These questions are suitable for Higher Tier students. Questions 1 to 14 should be done without a calculator.

Transcription

1 GCSE MATHEMATICS KEY TOPIC PRACTICE SHEETS EXPRESSIONS, FORMULAE AND SUBSTITUTION (AQA HIGHER) These questions are suitable for Higher Tier students. Questions 1 to 14 should be done without a calculator. Question 15 can be done with a calculator.

2 Key Topic Practice Sheets 1 u = v at What is the value of u in when v = 8, a = 2 and t = 12 Circle the correct answer. [1 mark] A shop sells small and large bags of potatoes. There are 10 potatoes in a small bag. There are 40 potatoes in a large bag. Hakim buys s small bags and l large bags. Circle the correct expression for the total number of potatoes bought by Hakim. [1 mark] s + l 10s + 40l 50 40s + 10l 3 Pressure = Force Area 1 kilonewton = 1000 newtons Find the pressure exerted by a force of 0.35 kilonewtons on an area of 7 m E. [2 marks] Answer newtons/m E Copyright tutor2u

3 Key Topic Practice Sheets 10 Express O P O Q as a single fraction. [2 marks] Answer. 11 It takes 16 minutes for a tap to completely fill a bathtub with 80 litres of water. 11 (a) If the bath has been filling up for y minutes, write down an expression for the amount of water that has been added. [2 marks] Answer. 11 (b) The bath currently contains x litres of water. Write down an expression for how long it took in minutes to supply the bath with x litres of water. [1 marks] Answer. Copyright tutor2u

4 Key Topic Practice Sheets 12 A tent is made in the shape of a semi-circular prism of length 3 metres. The tent includes a built-in groundsheet. x The radius of the semi-circle at the end of the tent is x metres. Find an expression for the total surface area of the tent material used. Give your answer in terms of π. [4 marks] 3 m Answer. Copyright tutor2u

5 Key Topic Practice Sheets 13 Paula drives from Sunderland to Newcastle at an average speed of 50 mph. She drives back at an average speed of 30 mph. The distance from Sunderland to Newcastle is d miles. 13 (a) Find an expression for the total journey time (in hours) in terms of d. [2 marks] Answer. 13 (b) Work out Paula s mean speed for the whole journey. Express your answer as simply as possible. [4 marks] Copyright tutor2u

6 Key Topic Practice Sheets 14 The formula for the graph of a cubic function is where a, b, c and d are constants. A cubic function has the following values: a = 1 b = 6 c = 11 d = 6 y = ax S + bx E + cx + d Does the graph touch the x-axis when x = 3? Explain your answer clearly. [4 marks] Copyright tutor2u

7 Key Topic Practice Sheets 15 The formula below is used to work out the final speed of a car v = u E + 2as Where u = initial speed (m/s) v = final speed (m/s) a = acceleration (m/s 2 ) s = distance travelled (m) A speed camera photographs a car when it passes at 10% or more above the speed limit. The speed limit is 70 miles per hour. A car passes under a bridge with an initial speed of 70 miles per hour, before it reaches a speed camera positioned 100 m after the bridge. The cars acceleration is 1 m/s 2. Does the car trigger the speed camera? Show your stages of working clearly and explain your answer. Use 5 miles = 8 kilometres. [6 marks] Copyright tutor2u

8 GCSE MATHEMATICS KEY TOPIC PRACTICE SHEETS EXPRESSIONS, FORMULAE AND SUBSTITUTION (AQA HIGHER) These questions are suitable for Higher Tier students. Questions 1 to 14 should be done without a calculator. Question 15 can be done with a calculator. MODEL ANSWERS

9 Key Topic Practice Sheets 12 A tent is made in the shape of a semi-circular prism of length 3 metres. The tent includes a built-in groundsheet. G SA RE M SO PL E U RC E 3J The radius of the semi-circle at the end of the tent is G metres. Find an expression for the total surface area of the tent material used. Give your answer in terms of R. [4 marks] Answer Copyright tutor2u

10 Key Topic Practice Sheets Copyright tutor2u Paula drives from Sunderland to Newcastle at an average speed of 50 mph. She drives back at an average speed of 30 mph. The distance from Sunderland to Newcastle is M miles. 13 (a) Find an expression for the total journey time (in hours) in terms of M. [2 marks] 13 (b) Work out Paula s mean speed for the whole journey. Express your answer as simply as possible. Answer. [4 marks]

11 Key Topic Practice Sheets 14 The formula for the graph of a cubic function is where %, N, I and M are constants. A cubic function has the following values: % = 1 N = 6 I = 11 M = 6 H = %G S + NG E + IG + M Does the graph touch the x-axis when G = 3? Explain your answer clearly. Copyright tutor2u [4 marks]

12 Key Topic Practice Sheets 15 The formula below is used to work out the final speed of a car #=!E + 2%* Where u = initial speed (m/s) v = final speed (m/s) a = acceleration (m/s2) s = distance travelled (m) A speed camera photographs a car when it passes at 10% or more above the speed limit. The speed limit is 70 miles per hour. SA RE M SO PL E U RC E A car passes under a bridge with an initial speed of 70 miles per hour, before it reaches a speed camera positioned 100 m after the bridge. The cars acceleration is 1 m/s2. Does the car trigger the speed camera? Show your stages of working clearly and explain your answer. Use 5 miles = 8 kilometres. [6 marks] Copyright tutor2u