19 Oliver records the distance from London to each of eight cities in the USA.

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1 DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE Title: Mock Set 3 Paper 2H Date: 1. Oliver records the distance from London to each of eight cities in the US. 19 Oliver records the distance from London to each of eight cities in the US. He also records the time taken to fly from London to each of these cities. He also records the time taken to fly from London to each of these cities. The scatter graph graph shows shows this information. this information Distance (miles) Distance (miles) Chicago is a city in the US. Chicago is 4200 miles from London Time taken (minutes) (a) (i) By drawing a line of best fit, find an estimate for the time taken to fly from London to Chicago. minutes (ii) Why is your answer to part (i) only an estimate? (1) 16 *S *

2 (b) (i) Calculate the gradient of your line of best fit. (ii) Give an interpretation of the gradient of your line of best fit (1) (Total for Question 1 is 6 marks) 20 2 y S 2 1 O x (a) Rotate (a) Rotate shape shape S 90 S clockwise, 90 clockwise, centre centre (5, 4) (5, 3) Label your Label image your T. image T. (b) Describe (b) Describe fully fully the single the single transformation transformation that that will will map map shape shape T T onto onto shape shape S. S..... (1) (1) (Total for Question 2 is 3 marks) x (Total for Question 20 is 3 marks)

3 DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE 3 21 Here Here are are two two rectangles. rectangles. 4x 4x 2x + 5 2x B 57 ll measurements are in centimetres. ll measurements are in centimetres. The The area area of of rectangle rectangle is is equal equal to to the the area area of of rectangle rectangle B. B. Work Work out out the the perimeter of rectangle B. B. cm cm (Total for Question 3 is 5 marks) (Total for Question 21 is 5 marks) *S * 19 Turn over

4 The diagram shows a fair 4-sided spinner. 4 The diagram shows a fair 4-sided spinner. 22 The diagram shows a fair 4-sided spinner. B B Hasmeet is going to spin the spinner twice. Hasmeet is going to spin the spinner twice. (a) Complete the the probability tree tree diagram. Hasmeet is going to spin the spinner twice. (a) Complete the probability tree diagram. First spin First spin Second spin Second spin lands on lands on lands on lands on lands on B lands on B lands on lands on B lands on lands on B lands on B (b) Work out the probability that the spinner will land on on the first spin and will land (b) Work out the probability that the spinner will land on B on the first spin on B on the second spin. and will land on on the second spin. lands on B (b) Work out the probability that the spinner will land on on the first spin and will land on B on the second spin. (Total for Question 4 is 4 marks) (Total for Question 22 is 4 marks)

5 5 S = π 2 (b 2 a 2 ) a = 10, b = 12 Calculate the value of S. Give your answer correct to 3 significant figures. (Total for Question 5 is 2 marks) 6 Only blue vans and white vans are made in a factory. The ratio of the number of blue vans to the number of white vans is 5 : 3 (a) Write down the fraction of vans that are blue. For blue vans, the number of small vans : the number of large vans = 7 : 3 (1) (b) Work out the fraction of the number of vans made in the factory that are blue and large. (3) (Total for Question 24 is 4 marks)

6 7 (a) Find the reciprocal of 6. (b) Use your calculator to work out 3 6 tan (1) Write down all the figures on your calculator display.... (Total for Question 7 is 3 marks) 8 Make t the subject of p = a + t 3 (Total for Question 8 is 3 marks)

7 DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE 9 9 x B C x D E F w G In the In diagram the diagram BC BC and and DEFG DEFG are are parallel parallel lines. lines. ngle ngle BE BED = x = x EB = EB EF= EF Show that = Show that w = x 2 Give Give a reason a reason for each for each stage stage of your of your working. working. (Total for Question 9 is 4 marks) (Total for Question 9 is 4 marks)

8 10 In 2016 the population of the UK was Laura wants to calculate an estimate for the population of the UK in She assumes that the population increases by 0.7% each year. (a) Using Laura s assumption, calculate an estimate for the population of the UK in Kieran also assumes that the population of the UK increases by 0.7% each year. He says that it will take over 71 years for the population to increase by 50% because 50 = Kieran s method is wrong. (b) Explain what is wrong with his method (1) ssuming that the population of the UK increases by 0.7% each year, (c) show that the population of the UK each year forms a geometric progression. (Total for Question 10 is 5 marks)

9 11 nna and Bill share some money in the ratio 3 : 5 nna gets Bill gets B Carl and Donna share twice as much money as nna and Bill share. They share the money in the ratio 4 : 1 Carl gets C Donna gets D Find : B : C : D Give your answer in its simplest form.... (Total for Question 11 is 3 marks)

10 Here is triangle PQR. 12 Here is triangle PQR. Q P R The length of QR is 60% of the length of PR. The length of QR is 70% of the length of PR. Find the value of sin QPR. Give your answer correct to 3 significant figures. Find the value of sin QPR. Give your answer correct to 3 significant figures... (Total for Question 12 is 3 marks) (Total for Question 12 is 3 marks)

11 13 Here are five graphs. Each graph shows either direct proportion or inverse proportion. B C D E The table shows five equations. Equation Graph y = kx 3 y = k x y = kx 2 y = x k y = kx Match the letter of each graph to its equation. (Total for Question 13 is 3 marks)

12 DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE 14 cafe owner sells 8 different types of sandwich. Rayheem buys a different type of sandwich on Monday, on Tuesday and on Wednesday. In how many ways can he do this? (Total for Question 14 is 2 marks) 15 The table shows information about the times a group of students took to do a park run. 15 The table shows information about the times a group of students took to do a park run. Time taken (t minutes) Draw a histogram for this information. Draw a histogram for this information. 0 < t < t < t < t < t < t 95 8 Time taken (t minutes) Frequency Frequency 0 < t < t < t < t < t < t (Total for Question 15 is 3 marks) Frequency density Time taken (t minutes) (Total for Question 15 is 3 marks) *S * 15 Turn over

13 16 (a) Show that the equation x 3 4x = 0 has a solution between x = 1 and x = 2 (b) Show that the equation x 3 4x = 0 can be rearranged to give x = 3 4x 2 6 (c) Starting with x 0 = 2, use the iteration formula x n + 1 = 3 4x 2 6 to find the value of x 2. (1) Give your answer correct to 3 decimal places. (3) (Total for Question 16 is 6 marks)

14 DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE factory makes ice cream tubs tubs in in two two sizes, sizes, small small and and large. large. Ice Cream 4cm 5 Ice Cream small The tubs are similar in shape. The tubs are similar in shape. The height of the small tub is 5 cm The height of the small tub is 4 cm. The volume of of the the small small tub tub is is cm cm 3 3. The volume of of the the large large tub tub is is cm cm 3 3. Work out the height of of the large tub. tub. Give your answer correct to to 3 3 significant figures. large cm (Total for Question 17 is 2 marks) cm (Total for Question 17 is 2 marks) *S * 17 Turn over

15 DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE E IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE 18 (x 6)(x + 8) = (x + a) 2 + b for all values of x. Find the value of a and the value of b. a = b = (Total for Question 18 is 3 marks) 19 The diagram shows a sector of circle of radius 9 cm. 19 The diagram shows a sector of a circle of radius 9 cm. 9 cm x 9 cm The sector has a perimeter of 25 cm. The sector has a perimeter of 22 cm. Work out the value of x. Work out Give the your value answer of correct x. to 1 decimal place. Give your answer correct to 1 decimal place. (Total for Question 19 is 4 marks)

16 DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE DO NOT WRITE IN THIS RE 1 20 m = ps p = 5.64 correct to 2 decimal places. s = 2.8 correct to 1 decimal place. Calculate the upper bound for the value for m. You must show your working. 21 The diagram shows an acute-angled triangle BC. 21 The diagram shows an acute-angled triangle BC. (Total for Question 20 is 3 marks) c b B a Prove that area of triangle BC = ½ ab sin C Prove that area of triangle BC = absin C C (Total for Question 21 is 3 marks) (Total for Question 21 is 3 marks)

17 22 solid cuboid has a volume of 60 cm 3. The cuboid has a total surface area of 140 cm 2. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 significant figures. cm (Total for Question 22 is 6 marks) TOTL FOR PPER IS 80 MRKS