Bronze. Instructions. Information

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1 Bronze Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer ALL questions. Answer the questions in the spaces provided there may be more space than you need. 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. 1

2 Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1. (a) Write and as improper fractions.... and... (b) Write your fractions found in part (a) with a common denominator.... and... (c) Hence work out (Total for Question 1 is 3 marks)

3 2. ABCDE is a pentagon. (a) Use Pythagoras theorem to work out the perpendicular height of the triangle ABE.... cm (2) (b) Work out the area of the triangle ABE.... cm (c) Work out the area of the rectangle BCDE.... cm (e) Thus work out the area of ABCDE.... cm 2 (Total for Question 3 is 5 marks) 3

4 3. Phone calls cost y for x minutes. The graph gives the values of y for values of x from 0 to 5. (a) (i) Write down an interpretation of the intercept of the graph on the y-axis (at the point (0, 0.5)) (ii) Write down an interpretation of the gradient (steepness) of the graph

5 (b) Find the gradient, m, of the straight line.... (c) Find the value of the y-intercept, c.... (d) Thus write down the equation of the straight line in the form y = mx + c.... (Total for Question 2 is 5 marks) 5

6 4. On Monday, Tarek travelled by train from Manchester to London. Tarek s train left Manchester at It got to London at The train travelled at an average speed of 110 miles per hour. (a) Work out how long Tarek s journey took. (b) Work out the distance from Manchester to London.. hours On Wednesday, Gill travelled by train from Manchester to London. Gill s train also left at but was diverted. The train had to travel an extra 37 miles. The train got to London at miles (c) Use this information and your answer to part (a) to work out the distance Gill travelled. (d) Work out how long Gill s journey took.. miles. hours 6

7 (e) Use your answers to parts (b) and (c) to find out the average speed of Gill s train.. miles per hour (f) Work out the difference between the average speed of Tarek s train and the average speed of Gill s train.... miles per hour (Total for Question 4 is 4 marks) 7

8 5. The diagram shows a rectangular wall. Frank is going to cover the wall with rectangular tiles. Each tile is 60 cm by 30 cm. 3 5 of the tiles will be white. Some of the tiles will be green. The rest of the tiles will be blue. (a) Work out how many tiles will be needed to cover the wall. (b) Work out how many tiles will be white... tiles (2) (c) Work out how many tiles will be green or blue... white tiles.. green or blue tiles 8

9 The ratio of the number of green tiles to the number of blue tiles will be 1 : 3 (d) Assuming there are no gaps between the tiles, how many tiles of each colour will Frank need? green tiles... blue tiles... Frank is told that he should leave gaps between the tiles. (e) If Frank leaves gaps between the tiles, how could this affect the number of tiles he needs? (Total for Question 5 is 6 marks) 9

10 6. On Monday Ria delivered a parcel to a hospital. The travel graph represents Ria s journey to the hospital. Ria left home at She drove for 30 minutes at a constant speed of 40 mph. She then stopped for a break. (a) Find the distance Ria drove before she stopped for a break. Ria then drove to the hospital at a constant speed. (b) Find the distance from Ria s home to the hospital... miles.. miles 10

11 Ria was at the hospital for 30 minutes. She then drove home at a constant speed of 32 mph. (c) Work out what time Ria left the hospital... (d) Using your answer to part (b), find how long Ria s journey home took. (e) Thus show that Ria does not arrive home before hours (Total for Question 6 is 4 marks) 11

12 7. (a) Write down 43.2 to one significant figure.. (b) Write down to one significant figure.. (c) Thus write down an estimate for (d) Write down to one significant figure.. (e) Thus work out an estimate for the value of (Total for Question 7 is 3 marks) 12

13 4 8. Shape A is translated by the vector to make Shape B. 7 3 Shape B is then translated by the vector to make Shape C. 2 (a) Work out (b) Describe the single transformation that maps Shape A onto Shape C.... (Total for Question 8 is 2 marks) 13

14 9. A company orders a number of bottles from a factory. The 8 machines in the factory could make all the bottles in 5 days. All the machines work at the same rate. (a) Multiply the number of machines by the number of days to find the number of machine days needed to make all the bottles. For the first 2 days, only 4 machines are used to make the bottles. From the 3rd day, all 8 machines are used to make the bottles. machine days (b) Work out how many machine days there are for each days of the week. Monday machine days Tuesday machine days Wednesday machine days Thursday machine days Friday machine days Total machine days (c) Using your answer to part (a), work out how many more machine days would be needed to make all the bottles. (d) Thus work out the total number of days taken to make all the bottles. machine days... days (Total for Question 9 is 3 marks) 14

15 (a) Find the value of 64 (i.e. the cube root of 64) (b) Find the value of 64 (i.e. the square of the value of your answer to part (a)).... (c) Thus find the value of (i.e. the reciprocal of your answer to part (b)).... (Total for Question 10 is 1 mark) 15

16 11. Joan measured the heights of students in four different classes. She drew a cumulative frequency graph and a box plot for each class. 16

17 By carefully comparing the means and interquartile ranges on the diagrams, match each cumulative frequency graph to its box plot. Cumulative frequency graph Box plot A B C D (Total for Question 11 is 2 marks) 17

18 12. In a sale, the price of a jacket is reduced. The jacket has a normal price of 52. The jacket has a sale price of (a) Find the amount the price of the jacket has been reduced... (b) Work out your answer to part (a) divided by the normal price of the jacket as a fraction... (c) Convert this fraction to work out the percentage reduction in the price of the jacket.... % (Total for Question 12 is 3 marks) 18

19 13. (a) Write down two expressions to represent two different odd numbers... and.. (b) Write down an expression to represent the difference between these odd numbers..... (c) Thus prove algebraically that the difference between any two different odd numbers is an even number. (Total for Question 13 is 3 marks) (a) Work out ( ) 100 (b) Rearrange to write your answer to part (a) as a fraction (c) Thus write as a fraction in its simplest form.... (Total for Question 14 is 3 marks) 19

20 15. Here is a sketch of a vertical cross section through the centre of a bowl. The cross-section is the shaded region between the curve and the x-axis. The curve has equation y = 2 x 3x where x and y are both measured in centimetres. 10 (a) Find the coordinates of the points where the curve crosses the x-axis.... and... (2) (b) Use your answer to part (a) to find the x-coordinate where the bowl is deepest. (c) Thus find the depth of the bowl cm (Total for Question 15 is 4 marks) 20

21 16. M is the point such that BM : MC is 1 : 2 Here is Charlie s method to find BM in terms of a and b. BC BA AC = ba = a b 1 BM BC 2 1 = a b 2 (a) Find what is wrong with Charlie s method Martin expands (2x + 1)(2x 3)(3x + 2) He gets 12x 3 4x 2 17x + 6 (b) Explain why Martin s solution cannot be correct (Total for Question 16 is 2 marks) 21

22 17. A, B and D are points on the circumference of a circle centre O. EDC is a tangent to the circle. Angle BDC = 57 (a) Find the size of angle ODB. From the list in the box on the page opposite, give a reason why you know this is true.... (b) Find the size of angle OBD. From the list in the box on the page opposite, give a reason why you know this is true

23 Base angles of an isosceles triangle are equal Angles on a straight line add up to 180 The tangent to a circle is perpendicular to the radius Angles in a triangle add up to 180 (c) Find the size of angle DOB. From the list in the box above, give a reason why you know this is true.... (d) Find the size of angle AOB. From the list in the box above, give a reason why you know this is true.... (Total for Question 17 is 4 marks) 23

24 18. The diagram shows the first 10 sides of a spiral pattern. It also gives the lengths, in cm, of the first 5 sides. The lengths, in cm, of the sides of the spiral form a sequence. (a) Write out the sequence formed... (b) Write out the sequence of first differences... (c) Write out the sequence of second differences... (d) Find an expression in terms of n for the length, in cm, of the nth side.... (2) (Total for Question 18 is 3 marks) 24

25 19. ABD is a right-angled triangle. C is the point on BD such that angle ACB = 90. (a) Write down the names of all the right angles in this diagram... (b) Write down the names of all the common angles in this diagram... (c) Use this information to show that ADC = BAC. (d) Thus prove that triangle ABD is similar to triangle CBA. (Total for Question 19 is 3 marks) 25

26 20. x 2 + y 2 = 18 x 2y = 3 (a) Rearrange x 2y = 3 to find an expression for x. x =.. (b) Substitute your answer to part (a) in x 2 + y 2 = (c) Rearrange your answer to part (b) to find an equation to solve. (d) Solve the equation given as your answer to part (c)... (e) Thus solve the simultaneous equations shown above... x = y =.. x = y =.. (Total for Question 20 is 5 marks) 26

27 21. (a) Work out (5 + 8) (5 8).. (b) Work out (5 8).. (c) Thus show that can be written (Total for Question 21 is 3 marks) 27

28 22. The graph of y = f(x) is shown on the grid. Graph A is a reflection of the graph of y = f(x). (a) Write down the equation of graph A.... The graph of y = g(x) is shown on the grid. Graph B is a translation of y = g(x). (b) Write down the equation of graph B

29 The graph of y = cos x is shown. (c) Write down the coordinates of the point marked C. (...,...) (Total for Question 22 is 3 marks) 29

30 23. The histogram shows information about the ages of the members of a football supporters club. There are 20 members aged between 25 and 30. (a) Use this information to work out the scale for the Frequency density axis. (b) Thus work out the area of each of the five bars. 0 10: 10 25: 25 30: 30 50: 50 80: 30

31 One member of the club is chosen at random. (c) What is the probability that this member is more than 30 years old?... (Total for Question 23 is 3 marks) 31

32 24. There are 6 black counters and 4 white counters in bag A 7 black counters and 3 white counters in bag B 5 black counters and 5 white counters in bag C Bernie takes at random a counter from bag A and puts the counter in bag B. (a) Work out the probability that Bernie will take a black counter from bag A. (b) If Bernie chooses a black counter, how many of each counter are then in bag B?..black counters..white counters (c) Work out the probability that Bernie will instead take a white counter from bag A. (d) If Bernie instead chooses a white counter, how many of each counter are then in bag B?..black counters..white counters 32

33 Bernie then takes at random a counter from bag B and puts the counter in bag C. (e) Work out the probability that Bernie takes a black counter from Bag A and a black counter from bag B. (f) Work out the probability that Bernie takes a white counter from Bag A and a black counter from bag B. (g) Thus find the probability that there are now more black counters than white counters in bag C.... (Total for Question 24 is 3 marks) TOTAL FOR PAPER: 80 MARKS 33

34 BLANK PAGE 34

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