ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC
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1 ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC WEEK Calculator paper Each set of questions is followed by solutions so you can check & mark your own work CONTENTS TOPIC PAGE NUMBER GCSE GRADE Date completed Marks GEOMETRY Compound measures ( speed, density ) Page 141 GEOMETRY Surface area of a -D shape Page 0 GEOMETRY Volume of prisms Page 00 GEOEMTRY : Volume of non- prisms Page 4
2 Density, Mass and Volume 1. The mass of 5 m of copper is kg. (a) Work out the density of copper. kg/m () The density of zinc is 710 kg/m. (b) Work out the mass of 5 m of zinc. kg ()..8 cm. Diagram NOT accurately drawn An ice hockey puck is in the shape of a cylinder with a radius of.8 cm, and a thickness of.. It is made out of rubber with a density of 1.5 grams per cm. Work out the mass of the ice hockey puck. Give your answer correct to significant figures... Grams. cm 10 cm The diagram shows a solid cuboid. The cuboid has length 10 cm, width 8 cm and height. 4. The cuboid is made of wood. The wood has a density of 0.6 grams per cm. Work out the mass of the cuboid.... Grams (Total 4 marks) 60 cm 4 cm The diagram shows a solid hexagonal prism. The area of the cross-section of the prism is 60 cm. The length of the prism is 4 cm. (a) Work out the volume of the prism.... cm () The prism is made from wood. The prism has a mass of 648 g. (b) Work out the density of the wood.... g/cm ()
3 5. cm cm The solid shape, shown in the diagram, is made by cutting a hole all the way through a wooden cube. The cube has edges of length. The hole has a square cross section of side cm. (a) Work out the volume of wood in the solid shape.... cm () The mass of the solid shape is 64 grams. (b) Work out the density of the wood.... grams per cm () (Total 4 marks) 6. The density of juice is 4 grams per cm. The density of water is 1 gram per cm. 1 of drink is made by mixing 1 of juice with 00 cm of water. Work out the density of the drink. SOLUTIONS... grams per cm 1. (a) (b) Vol = π.8.5 = π = = Mass = = (= 400) = (a) 60 4 (= 1440) = 1440 (b) = (a) (5 5 ) 5 (5 9) = 80 (b) Mass of water = 00 1= 00 g Mass of juice = 15 4 = 60g Total mass = 60 Total volume = 15 Density = 60 15
4 Speed, Time & Distance 1. Kelly runs a distance of 100 metres in a time of 10.5 seconds. The distance of 100 metres was measured to the nearest metre. The time of 10.5 seconds was measured to the nearest hundredth of a second. (a) Write down the upper bound for the distance of 100 metres.... metres (1) (b) Write down the lower bound for the time of 10.5 seconds... seconds (1) (c) (d) Calculate the upper bound for Kelly s average speed. Write down all the figures on your calculator display... metres per second () Calculate the lower bound for Kelly s average speed. Write down all the figures on your calculator display.... metres per second () (Total 6 marks). A tank contains 480 litres of water. A tap is opened, and water flows out of the tank at the rate of 0. litres per second. How long will it take to empty the tank? 40 minutes 96 minutes 960 minutes 400 minutes 4800 minutes A B C D E. A tank contained cm of salt. The salt was removed from the tank at a constant rate. It took hours and 40 minutes to empty the tank completely. At what rate, in cm per second, was the salt removed from the tank? A B C D E 4. There are 960 litres of water in a tank. A workman empties the tank. The water flows out of the tank at a constant rate of 0.4 litres per second. How long, in minutes, does it take the workman to empty the tank completely? A B C D E 5. Water flows from a container at a constant rate of 0.1 litres per second. How long does it take to fill a can with 9 litres of water? 9 seconds 90 seconds 9 minutes 10 seconds 90 minutes A B C D E 6. A plane is flying at a speed of 1440 kilometres per hour. How long, in seconds, will the plane take to fly a distance of 1 kilometre? 0.4 seconds.4 seconds.5 seconds 4 seconds 4 seconds A B C D E (Total 1 mark
5 SOLUTIONS: 1. (a) (b) (c) = (d) [6]
6 VOLUME 1. 4 cm Diagram NOT accurately drawn 10 cm The diagram shows a cylinder with a height of 10 cm and a radius of 4 cm. (a) Calculate the volume of the cylinder. Give your answer correct to significant figures....cm () The length of a pencil is 1 cm. The pencil cannot be broken. (b) Show that this pencil cannot fit inside the cylinder. () (Total 5 marks). A cuboid has a square base of side x cm. The height of the cuboid is 1 cm more than the length x cm. The volume of the cuboid is 0 cm.. (a) Show that x + x = 0 ) Diagram NOT accurately drawn A A 10 cm 10 cm B 0 cm B 0 cm 1 1 The diagram represents a large cone of height 0 cm and base diameter 1. The large cone is made by placing a small cone A of height 10 cm and base diameter on top of a frustum B. (a) Calculate the volume of the frustum B Give your answer correct to significant figures....cm ()
7 d cm h cm Diagram NOT accurately drawn d cm The diagram shows a frustum. The diameter of the base is d cm and the diameter of the top is d cm. The height of the frustum is h cm. The formula for the curved surface area, S cm, of the frustum is S = πd h d (b) Rearrange the formula to make h the subject. h =...() Two mathematically similar frustums have heights of 0 cm and 0 cm. smaller frustum is 450 cm. The surface area of the (c) Calculate the surface area of the larger frustum...cm () (Total 8 marks) cm Diagram NOT accurately drawn 10 cm The diagram shows a model. The model is a cuboid with a pyramid on top. The base of the model is a square with sides of length. The height of the cuboid in the model is 10 cm. The height of the pyramid in the model is 6 cm (a) Calculate the volume of the model.... cm () 5. The diagram shows a prism of length 90 cm. The cross section, PQRST, of the prism is a semi-circle above a rectangle. PQRT is a rectangle. RST is a semi-circle with diameter RT. PQ = RT = 60 cm. PT = QR = 4. Calculate the volume of the prism. Give your answer correct to significant figures... cm (Total 4 marks)
8 6. The diagram shows a cylinder and a sphere. 7. The radius of the base of the cylinder is x cm and the height of the cylinder is h cm. The radius of the sphere is x cm. The volume of the cylinder is equal to the volume of the sphere. Express h in terms of x. Give your answer in its simplest form. h =... (Total marks) Diagram accurately NOT drawn A cone has a base radius of and a vertical height of 8 cm. (a) Calculate the volume of the cone. Give your answer correct to significant figures.... cm () 8. A cylinder has base radius x cm and height x cm. A cone has base radius x cm and height h cm The volume of the cylinder and the volume of the cone are equal. Find h in terms of x. Give your answer in its simplest form. h cm x cm h =... (Total marks) 9. The diagram shows a storage tank. x cm x cm The storage tank consists of a hemisphere on top of a cylinder. The height of the cylinder is 0 metres. The radius of the cylinder is metres. The radius of the hemisphere is metres. m m (a) Calculate the total volume of the storage tank. 0 m Give your answer correct to significant figures.... m m A sphere has a volume of 500 m. (b) Calculate the radius of the sphere Give your answer correct to significant figures.... m () (Total 6 marks)
9 10. 4 cm 4 cm A cylinder has a height of 4 cm and a radius of 4 cm. Work out the volume of the cylinder. Give your answer correct to significant figures. 11. A clay bowl is in the shape of a hollow hemisphere. cm (Total marks) 8. cm 7.7 cm The external radius of the bowl is 8. cm. The internal radius of the bowl is 7.7 cm. Both measurements are correct to the nearest 0.1 cm. The upper bound for the volume of clay is k cm. Find the exact value of k. k =..(Total 4 marks) 1. The diagram represents a large cone of height 6 cm and base diameter 18 cm. The large cone is made by placing a small cone A of height cm and base diameter 6 cm on top of a frustum B. Calculate the volume of the frustum B. Give your answer in terms of π.... (Total 4 marks)
10 1. 50 cm 1. cm The diagram shows a piece of wood. The piece of wood is a prism of length 50 cm. The cross-section of the prism is a semi-circle with diameter 1. cm. Calculate the volume of the piece of wood. Give your answer correct to significant figures. cm (Total 4 marks) 14. Diagram NOT accurately drawn 10 cm 11 cm 1 cm. A rectangular container is 1 cm long, 11 cm wide and 10 cm high. The container is filled with water to a depth of 8 cm. A metal sphere of radius. is placed in the water. It sinks to the bottom. Calculate the rise in the water level. Give your answer correct to significant figures...cm (Total 4 marks) 15. r cm 10 cm The diagram shows a cylinder. The radius of the cylinder is r cm. The length of the cylinder is 10 cm. The volume of the cylinder is 140 cm. Work out the value of r. Give your answer correct to significant figures. r =...(Total marks)
11 Solutions: 1. (a) cm V = 4 10 (b) P = P = 164. (a) AG x (x + 1) = 0. (a) S 4 d (b) h 4 d S d S d (c) or (a) = = (b) Area scale factor is 0 h h d 4 d 90 0 = cm ( ) 90 4 (1/ ) 90 ( ) = = = 4 h "4800" " " = ( x) h (x) 4 (x) h = 9x (x)
12 7. πx 1 (x) = π(x) h 6x 8. (a) V c 0 V h V c V h (b) 4 R R cm (1.1 ) "1.1..." Vol sphere = π.5 = "179.59" Height = = r 10 r = 140/10 (= ).11
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