Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Qamar goes to work 5 days a wee

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1 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 3A 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 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 EH3A Page 1 Churchill Maths Limited

2 Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Qamar goes to work 5 days a week. On 2 days each week he travels by train. On 3 days each week he travels by bus. Here is some information about the cost of his travel to work. Train: One-day pass 7.80 One-week pass Bus: One-day pass 6.00 One-week pass (a) How much does Qamar spend a week if he buys a one-day pass each day?... Qamar works for 46 weeks each year. Martin says Qamar could save over 300 in a year if he always travelled by bus and bought a one-week pass each week. (b) Is Martin correct? You must show how you get your answer. (3) (Total for Question 1 is 5 marks) 2017 EH3A Page 2 Churchill Maths Limited

3 2 Henri has to estimate the value of (7.8) He does this by rounding each of the numbers 7.8, 3.05 and 6.92 to 1 significant figure. (a) Work out Henri's estimate. (b) Calculate the percentage error in Henri's estimate.... % (3) (Total for Question 2 is 5 marks) 3 A company employs workers to check pre-owned mobile phones. One day, 2 workers check 120 phones in 6 hours. Assuming they work at the same rate, how long will it take 5 workers to check 400 phones?... hours (Total for Question 3 is 2 marks) 2017 EH3A Page 3 Churchill Maths Limited

4 4 Here is a function machine. Input Output (a) A number is input into the machine. The output is 21. Work out the number that was input into the machine. (b) A number is input into the machine. The output is three times the input. Work out the number that was input into the machine. (c) A whole number is input into the machine. The output is then used as a new input to produce a second output. Rosa says the last digit of the second output must be a 5. Is Rosa correct? Explain your answer. (1) (Total for Question 4 is 5 marks) 2017 EH3A Page 4 Churchill Maths Limited

5 5 A primary school has 240 pupils. 90 of these pupils have no siblings. A nearby secondary school has 960 pupils. (a) Use this information to estimate how many pupils at the secondary school have no siblings. (b) Is your answer to part (a) likely to be an overestimate or an underestimate. Explain why. (Total for Question 5 is 4 marks) 2017 EH3A Page 5 Churchill Maths Limited

6 6 10 cm The diagram shows a square and two circles. The inner circle is the largest one that can be drawn inside the square. The outer circle is the smallest one that can be drawn with the square inside it. Prove that the shaded area between the two circles is the same as the area enclosed by the inner circle. (Total for Question 6 is 4 marks) 2017 EH3A Page 6 Churchill Maths Limited

7 7 Factorise x (Total for Question 7 is 2 marks) 8 In Mr. Hamid's class, the ratio of girls to boys is 5 : 4 If there were 3 more boys in his class then the ratio of girls to boys would be 1 : 1 Work out the total number of girls and boys in Mr. Hamid's class. (Total for Question 8 is 3 marks) 2017 EH3A Page 7 Churchill Maths Limited

8 9 A construction toy consists of identical rectangular sheets of plastic. Melanie uses 16 of the plastic pieces to make the cuboid shown above. The 3 hidden faces of the cuboid are made in the same way as the 3 faces shown. There are no gaps between the pieces. Given that the surface area of the cuboid is 288 cm 2, work out the volume of the cuboid.... cm 3 (Total for Question 9 is 4 marks) 2017 EH3A Page 8 Churchill Maths Limited

9 10 The graph shows the distance travelled by a motorbike during the first minute of a journey. Distance (metres) O Time (seconds) Work out an estimate for the highest speed the motorbike reaches during this minute.... m/s (Total for Question 10 is 3 marks) 2017 EH3A Page 9 Churchill Maths Limited

10 11 For each statement, say whether it is TRUE or FALSE and justify your answer. (a) The straight lines 3y = x + 6 and 3y = x 3 are parallel. (b) The straight lines y = 5 2x and 2y = 2 x are perpendicular. (3) (c) The curve y = x 2 6x + 9 meets the x-axis at exactly one point. (Total for Question 11 is 7 marks) 2017 EH3A Page 10 Churchill Maths Limited

11 12 Show that (2p + 1)(p 1)(p + 4) = 2p 3 + mp 2 5p + n for all values of p, where m and n are integers to be found. 13 Marcus says (Total for Question 12 is 3 marks) If you increase a number by 20% and then take the answer and decrease it by 20% you don't get back to the number you started with. Is Marcus correct? Explain how you know. (Total for Question 13 is 2 marks) 2017 EH3A Page 11 Churchill Maths Limited

12 14 A bag contains only red counters, orange counters, yellow counters and white counters. A counter is picked at random from the bag. The probability of it being red is 0.36 The probability of it being orange is 4 times the probability of it being white. The probability of it being yellow is 3 times the probability of it being white. Given that there are 18 yellow counters in the bag, work out how many red counters there are in the bag. (Total for Question 14 is 4 marks) 2017 EH3A Page 12 Churchill Maths Limited

13 15 One day Latif drives to visit his friend. On the way to his friend's house, Latif drives at an average speed of 50 km/h. When he returns home, Latif takes a longer route that has better roads. On the return journey, he drives an extra 23 km, his average speed is 6 km/h higher and the journey takes him an extra 15 minutes. Work out how long the return journey took. 16 Prove that... (Total for Question 15 is 4 marks) = 7 18 (Total for Question 16 is 2 marks) 2017 EH3A Page 13 Churchill Maths Limited

14 17 Each day, the probability that Gail doesn't receive any post is 0.18 (a) Work out the probability that Gail receives no post on two consecutive days. (b) Work out the probability that Gail receives at least one item of post over four consecutive days. (Total for Question 17 is 4 marks) 2017 EH3A Page 14 Churchill Maths Limited

15 18 A box is being designed to contain 4 stacks of chocolate wafers. Each chocolate wafer is in the shape of a regular hexagon of side length 3 cm. Each layer of chocolates fits into the box as shown in this view from above. Find the area of the rectangular base of the box. Give your answer in square centimetres in the form k 3 where k is rational.... cm 2 (Total for Question 18 is 5 marks) 2017 EH3A Page 15 Churchill Maths Limited

16 19 The first 6 terms of a quadratic sequence are k 37 (a) Find the value of k. (b) Find an expression for the nth term of the sequence.... (4) (Total for Question 19 is 6 marks) 2017 EH3A Page 16 Churchill Maths Limited

17 20 A B H C M G D F E ABCDEFGH is a regular octagon. M is the midpoint of BF. Prove that triangles AMG and BDF are similar. (Total for Question 20 is 3 marks) 2017 EH3A Page 17 Churchill Maths Limited

18 21 The histogram shows the times Irena has run for the 400m. Frequency Density Time (seconds) of her times have been 57.2 seconds or slower. Work out how many of the times she has run have been quicker than 56.6 seconds EH3A Page 18 Churchill Maths Limited

19 (Total for Question 21 is 3 marks) TOTAL FOR PAPER IS 80 MARKS 2017 EH3A Page 19 Churchill Maths Limited