1. A Spanish family went to Scotland for a holiday. The original cost of the holiday was reduced by 10% to €4347.00. Calculate the original cost. [2] 2. Use the formula P= V2 R to calculate the value of P when V = 6 × 106 and R = 7.2 × 108. Answer P = …….……………… [2] 3. There are 109 nanoseconds in 1 second. Find the number of nanoseconds in 5 minutes, giving your answer in standard form. Answer …….…………………… [2] 4. Simplify x+2 x − . x x+2 Write your answer as a fraction in its simplest form. Answer ….....……..………………….…… [3] 5. Make d the subject of the formula c= d3 + 5, 2 Answer d = ………….………….………… [3] 6. [The surface area of a sphere of radius r is 4πr2 and the volume is 4 3 πr . ] 3 A metal sphere has a mass of 1 kilogram. One cubic centimetre of this metal has a mass of 4.8 grams. Calculate the radius of this sphere. [3] 7. The planet Neptune is 4 496 000 000 kilometres from the Sun. Write this distance in standard form. Answer ……………………………… km [1] 1 8. A block of cheese, of mass 8 kilograms, is cut by a machine into 500 equal slices. (a) Calculate the mass of one slice of cheese in kilograms. Answer (a) ……….………………….…… kg [1] (b) Write your answer to part (a) in standard form. Answer (b) ……….………………….…… kg [1] 9. In 2004 Colin had a salary of $7200. (a) This was an increase of 20% on his salary in 2002. Calculate his salary in 2002. Answer (a)$ ………..….………………… [2] (b) In 2006 his salary increased to $8100. Calculate the percentage increase from 2004 to 2006. Answer (b) …………………………… % [2] 10. 2 5 x + = . 3 6 2 (a) Find the value of x. Answer (a) x = …….……………………… [1] 5 3 40 ÷ = , 3 y 9 (b) Find the value of y. Answer (b) y = …….……………………… [1] 11. A tin of soup has the following information on the label. 200 grams of soup contains (a) Protein Carbohydrate Fat 4g 8.7 g 5.8 g What fraction of the soup is Protein? Give your answer in its simplest form. Answer (a) ……………………. [1] (b) What percentage of the soup is Carbohydrate? Answer (b) ………………….. % [1] 2 12. Each year a school organises a concert. (i) In 2004 the cost of organising the concert was $385. In 2005 the cost was 10% less than in 2004. Calculate the cost in 2005. [2] (ii) The cost of $385 in 2004 was 10% more than the cost in 2003. Calculate the cost in 2003. [2] 13. A spacecraft made 58 376 orbits of the Earth and travelled a distance of 2.656 × 109 kilometres. (a) Calculate the distance travelled in 1 orbit correct to the nearest kilometre. Answer (a) ………………… km [2] (b) The orbit of the spacecraft is a circle. Calculate the radius of the orbit. Answer (b) ………………… km [2] 14. A light on a computer comes on for 38 500 microseconds. One microsecond is 10–6 seconds. Work out the length of time, in seconds, that the light is on (a) in standard form, Answer (a) …….….…..……… s [1] (b) as a decimal. Answer (b) …….….……..…… s [1] 15. Factorise completely (a) 7ac + 14a, Answer (a) ………….……….…………… [1] (b) 12ax3 + 18xa3. Answer (b) ………….……….…………… [2] 3 16. Angharad had an operation costing $500. She was in hospital for x days. The cost of nursing care was $170 for each day she was in hospital. (a) Write down, in terms of x, an expression for the total cost of her operation and nursing care. Answer (a)$ ……………………………… [1] (b) The total cost of her operation and nursing care was $2370. Work out how many days Angharad was in hospital. Answer (b) …….………………………… [2] 17. (i) On Monday a shop receives $60.30 by selling bottles of water at 45 cents each. How many bottles are sold? [1] (ii) On Tuesday the shop receives x cents by selling bottles of water at 45 cents each. In terms of x, how many bottles are sold? [1] (iii) On Wednesday the shop receives (x – 75) cents by selling bottles of water at 48 cents each. In terms of x, how many bottles are sold? [1] (iv) The number of bottles sold on Tuesday was 7 more than the number of bottles sold on Wednesday. Write down an equation in x and solve your equation. [4] 18. The equation of a straight line can be written in the form 3x + 2y – 8 = 0. (a) Rearrange this equation to make y the subject. Answer (a) y = ……...………… [2] (b) Write down the gradient of the line. Answer (b) ………….………… [1] (c) Write down the co-ordinates of the point where the line crosses the y axis. Answer (c) (…….… , .……..…) [1] 4 19. NOT TO SCALE l 0.7 cm h 16.5 cm 1.5 cm The diagram shows a pencil of length 18 cm. It is made from a cylinder and a cone. The cylinder has diameter 0.7 cm and length 16.5 cm. The cone has diameter 0.7 cm and length 1.5 cm. (a) Calculate the volume of the pencil. [The volume, V, of a cone of radius r and height h is given by V = 1 2 πr h. 3 [3] (b) 18 cm x cm w cm NOT TO SCALE Twelve of these pencils just fit into a rectangular box of length 18 cm, width w cm and height x cm. The pencils are in 2 rows of 6 as shown in the diagram. (i) Write down the values of w and x. [2] (ii) Calculate the volume of the box. [2] (iii) Calculate the percentage of the volume of the box occupied by the pencils. [2] (c) Showing all your working, calculate (i) the slant height, l, of the cone, [2] (ii) the total surface area of one pencil, giving your answer correct to 3 significant figures. [The curved surface area, A, of a cone of radius r and slant height l is given by A = πrl.] [6] 5 P 12 cm R 6 cm O 30° S Q 20. NOT TO SCALE OPQ is a sector of a circle, radius 12 cm, centre O. Angle POQ = 50°. ORS is a sector of a circle, radius 6 cm, also centre O. Angle ROS = 30°. (a) Calculate the shaded area. Answer (a) ………………… cm2 [3] (b) Calculate the perimeter of the shaded area, PORSOQP. Answer (b) ….……………… cm [3] 6 21. 35 m 1.1 m 24 m D C 2.5 m B A NOT TO SCALE The diagram shows a swimming pool of length 35 m and width 24 m. A cross-section of the pool, ABCD, is a trapezium with AD = 2.5 m and BC = 1.1 m. (a) Calculate (i) the area of the trapezium ABCD, [2] (ii) the volume of the pool, [2] (iii) the number of litres of water in the pool, when it is full. [1] (b) AB = 35.03 m correct to 2 decimal places. The sloping rectangular floor of the pool is painted. It costs $2.25 to paint one square metre. (i) Calculate the cost of painting the floor of the pool. [2] (ii) Write your answer to part (b)(i) correct to the nearest hundred dollars. [1] (c) (i) Calculate the volume of a cylinder, radius 12.5 cm and height 14 cm. [2] (ii) When the pool is emptied, the water flows through a cylindrical pipe of radius 12.5 cm. The water flows along this pipe at a rate of 14 centimetres per second. Calculate the time taken to empty the pool. Give your answer in days and hours, correct to the nearest hour. [4] 7