PPE April PAPER 2H Calculator allowed

Transcription

1 Name Class PPE April 2016 Higher Tier Edexcel Style PAPER 2H Calculator allowed Time 1 hour 45 minutes Marks Available 100 Commissioned by The PiXL Club Ltd. Question Mark Maximum mark Total 100 1

2 2

3 Question 1 A company sells ice cream and records the midday temperature and the sales of ice-creams in The scatter graph shows this information for January to November. In December the average midday temperature was 4 0 C and 20 tonnes of ice-cream were sold. (a) Show this information on the scatter graph. (1) (b) What type of correlation does the scatter graph show?... (1) In July 2016, the average midday temperature is predicted to be 22 0 C. (c) Estimate the sales of ice-cream in July tonnes (2) (Total 4 marks) 3

4 Question 2 (a) Use your calculator to work out. Write down all the figures on your calculator display.... (2) (b) Write your answer to part (a) correct to 3 significant figures.... (1) 4 (Total 3 marks)

5 Question 3 Anne is mixing antifreeze and water. She has 10 litres of a mixture of antifreeze and water in the ratio 3:5. How much antifreeze does she need to add to make the ratio 1:1? litres 5 (Total 4 marks)

6 Question 4 Here is a tile in the shape of a semicircle. Diagram NOT drawn accurately The diameter of the semicircle is 11 cm. Work out the perimeter of the tile. Give your answer correct to 3 significant figures... cm (Total 3 marks) 6

7 Question 5 There are 150 members at a village leisure centre. Each student attends one of Boxercise classes, Pilates classes or Yoga classes. 65 of the members are female. 11 of the female members attend Boxercise classes. 68 of the members attend Pilates classes. 52 of the female members attend Pilates classes. 6 of the male members attend Yoga classes. How many of the male members attend Boxercise classes?... (Total 4 marks) 7

8 Question 6 A rectangular field has an area of 5 km 2. Write this area in m (Total 2 marks) 8

9 *Question 7 A large vegetable patch is in the shape of an isosceles trapezium. 6 m 2 m Diagram NOT drawn accurately 4 m Annette would like to put a wire fence around the outside of the vegetable patch. She has 13 m of fence. Does she have enough fence? You must show all your working. (Total 5 marks) 9

10 *Question 8 Plants are sold in three different sizes of tray. A small tray of 30 plants costs A medium tray of 40 plants costs A large tray of 50 plants costs Maria wants to buy the tray of plants that is the best value for money. Which size tray of plants should she buy? You must show all your working. (Total 4 marks) 10

11 Question 9 Use ruler and compasses to construct the perpendicular from point P to the line MN. You must show all your construction lines. P M N (Total 2 marks) 11

12 Question 10 The equation x 3 6x = - 1 has a solution between 2 and 3. Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working. x =... (Total 4 marks) 12

13 Question 11 (a) Solve... (b) Simplify (2)... (1) (c) Simplify 3a 3 c 5a 4 c 4... (2) (d) Simplify (a 3 ) 4... (1) (Total 6 marks) 13

14 Question 12 (a) Describe fully the single transformation that maps shape A onto shape B (3) 14

15 A (b) On the grid, reflect shape A in the line y = x. (2) 15 (Total 5 marks)

16 Question 13-8 < 2n 2 n is an integer. (a) Write down all the possible values of n.... (2) (b) Solve 3x 3 > 7 x... (2) (Total 4 marks) 16

17 *Question 14 Sophia has to invest in a savings account for 2 years. She finds information about two savings accounts. Super Saver Fixed Rate Compound interest 2.5% each year Compound interest 3% for the first year then 1.5% each year Sophia wants to have as much money as possible in her savings account at the end of 2 years. Which of these savings accounts should she choose? (Total 4 marks) 17

18 Question 15 The table gives information about the temperature, T C, at noon in a town for 50 days. Temperature (T C) Frequency 8 < T < T < T < T < T 28 3 (a) Calculate an estimate for the mean temperature... C (4) *(b) Danny says that on at least a quarter of the days the temperature was less than 16 C. Is Danny correct? You must explain your answer. (3) 18 (Total 7 marks)

19 Question 16 Diagram NOT drawn accurately A, B, C and D are points on the circumference of a circle, centre O. AC is a diameter of the circle. AC and BD intersect at E. Angle CAB = 25 Angle DEC = 110 Work out the size of angle DAC You must show all your working.... (4) (Total 4 marks) 19

20 Question 17 The volume of Venus in m 3, is 9.28 x The volume of Mercury, is 6.08 x How many times larger is the volume of Venus to that of Mercury? Give your answer correct to 3 significant figures.... (Total 2 marks) 20

21 Question 18 L 1 and L 2 are perpendicular lines. The equation of L 1 is y = 2x - 1 L 2 passes through the point (-4, 2). Find an equation for L (Total 3 marks)

22 Question 19 The students in a class kept a record of the amount of time, in minutes, they spent doing homework last week. The table shows information about the amount of time the girls spent doing homework last week. Minutes Least amount of time 60 Range 220 Median 160 Lower quartile 100 Upper quartile 220 (a) On the grid, draw a box plot for the information in the table. The box plot below shows information about the amount of time the boys spent doing homework last week. (2) 22

23 *(b) Compare the amount of time the girls spent doing homework with the amount of time the boys spent doing homework (2) 23 (Total 4 marks)

24 Question 20 A town has a population of , correct to the nearest ten thousand, and an area of 56 km 2, correct to the nearest whole number. (a) Write down the upper bound of the population.... (1) (b) Work out the upper bound of the population density. You must show all your working....people/ km 2 (3) 24 (Total 4 marks)

25 Question 21 Show that (n + 1) 2 (n 1) 2 is an even number for all positive integer values of n. 25 (Total 3 marks)

26 Question students sat a test. Each student attained a Grade A, B or C. The table below gives information about these students. A B C Male Female The teacher takes a sample of 50 of these students. The sample is stratified by gender and by grade attained. Work out the number of students in the sample who are female and attained a grade C (Total 2 marks)

27 Question 23 Solve 3x 2 5x 3 = 0 Give your solutions correct to 3 significant figures.... (Total 3 marks) 27

28 Question 24 Diagram NOT Drawn accurately OAB is a triangle. P is the point on AC such that AP: PB = 3 : 5 = 2a = 2b = m (5a + 3b). Find the value of m.. 28 (Total 4 marks)

29 Question 25 C E Diagram NOT Drawn accurately AC = 8 cm. AB = 4 cm. DE = 18 cm. Angle ABC = angle CBD = angle BDE = 90. Angle BDC = 48. A B D (a) Calculate the length of CD. Give your answer correct to 3 significant figures. (b) Calculate the length of CE. Give your answer correct to 3 significant figures.... cm (4)... cm (3) (Total 7 marks) 29

30 Question 26 y y f(x) x The diagram shows part of the curve with equation y = f(x). The coordinates of the minimum point of this curve are (6, 10). Write down the coordinates of the minimum point of the curve with equation (i) ( ) (...,...) (ii) ( ) (...,...) (iii) ( ) (...,...) (Total 3 marks) TOTAL FOR PAPER: 100 marks 30