Name Class For Pearson Edexcel Level 1/Level 2 GCSE (9 1) Mathematics Paper 3 (Calculator) Higher Tier Time: 1 hour 30 minutes Churchill Paper 3B You must have: Ruler graduated in centimetres and millimetres, Total Marks protractor, pair of compasses, pen, HB pencil, eraser, calculator. Instructions Use black ink or ball-point pen. Write your name in the box at the top of this page. Answer all questions in the spaces provided. Calculators may be used. If your calculator does not have a π button, take the value of π to be 3.142 unless the question instructs otherwise. Diagrams are NOT accurately drawn, unless otherwise indicated. You must show all your working out. Information The total mark for this paper is 80. The marks for each question are shown in brackets. - use this as a guide as to how much time to spend on each question. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Written by Shaun Armstrong Only to be copied for use in a single school or college having purchased a licence 2017 EH3B Page 1 Churchill Maths Limited
Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 v = u + at (a) Find the value of v when u = 2.1, a = 4.5, t = 8.6... (b) Make t the subject of the formula v = u + at... (2) (Total for Question 1 is 3 marks) 2017 EH3B Page 2 Churchill Maths Limited
2 Pete asks two plumbers for a quote to repair his bathroom. The first plumber, Adira, says the price is fixed so will be exactly what she has quoted. Adira provides this information: Plumber 30 hours work @ 22.50 per hour Assistant 40 hours work @ 15.50 per hour Materials Normal cost 860 but I can get 10% trade discount The second plumber, Ben, doesn't give a fixed quote but a range of possible costs as follows: Labour 60 to 90 hours work @ 20 per hour Other costs 500 to 700 Write down advice as to which plumber Pete should use. You must show calculations to support your advice. (Total for Question 2 is 5 marks) 2017 EH3B Page 3 Churchill Maths Limited
3 Emma recorded the number of contactless payments made each lunchtime in her coffee shop. The diagram shows the results for 35 days. Frequency 10 8 6 4 2 0 5 6 7 8 9 10 Number of payments Emma says The mean number of contactless payments is higher than the median. Show that Emma is incorrect. (Total for Question 3 is 3 marks) 2017 EH3B Page 4 Churchill Maths Limited
4 Daisy drives a delivery van. She estimates what her average speed for a journey will be using this rough guide. Distance (miles) Average Speed (mph) Less than 5 25 5 to 15 30 15 to 40 40 More than 40 50 (a) Suggest a reason for longer journeys having a higher average speed. (b) Use Daisy's guide to estimate how much longer a 20 mile journey will take than a 10 mile journey.... minutes Rob says that Daisy's guide predicts that a 16 mile journey will take less time than a 14 mile journey. (2) (c) Is Rob correct? Show calculations to support your answer.... (2) (Total for Question 4 is 5 marks) 2017 EH3B Page 5 Churchill Maths Limited
5 At a birthday party, there is a 750 g chocolate cake and a 600 g carrot cake. At the party, 50% of the total weight of cake was eaten. Given that 54% of the chocolate cake was eaten, work out the percentage of the carrot cake that was eaten.... % (Total for Question 5 is 3 marks) 6 (a) Write 3 5 in standard form.... (b) Work out half of 1.8 10 5. Give your answer in standard form.... (Total for Question 6 is 2 marks) 2017 EH3B Page 6 Churchill Maths Limited
7 (a) Find out how many numbers are common factors of both 60 and 70.... (3) (b) X = a 3 bc and Y = ab 2 c where a, b and c are prime numbers. (i) Write down an expression for the Highest Common Factor (HCF) of X and Y.... (ii) Write down an expression for the Lowest Common Multiple (LCM) of X and Y.... (Total for Question 7 is 5 marks) 2017 EH3B Page 7 Churchill Maths Limited
8 Martin and Sarah are each given a coin. They have to investigate whether their coin is fair or biased. Martin flips his coin 10 times and gets 6 heads and 4 tails. He says This coin is biased, you're 50% more likely to get a head than a tail. (a) Make two criticisms of Martin's statement. Sarah flips her coin 100 times and gets 59 heads and 41 tails. She says This coin is fair, I got close to 50 heads and 50 tails. (2) (b) Comment on Sarah's statement. Kris is given a coin that is biased. When the coin is flipped once, the probability of getting a head is 1 3. Kris says As 3 1 3 = 1, if I flip this coin 3 times I'm certain to get a head. (c) Comment on Kris's statement. (2) (Total for Question 8 is 5 marks) 2017 EH3B Page 8 Churchill Maths Limited
9 (a) Find an expression for the nth term of this arithmetic progression. 7, 15, 23, 31, 39,... (2) (b) Find the value of the 10th term of this geometric progression. 2 3, 12, 24 3, 144, 288 3, You must simplify your answer.... (2) (Total for Question 9 is 4 marks) 2017 EH3B Page 9 Churchill Maths Limited
10 The amount of money, P, in a savings account t years after 1 st January 2011 is given by the formula P = 6000 1.05 t (a) Work out how much money is in the account on 1 st January 2016.... (2) (b) What is the annual rate of interest on the account?... % (c) Does the account pay simple or compound interest? Explain how you know. (Total for Question 10 is 4 marks) 2017 EH3B Page 10 Churchill Maths Limited
11 Raisa is trying to find solutions to the equation x 3 5x 2 + 8 = 0. (a) Complete this table of values. x 0 1 2 3 4 5 x 3 5x 2 + 8 10 8 8 (b) How many solutions does the equation x 3 5x 2 + 8 = 0 have in the interval 0 < x < 5? Give a reason for your answer. (2) Raisa uses the iteration formula x n + 1 8 = to find an approximate solution to the equation 5 x n x 3 5x 2 + 8 = 0. (c) Explain why this doesn't work with x 1 = 5. (d) Using x 1 = 1, find one solution to the equation, correct to 2 decimal places.... (3) (Total for Question 11 is 7 marks) 2017 EH3B Page 11 Churchill Maths Limited
12 A small empty barrel is filled with water from a tap. This graph shows the rate of flow of the water into the barrel. 300 Water flow (cm 3 /s) 200 100 0 0 10 20 30 40 Time (s) The barrel is cylindrical in shape and one circular end lies on a horizontal surface. (a) Sketch a graph to show how the depth of the water in the barrel changes over time. Your graph should cover the same 40 second interval as the graph above. Depth of water (cm) 0 0 10 20 30 40 Time (s) (2) 2017 EH3B Page 12 Churchill Maths Limited
(b) Calculate the total volume of water in the barrel after it has been filled. Give your answer in litres.... litres (3) (Total for Question 12 is 5 marks) 13 Given that x = 9 is a solution to the equation 3 1 2 x kx 2 = 6 find the value of the constant k.... (Total for Question 13 is 3 marks) 2017 EH3B Page 13 Churchill Maths Limited
14 y S 6 4 2 6 O 4 2 2 4 6 x 2 4 Enlarge shape S by scale factor 1, centre (0, 5). 2 Label the image T. (Total for Question 14 is 3 marks) 2017 EH3B Page 14 Churchill Maths Limited
15 y 1 360 x 1 A sketch of the graph of y = cos xº for 0 x 360 is shown above. (a) Write down the coordinates of the points where the graph crosses the x-axis.... and... (b) On this copy of the diagram above, sketch the graph of y = cos xº for 0 x 360. y 1 360 x 1 (c) On this copy of the diagram above, sketch the graph of y = 1 + cos xº for 0 x 360. y 1 360 x 1 (Total for Question 15 is 3 marks) 2017 EH3B Page 15 Churchill Maths Limited
16 A rectangle has length L cm and width W cm. L is larger than W. L W Two of these rectangles are put together to make a larger rectangle. This can be done in two ways, either with the longer sides touching or with the shorter sides touching. When the shorter sides are touching, the perimeter of the rectangle they form is 50% larger than when the longer sides are touching. Use algebra to work out the ratio W : L... (Total for Question 16 is 4 marks) 2017 EH3B Page 16 Churchill Maths Limited
17 18 mm 8 mm 15 cm A pencil is in the shape of a cylinder with one end made into a cone. Its dimensions are shown above. Find the volume of the pencil in cubic centimetres. [The volume V of a cone with base radius r and height h is V = 1 3 π r 2 h.]... cm 3 (Total for Question 17 is 3 marks) 2017 EH3B Page 17 Churchill Maths Limited
18 9.4 cm a 17.1 cm A right-angled triangle is shown above. The measurements of 9.4 cm and 17.1 cm are both correct to 1 decimal place. Tim says Angle a must be 29º to the nearest degree. Show that Tim is correct. (Total for Question 18 is 4 marks) 2017 EH3B Page 18 Churchill Maths Limited
19 y B C A O x y = 20 3x O is the origin, (0, 0). The points A and B lie on the line with equation y = 20 3x. Given that OABC is a square, find a possible set of coordinates for point C.... (Total for Question 19 is 5 marks) 2017 EH3B Page 19 Churchill Maths Limited
20 y is inversely proportional to x. When x = 9, y = c, where c is a constant. When x = 25, y = c 16. Show that when x = 36, y = 20. (Total for Question 20 is 4 marks) TOTAL FOR PAPER IS 80 MARKS 2017 EH3B Page 20 Churchill Maths Limited