Question Mark Out of Pre Public Examination GCSE Mathematics (Edexcel style) March 2017 Higher Tier Paper 1H Worked Solutions Name Class TIME ALLOWED 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES Answer all the questions. Read each question carefully. Make sure you know what you have to do before starting your answer. You are NOT permitted to use a calculator in this paper. Do all rough work in this book. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question on the Question Paper. You are reminded of the need for clear presentation in your answers. The total number of marks for this paper is 80. 1 3 2 5 3 5 4 6 5 6 6 4 7 3 8 2 9 3 10 1 11 2 12 3 13 4 14 3 15 4 16 2 17 4 18 3 19 5 20 3 21 3 22 3 23 3 Total 80 The PiXL Club Limited 2017 This resource is strictly for the use of member schools for as long as they remain members of The PiXL Club. It may not be copied, sold nor transferred to a third party or used by the school after membership ceases. Until such time it may be freely used within the member school. All opinions and contributions are those of the authors. The contents of this resource are not connected with nor endorsed by any other company, organisation or institution.
Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. Question 1. Work out 3-1 - = - M1 = M1 1 A1 (Total 3 mark) Question 2. y 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 The graph gives the values of y for values of x from 0 to 8. (a) (i) Give an interpretation of the intercept of the graph on the y-axis. When x = 0 y = 1.5 or starting point is 1.5 C1 (ii) Give an interpretation of the gradient of the graph. For every one value of x, y increases by 0.5 C1 x (2) 2
(b) Find the equation of the straight line in the form Gradient 0.5 1 = 0.5 M1 y = 0.5x + C M1 y = m x + c y = 0.5x + 1.5 A1 (3) (Total 5 marks) Question 3. The diagram shows the plan of a field. The farmer sells the field for 3 per square metre. Work out the total amount of money the farmer should get for the field. 100 75 = 7500 P1 160 75 = 85 100 30 = 70 M1 (85 70) 2 = 2975 M1 7500 + 2975 = 10475 M1 10475 3 = 31425 31425 A1 (Total 5 marks) 3
Question 4. Here is part of a railway timetable. Departure Times Newcastle 0840 0935 1040 1122 York 0943 1034 1144 1225 Leeds 1010 1210 Derby 1124 1157 1324 1355 Birmingham 1215 1315 1415 1515 A train leaves Newcastle at 1040. (a) How long is the journey to Birmingham for this train? Give your answer in hours and minutes. 10.40 to 11.00 is 20min P1 11.00 to 14.00 is 3hrs M1 14.00 to 14.15 is 15min 3hrs + 20min + 15min (b) The train ticket from York to Derby costs 64 plus 2.5% booking fee. Workout how much a ticket from York to Derby will cost in total. 64 10 = 6.40 P1 6.40 2 = 3.20 3.20 2 = 1.60 P1 64 + 1.60 = 3hrs 35mins A1 (3) 65.60 A1 (3) (Total 6 marks) 4
Question 5. The diagram shows a rectangular garden with a path around the edge. 8m 5m Lawn 1.3m 2.2m Farhan is going to cover the path with rectangular tiles. Each tile is 25 cm by 10 cm. He chooses to tile the path in white, red and black colours. The ratio of the number of white tiles to the number of red tiles to the number of black tiles will be 5 : 3 : 4. (a) Assuming there are no gaps between the tiles, how many tiles of each colour will Farhan need? 800 220 = 176000 500 130 = 65000 B1 176000 65000 = 111000cm2 25 10 = 250cm2 111000 250 = 444 tiles M1 444 12 = 37 1 part M1 37 5 = 185 white tiles M1 37 3 = 111 red tiles 37 4 = 148 black tiles white tiles 185 red tiles 111 black tiles 148 A1 Farhan is told that he should leave gaps between the tiles. (5) (b) If Farhan leaves gaps between the tiles, how could this affect the number of tiles he needs? He will need less tiles C1 (1) (Total 6 marks) 5
Question 6. Judy drove from her home to the airport. She waited at the airport. Then she drove home. Here is the distance-time graph for Judy s complete journey. (a) What is the distance from Judy s home to the airport? (b) For how many minutes did Judy wait at the airport? (c) Work out Judy s average speed on her journey home from the airport. Give your answer in kilometres per hour. 40 0.5 M1 40km B1 (1) 45 minutes B1 (1) 80 kilometres per hour A1 (2) (Total 4 marks) 6
Question 7. Write 420 as a product of its prime factors. 420 42 10 7 6 5 2 3 2 M1 for a correct start to a factor tree (2 correct branches) M1 for a fully correct tree or correct factors as a list 2 2 3 5 7 A1 (Total 3 marks) Question 8. Shape A is translated by the vector ( ) to make Shape B. Shape B is then translated by the vector ( ) to make Shape C. Describe the single transformation that maps Shape A onto Shape C. 3 + -5 = -2-4 + -1 = -5 M1 ( ) A1 (Total 2 marks) 7
Question 9. To complete a task in 15 days a company needs 4 people each working for 8 hours per day. The company decides to have 5 people each working for 6 hours per day. Assume that each person works at the same rate. How many days will the task take to complete? You must show your working. 4 8 = 32 32 15 = 480hrs P1 5 6 = 30hrs is one day M1 480 30 16 days A1 (Total 3 marks) Question 10. Find the value of 1/ 1/ = 5 1/5 2 = 1/25 A1 (Total 1 mark) 8
Question 11. The table shows information about the heights of 40 bushes. Height (h cm) Cumulative Frequency 170 h < 175 5 170 h < 180 23 170 h < 185 35 170 h < 190 39 170 h < 195 40 On the grid below, draw a cumulative frequency graph for your table. Cumulative frequency 40 X X X 30 20 X 10 X 0 170 175 180 185 190 195 B1 for at least 3 points plotted correctly Height ( h cm) B1 for correct cumulative graph drawn (Total 2 marks) 9
Question 12. In a sale, the price of a television is reduced. The television has a normal price of 1235. The television has a sale price of 988. Work out the percentage reduction in the price of the television. 988 1235 P1 (988 1235) 100 = 80% M1 100 80 20% A1 (Total 3 marks) Question 13. Prove that (n + 1) 2 (n 1) 2 + 1 is always odd for all positive integer values of n. (n + 1) 2 (n 1) 2 + 1 n 2 + 2n + 1 (n 2-2n +1) + 1 P1 n 2 + 2n + 1 n 2 + 2n -1 + 1 M1 4n + 1 M1 Any number multiplied by 4 is even. Add 1 will make it odd number. C1 (Total 4 marks) 10
Question 14. Write 0.3 as a fraction in its simplest form. x = 0.3 10x = 3. 1000x = 356. M1 990x = 353 M1 x = A1 (Total 3 marks) Question 15. The equation of a curve is y = f(x) where f(x) = x 2 8x + 21. Write down the coordinates of the minimum point of this curve. f(x) = x 2 8x + 21 f(x) = (x 4) 2 16 + 21 P1 f(x) = (x 4) 2 + 5 P1 Substitute x = 4, f(x) = (4 4) 2 + 5 y = 5 M1 (4,5) A1 (Total 4 marks) 11
Question 16. Expand (3x + 1) (2x 2) (3x + 4) (3x + 1) (2x 2) (3x + 4) (6x 2 4x 2) (3x + 4) M1 18x 3 + 24x 2-12x 2 16x 6x 8 18x 3 + 12x 2 22x 8 A1 (Total 2 marks) 12
Question 17. The tangent DB is extended to T. The line AO is added to the diagram. Angle TBA = 62 and BDC = 40 (a) Work out the value of x. The angle between a tangent and a radius is 90 therefore OBT is 90. ABO = 90 62 = 28 M1 AOB is isosceles triangle therefore angle ABO=OAB. AOB = 180 (28+28) 124 A1 (2) (b) Work out the value of y. 360 (90+90+40) = 140 360 (140+124) = 96 M1 180 96 = 84 84 2 = 42 A1 (2) (Total 4 marks) 13
Question 18. In the diagram, the lines AC and BD intersect at E. AB and DC are parallel and AB = DC. x y y x Prove that triangles ABE and CDE are congruent. Angle BAC = ACD alternate angles are equal. P1 Angle ABD = BDC alternate angles are equal P1 AB = DC Therefore AAS both triangles are congruent. C1 14 (Total 3 marks)
Question 19. Solve these simultaneous equations y 2 + x 2 = 10 y = x 2 (x 2) 2 + x 2 = 10 P1 2x 2 4x 6 = 0 M1 (2x 6) (x + 1) = 0 M1 x = 3 & x = -1 M1 Substitute into y = x 2 y = 1 and y = -3 x = 3 y = 1 or x = -1 y = -3 A1 (Total 5 marks) 15
Question 20. Express (2 3) 2 in the form b + c 3, where b and c are integers to be found. (2 3) (2 3) P1 4 2 3 2 3 + 3 M1 7 4 3 A1 (Total 3 marks) 16
Question 21. The curve with equation y = f(x) is translated so that the point at (0, 0) is mapped onto the point (2, 0). (a) Find an equation of the translated curve. y = f(x 2) B1 (1) (b) Write down the coordinates of the minimum point of the curve with the equation y = f(x + 5) + 6 3 5 = -2-4 + 6 = 2 17 (-2, 2) A2 (2) (Total 3 marks)
Question 22. (a) How many plants are represented by the histogram? (10 1.5) + (5 5) + (10 2.5) + (10 2) + (5 1) 15 + 25 + 25 + 20 + 5 = 90 90 B1 (1) (b) Estimate the median height of the plants. 90 2 = 45 Use graph to find height of 45 th plant M1 22 A1 (2) (Total 3 marks) 18
Question 23. There are three different types of sandwiches on a shelf. There are: 4 egg sandwiches, 5 cheese sandwiches and 2 ham sandwiches. Erin takes at random 2 of these sandwiches. Work out the probability that she takes 2 different types of sandwiches. 1 (CC + HH + EE) P1 5 4 11 10 1-2 1 + 11 10 4 3 + 11 10 P1 or A1 (Total 3 marks) TOTAL FOR PAPER IS 80 MARKS 19