Name Class For Pearson Edexcel Level 1/Level 2 GCSE (9 1) Mathematics Paper 1 (Non-Calculator) Higher Tier Time: 1 hour 30 minutes Churchill Paper 1C You must have: Ruler graduated in centimetres and millimetres, Total Marks protractor, pair of compasses, pen, HB pencil, eraser. 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 not be used. 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 EH1C 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 In a table tennis competition no matches are drawn each match is won or lost. In each round of the competition, only the winners go into the next round. 50 members of the Tabletop club enter a competition. 40% of them win their 1st round matches. 75% of the Tabletop club members in the 2nd round win their 2nd round matches. 9 members of the Tabletop club reach the 4th round of the competition. Work out the percentage of the Tabletop club members in the 3rd round who win their 3rd round matches. % (Total for Question 1 is 3 marks) 2017 EH1C Page 2 Churchill Maths Limited
2 Work out (a) 1 2 4 7 (2) 2 2 5 3 3 4 (Total for Question 2 is 5 marks) 3 Martha is playing with Minibricks. She has 300 of each type of brick the twospot, the fourspot and the eightspot. Martha uses some of her bricks to make zombies. To make zombies, she uses twospots, fourspots and eightspots in the ratio 3 : 1 : 2 When she has finished making zombies, she has twice as many fourspots left as twospots. Work out how many eightspots Martha has left. (Total for Question 3 is 3 marks) 2017 EH1C Page 3 Churchill Maths Limited
4 (a) The first five terms of a sequence are 12, 18, 24, 30, 36, Find an expression for the nth term of this sequence.... (2) Another sequence is defined by this term-to-term rule: u n + 1 = 16 u n 2 Given that u 3 = 8, show that u 1 = 6. (Total for Question 4 is 5 marks) 2017 EH1C Page 4 Churchill Maths Limited
5 (a) Find the Highest Common Factor of 110 and 264. Write down 2 numbers with a Highest Common Factor that is twice your answer to part (a).... (Total for Question 5 is 4 marks) 2017 EH1C Page 5 Churchill Maths Limited
6 4 5 2 2 2 6 Stage 1 Stage 2 Stage 3 Nathan is making a zig-zag shape from rectangles. Stage 1 is a rectangle measuring 2 cm by 4 cm. For stage 2, Nathan adds a second rectangle measuring 2 cm by 5 cm as shown above. For stage 3, Nathan adds a third rectangle measuring 2 cm by 6 cm as shown above. He continues adding rectangles like this. Each rectangle is 1 cm longer than the one before. (a) Complete this table showing the perimeter of each stage. Stage 1 2 3 Perimeter (cm) 12 The perimeter, P cm, of stage n is given by the formula P = n 2 + 7n + 4 Work out the perimeter of stage 11. cm 2017 EH1C Page 6 Churchill Maths Limited
(c) By solving a suitable equation, find out which stage has a perimeter of 82 cm. 7 The ratio of right-handed to left-handed people in a company is 15 : 2... (Total for Question 6 is 7 marks) 12 right-handed people join the company. The ratio of right-handed to left-handed people in the company is now 9 : 1 How many left-handed people are there in the company? (Total for Question 7 is 3 marks) 2017 EH1C Page 7 Churchill Maths Limited
8 Some properties of the numbers from 1 to 15 are to be represented on a Venn diagram. ξ = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 } R = prime numbers G = numbers greater than 10 E = even numbers (a) Complete the Venn diagram. The numbers 1, 2, 3, 4 and 5 have already been entered. ξ R G 3 5 2 1 4 E (2) One of the numbers is chosen at random. (c) (d) Write down P (E). Write down P (R G). Find P (E G). (2) (Total for Question 8 is 6 marks) 2017 EH1C Page 8 Churchill Maths Limited
9 (4x + 7)º (3x + 20)º (4x 3)º Find the size of the smallest angle of the cyclic quadrilateral shown above. You must show that your answer is the smallest angle. º (Total for Question 9 is 4 marks) 2017 EH1C Page 9 Churchill Maths Limited
10 Gabby has a collection of ammonite fossils. This table gives information about the maximum width of the fossils in her collection. Width (w cm) Number of fossils 0 w < 5 0 5 w < 10 14 10 w < 15 18 15 w < 20 13 20 w < 25 6 25 w < 30 5 30 w < 35 3 35 w < 40 1 (a) On the grid, draw a cumulative frequency graph for this data. 60 Cumulative frequency 50 40 30 20 10 O 10 20 30 40 Width (cm) 50 2017 EH1C Page 10 Churchill Maths Limited
Gabby wants to sell her collection. Another collector offers to pay her these prices. 6 for fossils of width 5 to 12 cm 20 for fossils of width 12 to 25 cm 50 for fossils of width 25 to 40 cm Calculate an estimate of how much Gabby could sell her collection for.... (Total for Question 10 is 6 marks) 11 In a sale, two models of television are on offer for the same price, 180. One of the models has been discounted by 1 4. The other model has been discounted by 40%. Work out the difference in price between the two television models before the sale. (Total for Question 11 is 4 marks) 2017 EH1C Page 11 Churchill Maths Limited
12 Jaime and Kira are set this question: Estimate the value of 0.32 (2.387 10 17 ) Give your answer in standard form. Jaime's method is to work out 1 3 (2.4 1017 ) (a) Work out the answer Jaime should get.... (2) Kira's method is to work out 3 10 (2.39 1017 ) Will Kira's method give an underestimate or an overestimate? Give a reason for your answer. (2) (c) Which method, Jaime's or Kira's, will give the more accurate estimate? Explain your answer. (2) (Total for Question 12 is 6 marks) 2017 EH1C Page 12 Churchill Maths Limited
13 B C D A E ABE is an equilateral triangle. C and D are the points on BE such that BC = CD = DE. (a) Explain why the area of triangle ABC is one third of the area of triangle ABE. (2) Prove that triangle ABC is congruent to triangle AED. (Total for Question 13 is 5 marks) 2017 EH1C Page 13 Churchill Maths Limited
14 y = 1 sin x y = 2 tan x y = x 3 + 1 y = 1 x y = x 3 2 y = 1 + sin x y = tan x y = 1 x y = 1 + cos x Write down the equation from the list above that could be represented by each graph. (a) y O x... y O x... (c) y O x... 2017 EH1C Page 14 Churchill Maths Limited
(d) y O x... (Total for Question 14 is 4 marks) 15 (a) Write down the exact value of tan 60º. Express 4 tan 45 o o in the form a + b 3 where a and b are integers. 2 tan 60... (Total for Question 15 is 4 marks) 2017 EH1C Page 15 Churchill Maths Limited
16 A bag contains 10 coloured counters. Two counters are picked at random from the bag. The probability of them both being red is 2 15. Use algebra to work out how many of the 10 counters in the bag are red. (Total for Question 16 is 4 marks) 2017 EH1C Page 16 Churchill Maths Limited
17 B 2x cm A 60º 3x cm C The area of triangle ABC is 24 3 cm 2. (a) Find the value of x. (4) Show that the length of BC is 4 7 cm. (Total for Question 17 is 7 marks) TOTAL FOR PAPER IS 80 MARKS 2017 EH1C Page 17 Churchill Maths Limited