides, K and L, and the area, M. h = 2N G + D Evaluate J when M = 48, K = 4 and L = 8. (Total for Question 7 is 2 marks) Copyright tutor2u 2017 4
8 A physical training session involves running around the perimeter of a tennis court and running around the perimeter of a football pitch. The perimeter of the tennis court is O metres. The perimeter of the football pitch is P metres. I ran 5 times around the tennis court and 3 times around the football pitch. (a) Find an expression in terms of O and P for the total number of metres I ran in total. You are now given that O = 64 and P = 300. (b) Using your answer to part (a) or otherwise, find the total distance I ran in metres. (1) (2) (Total for Question 8 is 3 marks) Copyright tutor2u 2017 5
9 In a rectangle, the length of the longer sides is Q centimetres. The length of the shorter sides is 5 centimetres less. (a) Write down, in terms of Q, the length of each shorter side. (1) (b) Write down, in terms of Q, the length of the perimeter of the rectangle. Give your answer as simply as possible. (2) (c) Given that the perimeter of the rectangle is 50 centimetres, find the lengths of the sides of the rectangle. (3) (Total for Question 9 is 6 marks) Copyright tutor2u 2017 6
10 'EC88/EC = R7EFC NECG 1 kilonewton = 1000 newtons Find the pressure exerted by a force of 0.35 kilonewtons on an area of 7 m ]. 11 $ =! F 6 Find Q when _ =6.2, O = 5.9 and 3 = 10. newtons/m ] (Total for Question 10 is 2 marks) (Total for Question 11 is 3 marks) Copyright tutor2u 2017 7
12 A car rental company, ABC Cars, hires out cars at a rate of 70 per day, plus a payment of 30 regardless of the number of days of hire. (a) Using C for the cost of hire in pounds ( ), and d for the number of days that the car is hired, write a formula for calculating the cost of hire. (2) Another car rental company, XYZ Cars, uses the following formula for calculating the cost of hire: N = 50> + 100 where A = the amount of the cost of hire in pounds ( ) and d = the number of days that the car is hired. The Smith family need to hire a car for 3 days. (b) Which rental company should the Smith family use? Show your working clearly and justify your answer. (3) (Total for Question 12 is 5 marks) Copyright tutor2u 2017 8
13 Sophie has one younger brother and one older sister. She was born 2 years before her brother and 5 years after her sister. Sophie s age is x years old. Find an expression for the mean age of Sophie, her brother and her sister. Write your answer as simply as possible. 14 A coffee shop sells tea, coffee and orange juice in the ratio 1 F 5. (Total for Question 13 is 3 marks) (a) Write an expression, as a fraction, for the proportion of drinks sold that were coffee. (2) (b) Given that F = 3, evaluate the proportion of drinks sold that were coffee, giving your answers as a simplified fraction. (2) (Total for Question 14 is 4 marks) Copyright tutor2u 2017 9
15 Toby is impressing his friends with a number puzzle. He gets his friend to think of a number, add 5 to it, then double their answer. His friend then tells Toby their final answer and Toby tells them what number they thought of. (a) If b is the number that Toby s friend thinks of and M is their final answer, write a formula for M in terms of b. (b) Toby s friend, Annabel, thinks of a number. Her final answer is 76. What number was Annabel first thinking of? (3) (3) (Total for Question 15 is 6 marks) Copyright tutor2u 2017 10