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* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name ……………………………………………. 1. Mark …………………/30 Grade ……… Use approximations to estimate the value of 37.48 62.13 (1.95) You must show your working. ................................................................................................................................................ ................................................................................................................................................ Answer ................................................................( 3 ) 2. (a) Express 144 as the product of its prime factors. Write your answer in index form. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .................................................................. (3) (b) Find the Highest Common Factor (HCF) of 60 and 144. ..................................................................................................................................... ..................................................................................................................................... Answer .................................................................. (2) 3. (a) Solve the equation 4(x + 3) = 9(x – 2) ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer x = ................................................................ (3) Wellsway School 1 (b) Solve these simultaneous equations 5x + 3y = 6 3x – 7y = 19 You must show your working. Do not use trial and improvement. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer x = ......................... , y = ........................... (4) 4. A sequence of numbers is shown. 5 (a) 9 13 17 21 Find an expression for the nth term of the sequence. ...................................................................................................................................... ...................................................................................................................................... Answer ................................................................ (2) (b) Explain why 83 will not be a term in this sequence. ...................................................................................................................................... ...................................................................................................................................... (2) 5. (a) There are 14 700 (to the nearest hundred) spectators at a football match. (i) What is the least possible number of spectators? ........................................................................................................................... Answer .................................................... (1) (ii) What is the maximum number of spectators? ........................................................................................................................... Answer .................................................... (1) Wellsway School 2 (b) The ratio of adults to children visiting a park is 3:5 One day 1740 adults go to the park. How many children go to the park on that day? ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .................................................... (2) (c) A large theme park attracts 7500 visitors each day. The park is open for 220 days. How many visitors come to the park? Give your answer in standard form. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .................................................... (2) (Total 6 marks) Wellsway School 3 6. The sketch shows the entrance to a tunnel. The uniform cross-section of the tunnel is in the shape of a semi-circle over a rectangle. 1.6 m 5m Not to scale The rectangle is 5 metres wide and 1.6 metres high. The tunnel is 230 metres long. Calculate the volume of earth removed in digging the tunnel. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ....................................................... m3 (Total 5 marks) Wellsway School 4