146 Mathematics Grade 5 17. The pie chart shows the number of gold medals won by four teams during the school sports day. The total number of events in the school sports day was 92. What fraction of the gold medals were won by the Blue Team? Red 25 Green 19 Blue Yellow 25 A 3 18 C 5 18 B 1 4 D 1 2 18. The pie chart shows the types of music preferred by a group of 324 pupils. Find the difference between the number of pupils who preferred pop music and the number of pupils who preferred R & B music. Classical 108 R & B 81 Pop Country 27 A 27 C 30 B 54 D 81 For Teachers Only
General Revision 2 147 A Choose the correct answer and write its number in the brackets provided. 1. Express 0.08 as a percentage. (1) 0.8% (2) 8% (3) 80% (4) 800% ( ) 2. Which of the following is true? (1) 50% of 100 is 10 (2) 3% of 27 is 9 (3) 25% of 12 cm is 3 cm (4) 80% of 20 is 4 ( ) 3. Farid saved Rp 12.000,00 last week. He saved 15% more this week. What is his total savings? (1) Rp 13.800,00 (2) Rp 15.600,00 (3) Rp 25.800,00 (4) Rp 27.600,00 ( ) 4. Express the ratio of 25 minutes to 2 hours in its simplest form. (1) 5 : 24 (2) 5 : 12 (3) 12 : 5 (4) 24 : 5 ( ) 5. Mrs Siva made chocolate muffins, banana muffins and vanilla muffins in the ratio of 7 : 3 : 4. If she made 280 muffins altogether, how many fewer banana muffins than chocolate muffins were there? (1) 20 (2) 60 (3) 70 (4) 80 ( ) 6. In a contest, the ratio of the number of points scored by Team Ato the number of points scored by Team B to the number of points scored by Team C was 8 : 5 : 12. Team C scored 16 points more than Team A. How many points did Team B score? (1) 16 (2) 20 (3) 32 (4) 40 ( ) 7. Ramesh is cycling at a speed of 20 km/h to school. If he takes 12 minutes to reach his school, how far is his school from his house? (1) 3 km (2) 4 km (3) 5 km (4) 6 km ( ) General Revision 2 2 3 1 1 4 2 2 For Teachers Only
Mathematics Grade 5 148 8. Mrs Anderson took 2 hours to travel from Town A to Town B at an average speed of 45 km/h. On her return journey, she took an extra 1 2 h. What was Mrs Anderson’s speed on her return journey? (1) 20 km/h (2) 36 km/h (3) 40 km/h (4) 72 km/h ( ) 9. Kenneth left his house at 8.20 a.m. and travelled 140 km to his grandparents’ house. If Kenneth travelled at a speed of 80 km/h, what time would he reach his grandparents’ house? (1) 09.05 a.m. (2) 10.05 a.m. (3) 10.50 a.m. (4) 11.05 a.m. ( ) 10. Sarah ran at a speed of 12 km/h for 3 minutes and then jogged at a speed of 6 km/h for 5 minutes. Find the total distance that Sarah had travelled. (1) 66 m (2) 110 m (3) 300 m (4) 1100 m ( ) 11. The solid above is made up of 1-cm cubes. What is the volume of the solid? (1) 8 cm3 (2) 9 cm3 (3) 10 cm3 (4) 12 cm3 ( ) 12. Solid A Solid B How many cubes must be taken away from Solid A to form Solid B? (1) 6 (2) 7 (3) 8 (4) 9 ( ) 13. An aquarium measures 28 cm by 16 cm by 8 cm. What is the capacity of the tank? 2 2 4 3 2 For Teachers Only
General Revision 2 149 (1) 3500 cm3 (2) 3548 cm3 (3) 3584 cm3 (4) 3854 cm3 ( ) 14. The figure below is made up of 1-cm cubes. They are glued together to form a solid. Find the total volume of the solid. 1 cm (1) 9 cm3 (2) 10 cm3 (3) 11 cm3 (4) 15 cm3 ( ) 15. What is 12 l 84 ml in cm3 ? (1) 1.284 cm3 (2) 12.084 cm3 (3) 12 840 cm3 (4) 12 084 cm3 ( ) 16. The volume of water in a pail is 1045 cm3 . Express the volume of water in l and ml. (1) 1 l 45 ml (2) 1 l 450 ml (3) 10 l 450 ml (4) 10 l 45 ml ( ) 17. The perimeter of the base of a cubical tank is 100 cm. What is the volume of the tank? (1) 1000 cm3 (2) 2500 cm3 (3) 15 625 cm3 (4) 1 000 000 cm3 ( ) 18. The tank contains 96 cm3 of water. The water level reaches 2 3 of the height of the tank. Find the height of the tank. 8 cm 2 cm (1) 6 cm (2) 9 cm (3) 32 cm (4) 64 cm ( ) 3 4 4 1 3 2 For Teachers Only
Mathematics Grade 5 150 19. The base area of Container A and B is both 16 cm2 . Container A has a height of 10 cm. The height of Container B is 3 5 of the height of Container A. What is the average volume of both containers? Container A Container B 16 cm2 16 cm2 10 cm 6 cm (1) 64 cm3 (2) 112 cm3 (3) 128 cm3 (4) 256 cm3 ( ) 20. The line graph shows the number of bowls of noodles sold in a school canteen for a week. 0 20 40 60 80 100 Mon Number of bowls of noodles sold in a school canteen Tue Wed Thu Fri Day Number of bowls of noodles sold On which two days recorded the greatest difference in sales? (1) Wednesday and Friday (2) Tuesday and Thursday (3) Monday and Tuesday (4) Tuesday and Friday ( ) 3 2 For Teachers Only
General Revision 2 151 B Answer the following questions. 1. Complete the following figure to form a cuboid. 2. Find the volume of each solid. (a) 15 cm 9 cm 4 cm (b) 12 cm 12 cm 12 cm Volume = cm3 Volume = cm3 3. How many 1-cm cubes are needed to fill up half of the container below? 5 cm 8 cm 4 cm 540 1728 80 Volume of container = 8 cm × 4 cm × 5 cm = 160 cm3 Half of the container = 1 2 × 160 cm3 = 80 cm3 80 1-cm cubes are needed. 80 1 For Teachers Only
Mathematics Grade 5 152 4. Express 13 25 as a percentage. 5. Express the ratio of 35 g to 1 kg in its simplest form. 6. 5 : 7 : 3 = 30 : P : 18, what is the value of P? 7. Find the volume of a cube of edge 27 cm. 8. Matthew ran 7.5 km in an hour. What is his average speed in m/min? 52% 7 : 200 42 19 683 cm3 125 m/min 13 25 × 100 = 52% 4 1 Edge = 27 cm Volume = 27 cm × 27 cm × 27 cm = 19 683 cm3 P = 7 × 6 = 42 35 : 1000 ÷ 5 ÷ 5 = 7 : 200 5 : 7 : 3 × 6 × 6 × 6 = 30 : P : 18 7.5 km = 7500 m 1 h = 60 min Speed = Distance Time = 7500 60 = 125 m/min 125 1 1 kg = 1000 g For Teachers Only
General Revision 2 153 9. Express 17 770 ml in cm3 . 10. A cuboid has a rectangular base of 5 cm by 6 cm. If its volume is 240 cm3 , what is the height of the cuboid? 11. A rectangular container 4 cm by 5 cm by 20 cm is filled with water up to 4 5 of its height. What is the volume of water in the container? 12. Nora received Rp 75.000,00 from her father. She spent Rp 63.750,00 and saved the rest. What percentage of her money did she save? 5 cm × 6 cm × Height = 240 cm3 30 cm2 × Height = 240 cm3 Height = 240 cm3 ÷ 30 cm2 = 8 cm Volume of water in container = 4 5 × 4 cm × 5 cm × 20 cm = 320 cm3 8 cm 15% 320 cm3 17 770 cm3 Amount saved = Rp 75.000,00 – Rp 63.750,00 = Rp 11.250,00 11250 75 000 × 100% = 3 20 × 100% = 15% She saved 15% of her money. 3 1 5 20 For Teachers Only
Mathematics Grade 5 154 13. Intan wants to buy a book which costs Rp 58.000,00. She only has 75% of the money that needed to buy the book. How much more money does she need? 14. Alya, Murni and Rosa shared some beads among themselves. Charlotte received 16% while Bernice received 60%. Bernice received 110 more beads than Charlotte. How many beads did Alison receive? 15. Lydia has Rp 800.000,00 in her savings account. After 1 year, her savings has increased to Rp 840.000,00. What was the interest rate per year offered by the bank? 16. A roll of ribbon measures 2 m 3 cm. Yasmin cuts cut 70% off it. Find the length of the remaining ribbon. Give your answer in cm. 75 100 × Rp 58.000,00 = Rp 43.500,00 Amount of money needed = Rp 58.000,00 – Rp 43.500,00 = Rp 14.500,00 She needs Rp 14.500,00 more. Charlotte 16% Bernice 60% Alison 100% – 60% – 16% = 24% Bernice received 44% more than Charlotte. 44% 110 1% = 110 ÷ 44 = 2.5 24% = 24 × 2.5 = 60 Alison received 60 beads. Rp 14.500,00 60 60.9 Rp 840.000,00 – Rp 800.000,00 = Rp 40.000,00 Rp 40 000 Rp 840 000 × 100% = 1 20× 100% = 5% The interest rate per year offered by the bank is 5%. 5% 1 1 20 5 Percentage of remaining ribbon = 100% – 70% = 30% 2 m 3 cm = 200 cm + 3 cm = 203 cm Length of the remaining ribbon = 30 100 × 203 cm = 60.9 cm For Teachers Only
General Revision 2 155 17. The ratio of the number of Steve’s marbles to the number of Ivan’s marbles to the number of Nigel’s marbles is 12 : 3 : 7. Ian has 36 fewer marbles than Steve. How many more marbles does Steve have than Nigel? 18. A rectangular tank with a square base is 2 5 filled with water. How much more water is needed to fill the tank to its brim? Give your answer in millilitres. 49 cm2 6 cm 15 cm 19. A toy robot moves at a speed of 70 m/min. If its speed increases by 20%, how far can it travel in an hour? Give your answer in km. 20. Susan took 48 minutes to travel from Town X to Town Y. Her speed was 75 km/h. If Matthew travelled at a speed of 90 km/h, how long would he take to travel the same journey? Steve : Ivan : Nigel 12 : 3 : 7 12 units – 3 units = 9 units = 36 marbles 1 unit 36 ÷ 9 = 4 marbles Volume of water needed to fill the tank to its brim = Remaining volume of tank = 49 cm2 × (15 cm – 6 cm) = 49 cm2 × 9 cm = 441 cm3 = 441 ml 12 units – 7 units = 5 units 5 × 4 = 20 Steve has 20 more marbles than Nigel. 20 441 ml 5.04 km 40 min 100% + 20% = 120% Speed = 120 100 × 70 m/min = 84 m/min 1 min = 84 m 1 h = 60 min 60 min = 60 × 84 m = 5040 m = 5040 m ÷ 1000 = 5.04 km Distance between Town X and Town Y = 48 60 h × 75 km/h = 60 km Time taken = Distance Speed = 60 90 = 2 3 h = 2 3 × 60 min = 40 min 12 15 4 1 2 3 20 1 For Teachers Only
Mathematics Grade 5 156 C Study the line graph below and answer the following questions. The line graph below shows the number of visitors to an art exhibition. Number of visitors Number of visitors to art exhibition 20 40 60 80 100 120 140 160 180 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month 1. Which month had the greatest number of visitors? 2. Which two months had the same number of visitors? 3. In which month did 120 people visit the art exhibition? 4. Between which two months did the number of visitors decrease the most? September January and March may August and September For Teachers Only
General Revision 2 157 D Solve the following word problems. 1. Water from a tap flows into an empty tank at 3.15 l per minute. How much water is in the tank after 8 minutes? Express your answer in litres and millilitres. 2. A rectangular tank is 80% filled with water. (a) What is the ratio of the volume of water in the tank to the capacity of the tank? (b) If the volume of water in the tank is 4200 cm3 , what is the capacity of the tank? 8 × 3.15 l = 25.2 l 0.2 l = 0.2 × 1000 = 200 ml 25.2 l = 25 l + 200 ml = 25 l 200 ml 25 l 200 ml of water is in the tank. (a) 80% : 100% = 8 : 10 = 4 : 5 The ratio of the volume of water in the tank to the capacity of the tank is 4 : 5. (b) 4 units 4200 cm3 1 unit 4200 cm3 ÷ 4 = 1050 cm3 5 units 5 × 1050 cm3 = 5250 cm3 The capacity of the tank is 5250 cm3 . For Teachers Only
Mathematics Grade 5 158 3. A rectangular container with a base area of 144 cm2 and a height of 10 cm is 2 5 filled with lemonade. All the lemonade is poured into some cups with a capacity of 18 ml each. How many cups are needed to hold all the lemonade in the container? 4. A cubical tank of edge 40 cm is 70% filled with water. If the water is pumped out at a constant rate of 25 ml per minute, how long will it take to empty the tank? Give your answer in hours and minutes. 144 cm2 × 10 cm = 1440 cm3 The volume of the container is 1440 cm3 . 2 5 × 1440 cm3 = 576 cm3 576 cm3 = 576 ml The amount of lemonade in the container is 576 ml. 576 ml ÷ 18 ml = 32 32 cups are needed to hold all the lemonade in the container. 1 288 40 cm × 40 cm × 40 cm = 64 000 cm3 The volume of the tank is 64 000 cm3 . 70% = 70 100 60 100 × 64 000 cm3 = 44 800 cm3 44 800 cm3 = 44 800 ml The amount of water in the tank is 44 800 ml. 44 800 ml ÷ 25 ml = 1792 min 1 h = 60 min 1792 min ÷ 60 = 29 R 52 = 29 h 52 min It takes 29 hours 52 minutes to empty the tank. For Teachers Only
General Revision 2 159 5. A rectangular tank measuring 17 cm by 15 cm by 12 cm is completely filled with water. Peter pours some of the water from the tank to fill up a cubical container to its brim. The edge of the container is 7 cm. (a) What is the capacity of the rectangular tank? (b) How much water is left in the rectangular tank? Give your answer in litres and millilitres. 6. The length and breadth of a rectangle are in the ratio 5 : 3. The perimeter of the rectangle is 48 cm. Find the area of the rectangle. (a) 17 cm × 15 cm × 12 cm = 3060 cm3 The capacity of the rectangular tank is 3060 cm3 . (b) 7 cm × 7 cm × 7 cm = 343 cm3 The volume of the container is 343 cm3 . 343 cm3 = 343 ml 3060 cm3 = 3060 ml 3060 ml – 343 ml = 2717 ml 2717 ml = 2000 ml + 717 ml = 2 l + 717 ml = 2 l 717 ml 2 l 717 ml of water is left in the rectangular tank. Length + Breadth = Perimeter ÷ 2 48 2 = 24 cm 8 units 24 cm 1 unit 24 8 = 3 cm The area of the rectangle is 135 cm2 . 3 units 5 units 24 cm Length Breadth Length = 5 units = 5 × 3 cm = 15 cm Breadth = 3 units = 3 × 3 cm = 9 cm Area of rectangle = 15 cm × 9 cm = 135 cm2 For Teachers Only
Mathematics Grade 5 160 7. There are red, blue and yellow balls in a box. 25% of the balls are red and 37% of them are blue. The total number of the red and yellow balls is 189. How many balls are there in the box? 8. The ratio of the length of a rectangle to its breadth is 5 : 4. The breadth of the rectangle is 19 cm shorter than the length of the rectangle. What is the perimeter of the rectangle? Red 25% Blue 37% Yellow 100% – 25% – 37% = 38% Red + Yellow = 25% + 38 = 63% 63% = 189 1% = 189 ÷ 63 = 3 There are 300 balls in the box. 19 cm Length Breadth ? ? ? ? 1 unit = 19 cm Length = 5 units = 5 × 19 = 95 cm Breadth = 4 units = 4 × 19 = 76 cm Perimeter = (95 + 76) × 2 = 171 × 2 = 342 cm The perimeter of the rectangle is 342 cm. Blue 37% 37 100 × 3 = 111 There are 111 blue balls in the box. Red + Yellow + Blue = 189 + 111 = 300 For Teachers Only
General Revision 2 161 9. Mr Leong drove 72 km from Town L to Town M at a speed of 108 km/h. He took a rest at Town M for 1 4 hour and drove for 45 minutes to Town N. The speed of his car was 120 km/h. (a) Find the distance between Town L and Town N. (b) Find the average speed of Mr Leong’s car from Town L to Town N. (a) Distance between Town L and Town N = 72 km Distance between Town M and Town N = 120 × 45 60 = 90 km Distance between Town L and Town N = 72 km + 90 km = 162 km The distance between Town L and Town N is 162 km. (b) Time taken from Town L to Town M = 72 108 = 2 3 h = 2 3 × 60 min = 40 min Total time taken = 40 min + 15 min + 45 min = 100 min = 100 60 h = 1 2 3 h Average speed = Total distance Total time taken = 162 ÷ 1 2 3 = 162 ÷ 5 3 = 162 × 3 5 = 97.2 km/h The average speed of Mr Leong’s car from Town L to Town N was 97.2 km/h. 2 1 5 3 6 93 2 20 1 For Teachers Only
Mathematics Grade 5 162 10. A motorist travels from Town A to Town B at a speed of 104 km/h. A lorry driver travels from Town B to Town A at a speed of 92 km/h. Both of them use the same route and set off at the same time. (a) If the motorist and the lorry driver meet each other at the highway 90 minutes later, find the distance between Town A and Town B. (b) Find the time taken by the motorist to travel from Town A to Town B. Give your answer in hours and minutes. (Round off your answer to the nearest minute.) (a) 90 min = 60 min + 30 min = 1 h + 30 min = 1 h 30 min = 1 1 2 h = 3 2 h Distance travelled by motorist = 104 km/h × 3 2 h = 156 km Distance travelled by lorry driver = 92 km/h × 3 2 h = 138 km Distance = 156 km + 138 km = 294 km The distance between Town A and Town B is 294 km. (b) Time taken = Distance Speed = 294 km 104 km/h = 2 43 52 h = 2 h + ( 43 52 × 60 min ) = 2 h + 49.62 min ≈ 2 h 50 min The motorist takes 2 h 50 min to travel from Town A to Town B. 52 46 1 1 104 km/h 92 km/h Town A Town B For Teachers Only
General Revision 2 163 11. 10.000,00 20.000,00 30.000,00 40.000,00 50.000,00 60.000,00 70.000,00 80.000,00 90.000,00 0 Savings (Rp) Jun July Aug Sept Month Nov Dec Yati’s savings from June to December The line graph above shows Yati’s savings over six months from June to December. (a) How much more money did Yati save in December than in June? (b) In which month did Yati’s savings grow 1 3 of the savings of its previous month? (a) Amount saved in December = Rp 70.000,00 Amount saved in June = Rp 30.000,00 Yati saved Rp 40.000,00 more in December than in June. (b) Amount saved in September = Rp 60.000,000 Amount saved in August = Rp 45.000,00 (Rp 60.000,00 – Rp 45.000,00) Rp 45.000,00 = Rp 15.000,00 Rp 45.000,00 = 1 3 In September, Yati’s savings grew 1 3 of the savings in August. 1 3 For Teachers Only
Mathematics Grade 5 164 12. The pie chart shows the different types of drinks sold in a coffee shop in a day. 272 glasses of drinks were sold. The ratio of the number of glasses of tea sold to the number of glasses of fruit juice sold to the number of glasses of vegetable juice sold was 5 : 2 : 1. (a) How many glasses of fruit juice were sold? (b) How many fewer fruit juice were sold than tea? Tea Fruit juice Vegetable juice Coffee (a) Tea : Fruit juice : Vegetable juice 5 : 2 : 1 Number of glasses of coffee = 1 2 × 272 = 136 glasses Total number of units of tea, fruit juice and vegetable juice = 5 units + 2 units + 1 unit = 8 units 8 units = 272 – 136 = 136 glasses. 1 unit = 136 8 = 17 glasses Number of glasses of fruit juice sold = 2 × 17 = 34 glasses 34 glasses of fruit juice were sold. (b) 51 glasses Tea = 5 units = 5 × 17 = 85 glasses 85 – 34 = 51 glasses 51 glasses fewer fruit juice were sold than tea. 1 136 1 17 For Teachers Only
MINDS-ON MATHS workbooks are written to complement the textbooks and to meet the learning needs of Indonesian pupils from Primary 1 to 6. This series uses the Singapore Maths Method which is proven to be one of the most effective teaching approaches in the world. It offers pupils essential practice to ensure a full understanding of the topics. These workbooks also provide a variety of exercises and word problems that correspond to every chapter in the textbooks, making them perfect for either classroom use or homework. SPECIAL FEATURES Exercises to reinforce essential concepts, skills and problem solving ability. Summary of key ideas at the beginning of each chapter help pupils to revise the mathematical concept taught. Worked examples to strengthen pupils’ understanding. General revisions for the consolidation of concepts and skills. JWRB211035 ISBN 978-981-17099-6-8 MINDS-ON MATHS comprises : Textbook Workbook Teacher’s Guide Digital Handbook For Teachers Only
