Y10 End of Year Revision Exercise - Express Level

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1 Y10 End of Year Revision Exercise - Express Level 1. The probability that a biased dice will land on a four is 0.2 Pam is going to roll the dice 200 times. Work out an estimate for the number of times the dice will land on a four.... (Total 2 marks) 2. The probability that a biased dice will land on a four is 0.2 Pam is going to roll the dice 200 times. Work out an estimate for the number of times the dice will land on a four.... The probability that the biased dice will land on a six is 0.4 Ted rolls the biased dice once. Work out the probability that the dice will land on either a four or a six. 3. A bag contains 3 black beads, 5 red beads and 2 green beads. Gianna takes a bead at random from the bag, records its colour and replaces it. She does this two more times.... (Total 4 marks) Work out the probability that, of the three beads Gianna takes, exactly two are the same colour.... (Total 5 marks) 4. The fraction, p, of an adult s dose of medicine which should be given to a child who weighs w kg is given by the formula 3 20 p w 200 Use the formula 3 20 p w to find the weight of a child whose dose is the same as an adult s dose. 200 Make w the subject of the formula 3 20 p w 200 kg w = 1

2 3w = A A 12 (c) Express A in terms of w. 5. Make u the subject of the formula A = (4) (Total 10 marks) D = ut + kt 2 u =... (Total 2 marks) 6. C 12.6 m A 41 B The diagram shows a right-angled triangle ABC. AC = 12.6 m. Angle CAB = 41 Angle ABC = 90 Find the length of the side AB. Give your answer correct to 3 significant figures. m 7. The diagram represents a vertical flagpole, AB. The flagpole is supported by two ropes, BC and BD, fixed to the horizontal ground at C and at D. B 12.8 m Diagram NOT accurately drawn C 6.8 m A 42 D AB = 12.8 m. AC = 6.8 m. Angle BDA = 42. Calculate the size of angle BCA. Give your answer correct to 3 significant figures. Calculate the length of the rope BD. Give your answer correct to 3 significant figures. m 2

3 8. This table shows some expressions. The letters a, b, c, and d represent lengths. and 4 are numbers that have no dimensions. Three of the expressions could represent volumes. (Total 6 marks) Tick the boxes underneath the three expressions which could represent volumes. abc d 4 a 3 4a 2 a 3 + bd (a + b)cd (c 2 + d 2 ) 2 4ad 9. Here are some expressions. 1 ac 2 c 2b 2ab 2 abc a(b + c) ab c a 2 The letters a, b and c represent lengths., 2 and 2 1 are numbers which have no dimensions. Three of the expressions could represent areas. Tick ( ) the boxes underneath the three expressions which could represent areas. 10. The diagram shows a sector of a circle with a radius of x cm and centre O. PQ is an arc of the circle. Angle POQ = 120. O 120 x cm P Diagram NOT accurately drawn Q Write down an expression in terms of and x for (i) the area of this sector,... (ii) the arc length of this sector.... 3

4 The sector is the net of the curved surface of this cone. Arc PQ forms the circumference of the circle that makes the base of the cone. h cm x cm The curved surface area of the cone is A cm 2. The volume of the cone is V cm 3. The height of the cone is h cm. Given that V = 3A, find the value of h (Total 5 marks) 10 cm 15 cm O 10 cm Diagram NOT accurately drawn The diagram shows a sector of a circle, centre O, radius 10 cm. The arc length of the sector is 15 cm. Calculate the area of the sector.... cm 2 (Total 4 marks) 4

5 12. Charles found out the length of reign of each of 41 kings. He used the information to complete the frequency table. Length of reign (L years) Number of kings 0 < L < L < L < L < L 50 2 Write down the class interval that contains the median... Calculate an estimate for the mean length of reign.. years (4) (Total 6 marks) 13. The grouped frequency table shows information about the weights, in kilograms, of 20 students, chosen at random from Year 11. There are 300 students in Year 11. Weight (w kg) Frequency 50 w < w < w < w < 90 2 Work out an estimate for the number of students in Year 11 whose weight is between 50 kg and 60 kg. 5

6 14. The table shows information about the heights of 40 bushes. Height (h cm) Frequency 170 h < h < h < h < h < Complete the cumulative frequency table. Height (h cm) 170 h < h < h < h < h < 195 Cumulative Frequency On the grid, draw a cumulative frequency graph for your table. 40 Cumulative frequency Height ( h cm) (c) Use the graph to find an estimate for the median height of the bushes. cm (Total 4 marks) 6

7 students took a test. The cumulative frequency graph gives information about their marks. 200 Cumulative frequency The lowest mark scored in the test was 10. The highest mark scored in the test was Mark Use this information and the cumulative frequency graph to draw a box plot showing information about the students marks Mark 16. Write as an ordinary number. Write the number in standard form (Total 2 marks) 7

8 17. Write in standard form. Write in standard form. 18. x = p q pq p = q = Calculate the value of x. Give your answer in standard form.. (Total 2 marks) 19. A nanosecond is second. Write the number in standard form. A computer does a calculation in 5 nanoseconds.... How many of these calculations can the computer do in 1 second? Give your answer in standard form cm 1.2 cm The diagram shows a piece of wood. The piece of wood is a prism of length 350 cm. The cross-section of the prism is a semi-circle with diameter 1.2 cm. Calculate the volume of the piece of wood. Give your answer correct to 3 significant figures. Diagram NOT accurately drawn cm 3 (Total 4 marks) 8

9 21. The length of a path is 14 m correct to the nearest metre. (i) Write down the minimum possible length of the path. m (ii) Write down the maximum possible length of the path. 22. Use your calculator to work out the value of m (Total 2 marks) Write down all the figures on your calculator display.. Give your answer to an appropriate degree of accuracy The time period, T seconds, of a pendulum is calculated using the formula T = L g where L metres is the length of the pendulum and g m/s 2 is the acceleration due to gravity. L = 1.36 correct to 2 decimal places. g = 9.8 correct to 1 decimal place. Find the difference between the lower bound of T and the upper bound of T (Total 5 marks) L m x Elliot did an experiment to find the value of g m/s 2, the acceleration due to gravity. He measured the time, T seconds, that a block took to slide L m down a smooth slope of angle x. He then used the formula g = T 2 2L sin x to calculate an estimate for g. T = 1.3 correct to 1 decimal place. L = 4.50 correct to 2 decimal places. x = 30 correct to the nearest integer. 9

10 Calculate the lower bound and the upper bound for the value of g. Give your answers correct to 3 decimal places. Lower bound... Upper bound... (4) Use your answers to part to write down the value of g to a suitable degree of accuracy. Explain your reasoning (Total 5 marks) 25. The incomplete table and histogram give some information about the ages of the people who live in a village. Frequency density Age in years Use the information in the histogram to complete the frequency table below. Age (x) in years Frequency 0 < x < x < x < x < x Complete the histogram. (Total 4 marks) 10

11 26. This histogram gives information about the books sold in a bookshop one Saturday. Frequency density (number of books per ) Price ( P) in pounds ( ) Use the histogram to complete the table. Price (P) in pounds ( ) 0 < P 5 5 < P < P < P 40 Frequency The frequency table below gives information about the books sold in a second bookshop on the same Saturday. Price (P) in pounds ( ) Frequency 0 < P < P < P < P On the grid below, draw a histogram to represent the information about the books sold in the second bookshop Price ( P) in pounds ( ) (Total 5 marks) 11

12 27. The table gives information about the heights, in centimetres, of some 15 year old students. Height (h cm) 145 < h < h < h 190 Frequency Use the table to draw a histogram Height ( h cm) 28. P R Diagram NOT accurately drawn O P, Q and R are points on a circle, centre O. POQ is a straight line. TQ and TR are tangents to the circle. Angle TQR = 56. Q 56 T Explain why angle PQR = Calculate the size of angle PRT. Give reasons for your answer... (Total 4 marks) 12

13 29. T O 40º A 30º B C Diagram NOT accurately drawn T, A and B are points on the circumference of the circle, centre O. AT is a diameter of the circle. Angle BTC = 40 Angle TAB = 30 Explain why TC cannot be a tangent to the circle. 30. (Total 2 marks) A Diagram NOT accurately drawn 11.7 m B m C AB = 11.7 m. BC = 28.3 m. Angle ABC = 67. Calculate the area of the triangle ABC. Give your answer correct to 3 significant figures.. m 2 2) Calculate the length of AC. Give your answer correct to 3 significant figures.. m (Total 5 marks) 13

14 31. N Diagram NOT accurately drawn N Hospital Cinema 72 Art gallery The diagram shows the position of each of three buildings in a town. The bearing of the Hospital from the Art gallery is 072. The Cinema is due East of the Hospital. The distance from the Hospital to the Art gallery is equal to the distance from the Hospital to the Cinema. Work out the bearing of the Cinema from the Art gallery. 32. Convert the recurring decimal to a fraction. (Total 2 marks) Change to a decimal. 11. Prove that the recurring decimal = (Total 4 marks) 34. Express as a fraction in its simplest form. x is an integer such that 1 x 9 Prove that 0.0 x x 99 (Total 5 marks) 14

15 35. Work out (i) (ii) (iii) (iv) (4) Given that x = 2 k and 4 c 2, find c in terms of k. x 36. Work out c =. (Total 5 marks) (i) (ii) (iii)

16 37. x = 2 p, y = 2 q Express in terms of x and/or y, (i) 2 p + q... (ii) 2 2q... (iii) 2 p 1 xy = 32 and 2xy 2 = 32 Find the value of p and the value of q.... p =... q =... (Total 5 marks) 16

17 Draw a circle around each irrational number in the list below Put a tick in the box underneath those numbers that are rational. 2 / / 17 There are 2.54 centimetres in 1 inch. There are 12 inches in 1 foot. There are 3 feet in 1 yard. i Calculate the number of yards in 10 metres. ii Calculate the number of metres in 10 yards. Two tangents are drawn from a point T to a circle centre O. They meet the circle at points A and B. Angle AOB is equal to 128º. In this question you MUST give reasons for your answers. Work out the size of the angles i APB, ii BAO, iii ABT. Calculate the standard deviation of the numbers 3, 3, 4, 5, 7, 9,

18 There are 12 inches in 1 foot. There are 3 feet in 1 yard. There are 2.54 centimetres in 1 inch. Express 1 metre in yards. Give your answer correct to 3 decimal places. There are 2.54 centimetres in 1 inch. There are 12 inches in 1 foot. There are 3 feet in 1 yard. i Calculate the number of yards in 10 metres. ii Calculate the number of metres in 10 yards. There are 14 pounds in a stone. There are 2.2 pounds in a kilogram. A man weighs 13 stone 6 pounds. Work out his weight in kilograms. Give your answer to the nearest kilogram. There are 6 groats in a florin and 5 florins in 10 shillings. Work out how many i groats there are in 5 florins, ii florins there are in 24 shillings, iii groats there are in 8 shillings. 18