P6 - Volume, Rate, Speed Whole, Numbers

for Primary 6 students | taught by Math Arena
  • 142 Videos
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Course Curriculum

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Volume Rate Speed Set A
P6VRSV1-A - learnbrill
1) A rectangular container is 33 cm by 20 cm by 22 cm. Find the maximum number of 5-cm cubes that can be placed into the container.
2) The total area of all the faces of a cube is 864 cm2. Find its volume.
3) If the volume of a cube is equal in value to its total surface area, find its length.
4) In the diagram below, not drawn to scale, PQRS is a rectangle piece of cardboard. 4 shaded squares are cut off and the remaining piece is folded along the dotted line to make an open box with rectangle base ABCD.
5) The figure below shows the net of a box with square base. The area of one of its rectangular faces is 312 cm2 and the area of one of its square faces is 676 cm2.
6) A cuboid measuring 18 cm by 24 cm has a smaller cuboid removed from its centre, forming the solid below.
7) Faith has 2 tanks, A and B of different capacities. If tank A is filled by a tap at a rate of 3 litres per minute and tank B is filled by a tap at a rate of 5 litres per minute, when tank A is completely filled,
8) A tank was 80% full of water. Ali poured 280 cm3 of water into the tank of water. a. How much more water was needed to fill up the tank completely? b. Ali used a mug with a capacity of 160 ml to fill up the tank completely.
9) The rectangle tank shown below was 16% filled with water. The water in the tank was poured into another cubical tank of edge 44 cm. The cubical tank was filled up completely.
10) The figure shows an empty transparent vase made from three containers. The two containers on top are in the form of cuboids which have square bases of side 6 cm and 4 cm as shown in the figure.
11) The diagram below shows a tank made of some identical sections. Figure A shows one section of the tank. a. Find the volume of figure A. b. 5616 cm3 of water was poured into the tank. Find the water level in the tank.
12) The figure below, not drawn to scale, shows a cube with 3 painted parts A, B and C. These painted parts are of the same area and they are touching the midpoints of the sides of the cube. The total area of the painted parts is 54 cm2.
13) Figure 1 shows a container, with a base area of 225cm2 holding some water. It was then inverted as shown in Figure 2.
14) The container shown below was filled with water to a height of 32 cm at first. Then, half of the water was poured out of the container. What was the height of the water level after that?
15) Figure A below shows a tank of height 70 cm and is made up of 4 different containers. The bottom 3 hollow cuboids have a height of 20 cm and square bases of sides 5 cm, 10 cm and 15 cm. The top container is in the form of a cube of side 50 cm.
16) A tank was 2/3 filled with water to a height of 20 cm. a. What is the capacity of the tank? b. When a glass ball was dropped into the tank, the height of the water level was 1.5 cm from the brim of the tank. Find the volume of the glass ball.
17) 3 identical cans were put into a tank with a base area of 50 cm × 30 cm as shown in the diagram. When all the cans were taken out, the water level dropped by 12 cm. a. What was the volume of one can? FREE PREVIEW
18) Mei Mei poured some water into Tank A and Tank B until the water levels in both tanks were the same. She then realised that the total amount of water in both tanks was 19 200 ml. FREE PREVIEW
20) An equal amount of water is poured into two tanks, Tank A and Tank B. The base area of Tank A is 30 cm2 and the base area of Tank B is 75 cm2. If Tank A is 3/4 filled with water, what is the height of the water level in Tank B? FREE PREVIEW
21) An empty Container G measures 45 cm by 18 cm by 37.5 cm. Container H with a base area of 1125 cm2 was completely filled with water. Ronald poured 5/11 of the water from container H into container G. The water filled 2/3 of Container G.
22) A rectangular tank measuring 10 m and 2.5 m wide is completely filled with water. When 30% of the water from the rectangular tank is poured into an empty cylindrical container, the container is only 25 % full.
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Volume Rate Speed Set B
P6VRSV1-B - learnbrill
1) Tom and Jerry take 1 hour to clean the fish tank together. If Tom takes 3 hours to clean the tank on his own, how long will it take Jerry to clean he tank alone?
2) Printer A can print 55 pages in a minute and Printer B can print 60 pages in a minute. If both printers start printing at the same time, how long will it take for both printers to print 3220 pages altogether?
3) Two taps, X and Y, were turned on at the same time to fill a tank 109 cm by 50 cm by 100 cm. The tank had a plug which was attached to the bottom. Water from the two taps flowed into the tank at 2.2 l/min and 1.7 l/min respectively.
4) A tank was 1/3 filled with water at first. Dillon turned on a tap and let water flow into the tank at a rate of 1.36L per minute. After 15 minutes, he turned off the tap. How much water had overflowed?
5) Two tanks, S and T, are shown below. Both tanks are filled to the brim in the beginning. At 1010, the tap at Tank T is turned on to drain the water from it. At 1012, the tap at Tank S is turned on.
6) A tank completely filled with water was being emptied by 2 taps as shown in the diagram below. Tap A was turned on first and after 5 minutes, Tap B was turned on. All the water in the tank was completely emptied after 25 minutes.
7) Tank K measuring 54 cm by 14 cm by 25 cm contains 4.7l of water. It is being filled with water flowing from Tap C at 0.9 l/min and Tap D at 995 ml/min.
8) A man parked his car in Changi Airport from 7.35 a.m. to noon. How much did he have to pay? *table below*
9) The water bill is charged at the following rates: *table below* a. Mr Tan's family used 28 units. How much did Mr Tan pay? b. Mr Lee's family used 48 units. How much did Mr Lee pay?
10) The table shows the parking charges at a car park. *table below* Mrs Lee parked her car for 3 ½ hours at the car park. a. How much did Mrs Lee pay for parking her car at the car park? Give your answer in term of b.
11) The table below shows the postage charges for sending parcels to Happyland. a. Find the postage charges for sending a parcel weighing 80g to Happyland.
12) The table below shows the rates for renting a bicycle at the kiosk. Gabriel paid $13.50. What is the longest possible time he had rented the bicycle? Give your answer in hours and minutes.
13) "Chatty" Phone Company offers mobile phone services and charges at the following rate: *table below* a. In February, Jane made 180 minutes of outgoing calls and sent a total of 1000 SMS. How much was her total bill if she had subscribed to Plan A?
14) Lincoln wants to subscribe to a mobile phone plan. The following plans are available: *table below* If Lincoln’s usage for a particular month is 2h 20min,
15) When Mr Lim started on his journey to Malaysia, he has 18.4 litres of petrol in the petrol tank of his car. After travelling for a few hours, he found that he had only 4.8 litres of petrol left. He then pumped in $40 worth of petrol.
16) Faizal took part in a 42-km triathlon. He completed the race by swimming 1 km, cycling for 1 ½ hours and running 5km. Find Faizal’s cycling speed.
17) A car travelled 90 km in 1 hour 20 minutes. It then travelled another 3 hours at 100 km/h. Find the average speed of the car for the whole journey.
18) Kalli cycles to school every day. If he cycles at a speed of 11 km/h, he would reach school at 6.50 am. If he cycles at 9 km/h, he would reach school 20 minutes later.
19) A car travelled at 70 km/h for 21/2 hours. Then it travelled at 84 km/h for 31/2 hours. What was its average speed for the whole journey?
20) Mr Kamal took a total of 35/6 hours to drive from City A to City B. His average speed for the whole journey was 90 km/h. He travelled the first 40% of the journey at a speed of 92 km/h. The next 30% of the journey took him 50 minutes.
21) After hiking for 30 km, Martin took a break before he continued hiking 1/3 of the remaining distance. He then realised that he still had 1/4 of the total distance not completed.
22) Jeremy left Town A and drove to Town C. After travelling 3/7 of the journey at an average speed of 72 km/h for 1 1/2h, he stopped at Town B. He took a 20 min break at Town B.
23) Car A and Car B travelled between Cape Town and Maxi Town. Car A took 8 hours to travel from Cape Town to Maxi Town while Car B took 10 hours to travel from Maxi Town to Cape Town. Both Car A and Car B left for their destination at the same time.
24) A van took 3 hours to travel from Town A to Town B at an average speed of 65km/h. A lorry travelled along the same route at an average speed of 75 km/h. The lorry arrived at Town B at 1630.
25) At 8.30am, a motorcycle left Town A for Town B travelling at 60 km/h. 1 ½ hour later, a car left Town a travelling at 85 km/h. The car overtook the motorcycle midway between Town A and Town B, and reached Town B first.
26) Alex, Bala and Charlie were all standing in a circular track for a race to start. All of them had to run in a clockwise direction as shown in the diagram below. Charlie was 300 m ahead of Bala and Bala was 100 m ahead of Alex.
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Volume Rate Speed Set C
P6VRSV1-C - learnbrill
1) Gerald and Bryan ran round a 800 m circular track. Gerald ran at a speed of 215 m/min and Bryan at a speed that was 50 m/min slower than Gerald throughout the race.
2) Khamed and Arafin started cycling from the same place but in the opposite directions. After 4 hours, they were 174 km apart. Khamed’s average cycling speed was 12.5 km/h slower than Afafin’s. What was Arafin’s average cycling speed?
3) Mandy and Candy started jogging from the same place but in opposite directions along a straight road. After 7 minutes, they were 1.75 km apart. Mandy’s average jogging speed was 50 m/min faster than Candy’s average jogging speed.
4) Leon and Ken started jogging at the same time from a flag pole in opposite directions along a straight path for 20 minutes. Leon’s average speed was twice that of Ken’s. Then both Leon and Ken made an about-turn and jogged
5) Jonathan and Benjamin started walking from Point A but in the opposite direction. After walking for 3/4 hours, they were 7.2 km apart. Jonathan’s speed was 1.4 km/h slower than Benjamin.
6) Randy and Owen left Town W for Town X at the same time. When Randy reached Town X in 4 hours, Owen had only completed 3/8 of the distance between the two towns. Owen's speed was 30 km/h slower than Randy. What was Randy's speed?
7) Paul and Sam started out on a 10-km walkathon at the same time. Both of them were walking at uniform speeds. When Sam completed the 10-km walkathon, Paul still had 2.5 km to walk.
8) A car and a lorry were travelling towards Suntec City. When the car overtook the lorry, they were 72 km away from Suntec City. The car arrived at Suntec City 45 minutes earlier than the lorry.
9) At 12 noon, a car left Town A for Town B at an average speed of 100 km/h while a bus left Town B for Town A at an average speed of 80 km/h. At 4.30pm, the two vehicles were 20 km apart. Find the distance between Town A and Town B.
10) Tim and Jeffrey both drove from Town A to Town B. Tim started his journey at 9am and travelled at an average speed of 75km/h. Jeffrey started his journey some time later. At 11am, Jeffrey overtook Tim.
11) A van and a car started travelling from Town X to Town Y at the same time. After 5 hours, the car reached Town Y while the van covered only 7/10 of the journey.
12) Ivan cycled from the school to the library at 80m/min. His sister cycled from the library to the school at 65 m/min. Both of them started cycling towards each other at the same time and did not change their speeds throughout their journey.
13) Mary started cycling from home to school at a speed of 300 m/min at 6 a.m. Her brother started cycling from home later. They were beside each other at 6.30 a.m. and her brother reached school at 7 a.m. while Mary was still 1800 m away.
14) A van left Town A for Town B at the same time when a car left Town B for Town A. The average speed of the van was 50 km/h and the average speed of the car was 75 km/h. The car took 90 min less than the van to reach their destination.
15) Aaron and Benjamin started jogging at the same time along a 4-km track from the same starting point. Both did not change their speeds from start to finish. Aaron jogged a 125 m/min. Benjamin took 8 minutes more to finish the jog.
16) Andrew and Benny both drove from Town A to Town B at constant speed. Andrew left Town A at 7.30am and travelled at an average speed of 80km/h. Benny started his journey some time later. At 12 noon,
17) Joe and Muthu took part in a 5 km race. Both of them did not change their speeds throughout the race. Muthu ran at a speed of 200 m/min. When Muthu reached the finishing line, Joe was 750 m behind him. What was Joe’s speed in km/h?
18) David and his brother John decided to cycle from his home to the library using the same route. They started cycling at the same time. David cycled at a speed of 15km/h. Both of them did not change their speed throughout the race.
19) Town Sinai and Town Malam were 375 km apart. Peter left Town Sinai for Town Malam at 10.00 am travelling at an average speed of 75 km/h. Fredd left Town Sinai sometime later than Peter and overtook him at 12 noon.
20) A van left Town E at 11 00 and travelled towards Town F. Two hours later, a car left Town E for Town F and travelled along the same route. The car passed the van at 16 00. The average speed of the car was 40 km/h faster than the van.
21) Andy started driving from Town A to Town B at an average speed of 80 km/h at 9 am. Benny started driving from Town B to Town A at an average speed of 100 km/h at 9.30 am. After 30 minutes of driving, Benny covered 1/5 of his journey.
22) John rode his bicycle at an average speed of 20 km/h from Town A to Town B at 1 pm. 30 minutes later, Ken started riding his bicycle at an average speed of 40 km/h from Town A to Town B. How much time did Ken need to catch up with John?
23) At noon, a lorry started from Town P and travelled towards Town Q. Three hours later, a car started from Town P and overtook the lorry at 6 pm. The lorry arrived at Town Q at 10 pm. At what time did the car reach Town Q?
24) At 08 00, Reuben started from Town X and travelled towards Town Y and did not change his speed. At 09 00, Mingwei started his journey from Town X towards Town Y at an average speed of 72 km/h. Mingwei overtook Reuben at 12 00. After overtaking,
25) Mr. Goh and Mr. Lim drove from Singapore to Kuala Lumpur. Mr. Goh left Singapore at 0540 and he took 5 hours to reach Kuala Lumpur. Mr. Lim started 30 minutes later than Mr. Goh and he took 4 hours to reach Kuala Lumpur.
26) Jack started driving from Town X towards Town Y at 13 40 at an average speed of 70 km/h. Muthu began driving from Town X towards Town Y at 15 10 at an average speed of 100 km/h.
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Whole Numbers Set A
P6WNV1-A - learnbrill
1) When Mr Young was 40 years old, his son’s age was twice of his daughter’s age. When his daughter is 28 years old, then Mr Young’s age would be twice of his son’s age. How old would Mr Young be when his daughter is 23 years old?
2) Mr Lee mixed 5 litres of syrup with 23 litres of water to make some fruit punch. He then poured all the fruit punch into cups. If each cup contained 200 ml of fruit punch and he sold each cup at $0.40,
3) What is the least number of children a family should have so that every child will have at least one brother and one sister?
4) Emily is 12 years old now. When she reaches her mother’s present age, their total age would be 84 years old. Her mother gave birth to her 3 years after getting married. How old was Emily’s mother when she married?
5) Amy had some money. If she bought a table and 5 identical chairs, she would spend all her money. If she wanted to buy a table and an oven that cost $254 more than a chair,
6) There were 120 participants in a baking competition. ½ of them won either the god or the silver award. 3/4 of them received the silver of the commendation award. How many of them received the silver award?
7) Calix and Brooklyn each had some savings. They wanted to buy a water-bottle of the same cost. Calix was short of $22 and Brooklyn was short of $3. When they combined their savings, they still did not have enough money to buy one water-bottle.
8) A concert ticket for an adult cost $48. A ticket for a child cost half the price of an adult’s ticket. Mrs. Tay bought twice as many adult tickets as children tickets and paid $2160. How many adult tickets did Mrs. Tay buy?
9) Mrs Qu bought 3kg of chicken and 8kg of prawns for $105. 1kg of prawns cost as much as 1.5kg of chicken. Find the cost of 1kg of chicken.
10) Mrs Tay needs 250 g of flour to make 12 cupcakes. She has 750 g of flour. What is the greatest number of cupcakes she can make?
11) 1 kg of crabs cost $67.20 and 1 kg of prawns cost $16.80. Ali paid $1713.60 for some crabs and prawns. He bought 3 kg more crabs than prawns. What was the mass of crabs bought by Ali?
12) When Jane started folding paper crane. Rose had already folded 80 paper cranes. For every 7 paper cranes that Jane folded, Rose folded 5 paper cranes. How many paper cranes would Jane have folded when both girls had the same number of paper cranes?
13) May put some $10 notes into envelope A and some $5 notes into envelope B. There were 10 more notes in B than in A but there was $40 more in A than in B. How much money did she put in A?
14) Adam had a total of 100 10¢, 20¢ and 50¢ coins in his piggy bank. The ratio of the number of 10¢ coins to the number of 50¢ coins is 9 : 17. Given that he had $32.60 in his piggy bank, how many 20¢ coins did he have?
15) Sue spent $153.15 on some key chains and bookmarks at a gift shop. A bookmark cost $3.80 and key chain cost $5.35. Sue bought 9 fewer key chains than bookmarks. How many key chains and bookmarks did she buy altogether?
16) Box A contains only 50-cent coins while Box B contains only 20-cent coins. There are 19 more coins in Box B than in Box A. The total amount of money in Box A and Box B is $15. How many 50-cent coins can all the 20-cent coins in Box B be changed into?
17) At a funfair, Maeve receive a total amount of $5334 from selling lollipops at 60ecnt each, 45cents each and $1.50 each. She sold 340 more lollipops at 60cents each than at $1.50 each.
18) May spent a total of $69 on some rulers, pen and erasers, 25% of them were rulers and cost 90cents each. The number of pens was 6 more than half the total number of items and the remaining were erasers.
19) The ratio of the number of 20-cent coins to the number of 50-cent coins to the number of $1 coins in a money box is 3 : 5 : 4. The difference in value between the 20-cent coins and the $1 coins is $88.40.
20) Pens and pencils were sold in packets of 2 pens and packets of 3 pencils respectively. Each packet of pens was sold at $5 and each packet of pencils was sold at $0.90. Mrs Chan bought 96 pens and pencils and paid $134.40.
21) During a sale, 6 shelves and 11 vases cost $1471.35. If Lydia bought 9 shelves and 16 vases, she would have spent all her money. Each shelf cost $172.55 more than a vase. Find the amount of money Lydia had at first.
22) At a football match, Patrick and Queenie sold 300 hotdogs in total, while Queenie and Rooney sold 100 hotdogs in total. Given that Patrick sold five times as many hotdogs as Rooney.
23) A pen cost $2.10. Mrs Wee bought 38 pens in January and some pens in February. At the end of the two months, Mrs Wee spent a total of $126 on the pens
24) Toyland factory had 2 machines, X and Y. For every 3 toy bears Machine X produced, Machine Y could produce 5 toy bears. Machine X was turned on first, and it produced 560 toy bears. Then Machine Y was turned on and both machines continued production.
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Whole Numbers Set B
P6WNV1-B - learnbrill
1) For every box of cookies Colleen sells, he earns $1.40. A bonus of $4 is given to him for every 25 boxes of cookies sold. How many boxes of cookies must he sell to earn $964?
2) Mrs Wong was paid $5 for every cooking pot she sold. She was paid a bonus of $20 for every 8 cooking pots she sold. She earned $500 for all the cooking pots she sold. How many cooking pots did she sell?
3) A plot of land with an area of 20 m2 was divided into smaller plots of land with an area of 3/8 m2 each. How many plots of land with area of 3/8 m2 were there? What area of the original plot of land was left?
4) Mrs Rajaratnam has 12.5 m of thread. She cuts the thread equally into shorter pieces. Each of the shorter pieces measures 2 m. a. How many 2-m pieces are there? b. What is the length of the remaining piece?
5) Mrs. Tan bought some files at $5 each. She also bought an equal number of pencil cases at a different price. The average price of a file and a pencil case was $4.
6) John spent $4968 on bags and shoes. The number of pair of shoes he bought was 2/5 the number of bags he bought. The cost of a pair of shoes was $12 more than the cost of a bag. He paid $1512 more on bags than on shoes. Find the cost of a bag.
7) The ratio of Jane’s amount of money to Leonard’s amount of money was 5 : 7. Jane received another $110 while Leonard spent $8. As a result, Leonard has $60 less than Jane. How much money did Jane have at first?
8) The price of a child ticket and an adult ticket to a concert are $3 and $8 respectively. The amount collected from the sale of the child tickets is $730 less than the amount from the sale of the adult tickets.
9) Mrs Lee went to the shop to buy some stationery. She spent half of her money on 45 pens and the other half of her money on 20 notebooks. Each pen costs $1 less than a notebook. How much did Mrs Lee bring?
10) Adeline went shopping with a sum of money She spent all of her money in 2 stores. In each store, she spent $18 more than half of what she had when she entered the store. a. How much did she spent at the second store?
11) Mrs Devi has some sweets for pupils in the Maths Club. If she give each pupils 2 sweets, she will have 3 sweets left. If she gives each pupil 3 sweets, she will need 42 more sweets. How many sweets does she have?
12) A container with 60 balls in it weighed 980 g. When 10 balls were removed from the container, the container with the remaining balls weighed 855 g. Find the mass of 1 ball.
13) In a pond, the number of guppies is 18 less than half of the number of goldfish. The number of goldfish is 2 more than 3 times the number of guppies. How many goldfish are there in the pond?
14) Mena has 4 times as many stickers as Pam plus 16 more. Mena has 8 times as many stickers as Nellie. Pam has 18 more stickers than Nellie. How many stickers does Pam have?
15) Linda had $85 more than Jessica. Michelle had $36 more than the total amount of what Linda and Jessica had. If Michelle had $974 more than Linda, how much money did Michelle have?
16) Geeta gets 50 cents more pocket money than Hani every day. Each of them spends 60 cents a day and saves the rest. If Hani saves $40, Geeta will have saved $20 more than Hani. How much is Hani’s daily pocket money?
17) A faulty weighing machine showed a certain reading even when nothing was placed on it. A box which contained 18 identical bags of flour measure 54.48 kg was put on the faulty weighing scale. After 8 bags were removed from the box,
18) Ahmad receives $5 more pocket money than Faizal each week. Both spend $15 per week on food and save the rest. After a few weeks, Ahmad saves $72 but Faizal only saves $32. a. What is Ahmad’s weekly pocket money?
19) Josiah, Gerald and Marcus had a total of 1280 stamps in their collection. Josiah gave away 2/5 of his stamp collections. Gerald gave away 120 stamps and Marcus gave away twice as many stamps as Josiah. In the end, they had 740 stamps left.
20) Sarah and Johari have some money each. If Sarah spent $22 and Johari spent $12 each day, Johari would still have $21 left when Sarah spent all her money. If Sarah spent $18 and Johari spent $10 each day,
21) Triangular flags, each 22 cm wide, are placed 7 cm apart from each other on a rope as shown in the diagram below. What is the length of the rope used to place 60 such flags?
22) In the diagram shown below, 23 identical toy wheels were placed between two walls with equally spaced gaps between them. The first toy wheel and the last toy wheel were touching the front wall and last wall respectively.
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Whole Numbers Set C
P6WNV1-C - learnbrill
1) Wei Ming and Muthu played a game for 10 rounds. In each round, the winner scored 2 points while the loser was deducted 2 points. At the end of the game, Muthu's total score was 4 points. How many rounds did Wei Ming lose?
3) In a test, 10 marks were awarded for every question answered correctly. 5 marks were deducted for every question answered incorrectly. A candidate answered 7 questions incorrectly and scored 195 marks. Find the total number of questions in the test.
4) There were 20 questions in a quiz. For each question answered correctly, 6 points were awarded. For each question answered incorrectly, 4 points were deducted. For each question left blank, no points were awarded or deducted.
5) In a tele-match, Ryan and Bala completed with each other to get from the starting line to the finishing line by playing the Scissors-Paper-Stone game. Each win of the game allows the winner to move forward by 3 steps.
6) A bus can carry 30 adults or 45 children. If the bus has already 20 adults and 10 children abroad, how many more children can the bus carry?
7) Mary bought a total of 12 vases and jugs for $129. She bought 2 more vases than jugs. A vase cost $3 more than a jug. How much did she pay for each jug?
8) Max paid $7.70 for 6 erasers and 4 pens. With the same amount of money, he could buy 14 erasers. If he had decided to buy pens only, how many pens could he buy with $19.80?
9) Alex and Jen had an equal amount of flour. Jen packed her flour equally into 6 big bags. Alex packed his flour into smaller bags and found her had twice as many bags as Jen. The mass of 3 small bags and 1 big bag of flour was 20kg.
10) The mass of a box containing 9 similar bags and 15 identical books is 48 kg. The mass of the empty box is 750 g. The mass of 3 bags is the same as the mass of 2 books. a. Find the mass of 1 bag in kg.
11) Ken had some big and small packets of flour. The amount of flour in a big packet was 4 times as much as the amount of flour in a small packet. If he repacked 2 big packets of flour into small packets,
12) In the figure below, different combinations of objects X,Y and Z are placed in three identical weighing scales. Find the mass of object Z.
13) Mrs Wong needed 60 apple pies for a party. How much money would she need to pay for the apple pies at the special promotion?
14) Catherine has the same number of 20 cent and 50 cent coins, which add up to a value of $28.00. What is the total number of coins she has?
15) Halimah bought 1 blouse and 4 T-shirts for $39.50. If she bought 4 blouses and 5 T-shirts, she would pay $36 more. How much did 1 blouse cost?
16) Wei Kang bought three times as many notebooks as storybooks and spent a total of $188. He spent $42 more on the storybooks than the notebooks. Given that a storybook cost $9 more than a notebook, find the cost of a notebook.
18) A bar of chocolate cost $0.40. A free bar of chocolate was given for every purchase of 5 bars of chocolate. Diana spent $60 buying some bars of chocolates. Then, she packed the bars of chocolate into packets of 3 each. She sold each packet for $4
19) An artist sprayed 2 different shapes using a stencil on the same wall of the library. She divided the upper part of the wall into equal parts of 1.2 m and sprayed 5 – shaped design on each part as shown in Figure 1.
20) Meng has a total of 1296 black and white buttons. He has 720 more black buttons than white buttons. He puts all the black buttons equally into empty black boxes and puts all the white buttons equally into empty white boxes.
21) Amanda received 2 coins from her mother every day. Each coin was either a 10-cent or a 50-cent coin. Amanda gave her younger brother two 10-cent coins every 5 days. The total value of her coins after 245 days was $125.60.
22) There are 40 boys and girls in a team. During training, each boy runs a distance of 2 km while each girl runs 0.8 km. Given that all the boys and girls have run a total of 53.6 km, how many boys are there in the team?
23) Grade A petrol, which costs $1.60 per litre, is mixed with Grade B petrol, which costs $1.10 per litre. Mr. Ho bought 35 litres of the mixed petrol for $46. How many litres of Grade A and how many litres of Grade B petrol did he buy?
24) 7 eggs cost $4 while 9 turnips cost $11. Mrs Tan bought a total of 1000 eggs and turnips with $999. How many more turnips than eggs did she buy?
25) In a class, each silver star is worth 3 points while each gold star is worth 5 points. Einstein earned a total of 56 stars while Newton earned a total of 48 stars. The ratio of Newton’s points to Einstein’s points is 5 : 6.
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Course description


This course is targeted at Singapore primary school level 6, but is also suitable for primary school level 5 students.

Students will be introduced to methods without use of bar models. Here is our blog post Comparing Bar Model and Non Bar Model Solutions. Here is our post discussing Freed from Singapore “Bar Model” Math.

Based on feedback, many parents have used the videos to learn the methods to help their children to learn faster.

Math Arena students gain an edge using techniques that we teach here in our videos, these methods provide accuracy and speed. We believe it also provides better understanding of their solution to the question that they are solving.

It can also be used as independent learning or for revision.

Take note in our PDF files. the questions are arranged by similarity for easy question pattern recognition.

The Number of stars indicates level of difficulty. One star is fundamental, 2 stars are moderate. 3 and 4 stars are difficult and challenging. Note due to the student’s ability he may experience difficult questions as easy and easy questions as difficult. So do not be over anxious, if an “easy question” stumped you, just keep practicing.

Course Content

You will :

  • be able to print from PDF files
  • be able to watch and learn from 140 videos
  • learn fast, accurate methods in solving Questions

Course Pre-requisites

You will need to know:

  • Fundamental Heuristic Concepts
  • How to watch videos on your computer


  • PDF files contain the questions, the videos are the solutions to the questions.
  • Question header may not contain the full question as it it limited to 255 characters.
  • Our Videos complements the student’s math lessons in Math Arena.
  • It is common that parents do learn from our videos and work with their children too.
  • The bar model is good for understanding but may be less useful for more complicated questions. It can also lead to harder transition to algebra in their secondary schools.

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Math Arena
Math Arena

The instructor is from Math Arena.The instructor is absolutely passionate about teaching and you'll find the lessons engaging and ultimately rewarding.