Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 (a) A bowl contains only red an

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1 Name Class For Pearson Edexcel Level 1/Level 2 GCSE (9 1) Mathematics Paper 2 (Calculator) Higher Tier Time: 1 hour 30 minutes Churchill Paper 2B 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 EH2B 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 (a) A bowl contains only red and blue dice. The ratio of red dice to blue dice is 3 : 5 What fraction of the dice in the bowl are red? (1) (b) In a company, the ratio of full-time to part-time employees is 8 : 5 There are 39 more full-time employees than part-time employees. Work out the number of part-time employees. (Total for Question 1 is 3 marks) 2017 EH2B Page 2 Churchill Maths Limited

3 2 Since January 2013, a factory has taken on a trainee every six months. This time series graph shows the number of applicants on each occasion. Number of Applicants Jan Jun Jan Jun Jan Jun Jan Jun Jan Jun Month and Year (a) Which month and year had the biggest decrease in the number of applicants compared with six months earlier?... (1) (b) Phil says Looking at the trend, June 2017 will have the lowest ever number of applicants Do you agree with Phil? Explain your answer (Total for Question 2 is 3 marks) 2017 EH2B Page 3 Churchill Maths Limited

4 3 N Loron Mackle Nagel Scale: 1 cm represents 2 km The map shows three towns Loron, Mackle and Nagel. (a) Use the scale to find the distance between Loron and Mackle. km A transmitter is to be built within 8 km of Loron. The transmitter must be closer to Mackle than it is to Nagel. (b) Construct the region where the transmitter can be placed on the map. Show the region by shading it. (3) (Total for Question 3 is 5 marks) 2017 EH2B Page 4 Churchill Maths Limited

5 4 A bag contains chocolates. Each chocolate has a centre that is fudge, nut, coffee or marzipan. This table shows the probability of getting each type of centre when a chocolate is picked at random from the bag. Centre Fudge Nut Coffee Marzipan Probability 0.2 x 0.5 x 2x Find the value of x. 5 Pete records all his maths test scores. Each score is a mark out of 100. After 9 tests his mean score is 59 After 10 tests his mean score is 58.5 After 11 tests his mean score is 60 Work out the difference between his scores on the 10th and 11th tests. (Total for Question 4 is 2 marks) (Total for Question 5 is 3 marks) 2017 EH2B Page 5 Churchill Maths Limited

6 6 124º x º Work out the value of x. 7 Jane records how many millimetres of rain fall each month in her garden. In February, there was 16 mm more rain than in January. In March, there was 5 mm more rain than in February. The total amount of rain for January, February and March was 172 mm. Work out the amount of rain in January. (Total for Question 6 is 3 marks) mm (Total for Question 7 is 3 marks) 2017 EH2B Page 6 Churchill Maths Limited

7 8 Sally makes a fruit drink by mixing pineapple juice and mango juice in the ratio 2 : 3 She buys pineapple juice in 1.5 litre cartons that cost 1.30 each. She buys mango juice in 1 litre cartons. The cartons are only sold in packs of 4 which cost Sally makes 60 litres of her fruit drink for a party. At the party, she fills 190 cups and sells all of them for 50p per cup. Work out how much profit she makes. (Total for Question 8 is 4 marks) 2017 EH2B Page 7 Churchill Maths Limited

8 9 An arithmetic sequence has first term a. The 4th term of the sequence is ka. The 7th term of the sequence is 9a. Find the value of k. (Total for Question 9 is 3 marks) 10 (a) Solve 4p 2 6p = 0... (b) Factorise 5m 2 + 7m 6... (Total for Question 10 is 4 marks) 2017 EH2B Page 8 Churchill Maths Limited

9 11 1 tonne = 1000 kg A block of stone has a mass of T tonnes. The density of the stone is 2.5 g/cm 3. Show that the volume of the block is 0.4T m 3. (Total for Question 11 is 3 marks) 2017 EH2B Page 9 Churchill Maths Limited

10 12 The probability that nobody is absent from Asam's class on Monday is 0.4 If nobody is absent on Monday, the probability of nobody being absent on Tuesday is 0.5 If one or more pupils are absent on Monday, the probability of one or more pupils being absent on Tuesday is 0.7 (a) Complete the probability tree diagram for this information. Monday Tuesday Nobody absent 0.4 Nobody absent 1 or more absent 1 or more absent Nobody absent 1 or more absent (b) Work out the probability of there being nobody absent on Tuesday. (c) Work out the probability of there being at least one pupil absent on at least one of these two days. (Total for Question 12 is 6 marks) 2017 EH2B Page 10 Churchill Maths Limited

11 13 B 7.3 cm C 4.7 cm A 58º D ABCD is a trapezium. Angle ADC = angle BCD = 90º. Angle BAD = 58º. AB = 4.7 cm and BC = 7.3 cm. (a) Show that AD = 9.8 cm correct to 1 decimal place. (3) (b) Find the size of angle ACB. º (3) (Total for Question 13 is 6 marks) 2017 EH2B Page 11 Churchill Maths Limited

12 14 Four students are asked to measure the length, L, of a phone. Here are the answers they gave. Student A B C D Length 13 cm truncated to the nearest cm 132 mm rounded to the nearest mm 13.3 cm truncated to 1 decimal place 130 mm rounded to 2 significant figures (a) Complete this error interval for the value of L, in cm, for student A. (b) Complete this error interval for the value of L, in cm, for student B.... L <... (1)... L <... (1) (c) Is it possible that all four students gave a correct measurement for their stated level of accuracy? Justify your answer (Total for Question 14 is 4 marks) 2017 EH2B Page 12 Churchill Maths Limited

13 15 Without using a calculator, (a) express as simply as possible with a rational denominator, (b) simplify fully (3) (Total for Question 15 is 5 marks) 2017 EH2B Page 13 Churchill Maths Limited

14 16 On the grid, show the region that satisfies these three inequalities. Label the region R. y > x + 1 y 2x + 3 x + y 6 y O x (Total for Question 16 is 4 marks) 2017 EH2B Page 14 Churchill Maths Limited

15 17 A magazine says that a new car's value drops by 30% in the first year. The car's value then drops by 15% each year after that. Greg says That means the value of a new car is halved in 3 years. Is Greg correct? Justify your answer (Total for Question 17 is 3 marks) 2017 EH2B Page 15 Churchill Maths Limited

16 18 D E C B A ABC and AED are straight lines. BE and CD are parallel. (a) Prove that triangle ACD is similar to triangle ABE. BC = 3 cm. The area of quadrilateral BCDE is the same as the area of triangle ABE. (b) Find the length of AB correct to 3 significant figures. cm (4) (Total for Question 18 is 6 marks) 2017 EH2B Page 16 Churchill Maths Limited

17 19 Solve the simultaneous equations y = x + 2 (y + x)(y x) = 0... (Total for Question 19 is 5 marks) 2017 EH2B Page 17 Churchill Maths Limited

18 20 18 cm 10 cm 10 cm O The diagram shows a rectangle measuring 10 cm by 18 cm and a circle of radius 10 cm. The centre of the circle, O, lies on one side of the rectangle. The edge of the circle touches two sides of the rectangle. Find the area of shaded region where the rectangle and circle overlap. cm 2 (Total for Question 20 is 5 marks) TOTAL FOR PAPER IS 80 MARKS 2017 EH2B Page 18 Churchill Maths Limited