P6 Maths SA Paper 2 Word Problems Tao Nan. Word Problem Worksheet & Solutions Tao Nan Paper. P6 Mathematics SA2 2017

Size: px

Start display at page:

Download "P6 Maths SA Paper 2 Word Problems Tao Nan. Word Problem Worksheet & Solutions Tao Nan Paper. P6 Mathematics SA2 2017"

Holly Charity Briggs
5 years ago
Views:

1 Word Problem Worksheet & Solutions Tao Nan Paper P6 Mathematics SA2 2017

2 Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. A list of 13 numbers has an average of 260. When two numbers are removed from the list, the average of the remaining numbers is 231. The difference between the two numbers that are removed is 1. What are the two numbers that have been removed? Ans: 7. ACDE is a rectangle and BDE is a right-angled triangle. ED = 10 cm, BD = 6 cm and BE = 8 cm. Find the length of CD. Ans:

3 8. In the figure, EFGH is a rectangle. ABC is an isosceles triangle and ADE is a rightangled triangle. AB = BC and BG = BH. ACB = 37 and FEJ = 32 Find (a) EJG (b) JAG Ans: (a) (b)

4 9. Debbie and Nick bought the same number of identical books at a bookstore. Debbie paid $165 for all the books she bought. Nick was given a 20% discount. With the discount, he could buy another 3 such books at the original price. What was the price of each book after discount? Ans: 10. Mr Sim and Mr low started driving from Town X to Town Y at the same time along the route shown below. Both did not change their speeds throughout. Mr Sim s average speed was 15 km/h slower than Mr Low s. After 20 min, Mr Low reached Town Y but Mr Sim had only covered 4 5 Low. Find Mr Sim s average speed in km/h of the distance covered by Mr Ans:

5 11. Packets of biscuits were divided equally among 21 families at a charity fair. 7 families gave away 3 4 of their share to the other families. As a result, the other families received 12 more packets of biscuits each. How many packets of biscuits were there at first? Ans: 12. In a kindergarten, 1 3 of the boys and 7 11 of the girls walk to school. 1 2 of the children in the kindergarten walk to school. There are 6 more girls than boys in the kindergarten. How many children are there in the kindergarten altogether? Ans:

6 13. Tank A is filled with water to a height of 64 cm. Tank B and Tank C are empty at first. Some water in Tank A is then poured into Tank B and Tank C until the water level in each of the three tanks has the same height. Find the volume of water in Tank B in the end. Ans:

7 14. In the figure, EFG is an equilateral triangle and HJKL is a rhombus. LHJ = 74 and JKF = 29. LNJ is a straight line. Find (a) (b) NMK HJF Ans: (a) (b)

8 15. Sheryl had $118. This amount of money was just enough to buy 4 large T-shirts and 3 small T-shirts. Sheryl bought 3 large T-shirts and 4 small T-shirts instead. She had $1.50 left. Find the cost of one large T-shirt. Ans:

9 16. Ali had $200 more than Kai Cong at first. After Ali spent $340 and Kai Cong received $120 from his father. Kai Cong had 5 times as much money as Ali. What was the total amount of money they had at first? Ans:

10 17. A club consists of swimmers and runners. There are 108 boys. The number of boys is 3 times the number of girls. The ratio of the number of swimmers to the number of runners is 7 : of the runners are girls. How many swimmers are boys? Ans:

11 18. A square cardboard of side 42 cm has a design formed by a 4-cm wide shaded strip. The outline of the design is made up of quarter circles with centre P and straight lines. All the straight lines meet at right angles. Find the area of the shaded part. (Take π = 3.14) Ans:

12 Answer Key Subject: Primary 6 Maths Word Problem Solutions Paper: SA Tao Nan , cm 8. a) 122 b) $ km/h packets children l 14. a) 137 b) $ $ cm2

13 Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. A list of 13 numbers has an average of 260. When two numbers are removed from the list, the average of the remaining numbers is 231. The difference between the two numbers that are removed is 1. What are the two numbers that have been removed? Grand total of 13 numbers = 260 x 13 = 3380 Grand total of 11 numbers = 231 x 11 = 2541 Total of two numbers removed = = 839 Excess = 1 Smaller number removed = (839 1) 2 = 419 Large number removed = = 420 Ans: 419, ACDE is a rectangle and BDE is a right-angled triangle. ED = 10 cm, BD = 6 cm and BE = 8 cm. Find the length of CD. Let u = length CD Area of triangle BDE = 8 x 6 x 1 2 = 24 cm2 Area of rest of rectangle = 10 x u x 1 2 = 24 5u = 24 u = 4.8 cm Ans: 4.8 cm

14 8. In the figure, EFGH is a rectangle. ABC is an isosceles triangle and ADE is a rightangled triangle. AB = BC and BG = BH. ACB = 37 and FEJ = 32 Find (a) EJG (b) JAG (a) FJE = = 58 EJG = = 122 (b) BAC = 37 EAC = 32 JAC = = 69 Ans: (a) 122 (b) 69

15 9. Debbie and Nick bought the same number of identical books at a bookstore. Debbie paid $165 for all the books she bought. Nick was given a 20% discount. With the discount, he could buy another 3 such books at the original price. What was the price of each book after discount? Discount = 0.2 x 165 = $33 Price per book = 33 3 = $11 Discounted book price = 0.8 x 11 = $8.80 Ans: $ Mr Sim and Mr low started driving from Town X to Town Y at the same time along the route shown below. Both did not change their speeds throughout. Mr Sim s average speed was 15 km/h slower than Mr Low s. After 20 min, Mr Low reached Town Y but Mr Sim had only covered 4 5 Low. Find Mr Sim s average speed in km/h of the distance covered by Mr Difference between distance travelled = 1 5 x total distance Let u = speed of Mr Low Difference in speed = 1 5 u = 15 u = 15 x 5 = 75 km/h Mr Sim s speed = = 60 km/h Ans: 60 km/h

16 11. Packets of biscuits were divided equally among 21 families at a charity fair. 7 families gave away 3 4 of their share to the other families. As a result, the other families received 12 more packets of biscuits each. How many packets of biscuits were there at first? Let u = number of packets received by each family originally Number of packets given away by 7 families = 3 4 x u x 7 = 12 x u = 168 u = 168 x 4 21 = 32 Number of packets at first = 21 x 32 = 672 Ans: 672 packets 12. In a kindergarten, 1 3 of the boys and 7 11 of the girls walk to school. 1 2 of the children in the kindergarten walk to school. There are 6 more girls than boys in the kindergarten. How many children are there in the kindergarten altogether? Let u = number of boys Number of girls = u + 6 Total children = u + u + 6 = 2u + 6 Half total children = u u (u+6) = u + 3 (1) 11u + 21u + 7 x 3 x 6 = 33u + 99 (2) = (1) x 33 u = = 27 Total number of children = 2u + 6 = 2 x = 60 Ans: 60 children

17 13. Tank A is filled with water to a height of 64 cm. Tank B and Tank C are empty at first. Some water in Tank A is then poured into Tank B and Tank C until the water level in each of the three tanks has the same height. Find the volume of water in Tank B in the end. Volume of water in Tank A = 45 x 25 x 64 = cm 3 Total base area = 45 x x x 10 = = 3000 cm 2 Common height of water in the end = = 24 cm In the end volume of water in Tank B = 24 x 57 x 25 = cm 3 = 34.2 l Ans: 34.2 l

18 14. In the figure, EFG is an equilateral triangle and HJKL is a rhombus. LHJ = 74 and JKF = 29. LNJ is a straight line. Find (a) (b) NMK HJF (a) LKJ = 74 EKM = = 77 GEF = 60, NMK = = 137 (b) KJH = = 106 KJF = = 91 HJF = = 163 Ans: (a) 137 (b) 163

19 15. Sheryl had $118. This amount of money was just enough to buy 4 large T-shirts and 3 small T-shirts. Sheryl bought 3 large T-shirts and 4 small T-shirts instead. She had $1.50 left. Find the cost of one large T-shirt. Let u = cost of 1 large T-shirt p = cost of 1 small T-shirt 4u + 3p = 118 (1) 3u + 4 p = = (2) 16u + 12p = 118 x 4 = 472 (3) = (1) x 4 9u + 12p = x 3 = (4) = (2) x 3 7u = (5) = (3) (4) u = Cost of 1 large T-shirt = $17.50 Ans: $17.50

20 16. Ali had $200 more than Kai Cong at first. After Ali spent $340 and Kai Cong received $120 from his father. Kai Cong had 5 times as much money as Ali. What was the total amount of money they had at first? Let u = amount Ali had in the end Amount Kai Cong had in the end = 5u At first, Amount Ali had = amount Kai Cong had u +340 = u 120 4u = = 260 u = = $65 Amount they had at the end = u + 5u = 6u = 6 x 65 = $390 Amount they had at first = = $610 Ans: $610

21 17. A club consists of swimmers and runners. There are 108 boys. The number of boys is 3 times the number of girls. The ratio of the number of swimmers to the number of runners is 7 : of the runners are girls. How many swimmers are boys? Number of girls = = 36 Total number in club = = 144 Ratio of swimmers vs runners 7 : 2 7u : 2u 7u + 2u = 144 9u = 144 u = = 16 Number of swimmers = 7u = 7 x 16 = 112 Number of runners = 2 x 16 = 32 Number of boy runners = 5 8 x 32 = 20 Number of boy swimmers = = 88 Ans: 88

18. A square cardboard of side 42 cm has a design formed by a 4-cm wide shaded strip. The outline of the design is made up of quarter circles with centre P and straight lines.

22 18. A square cardboard of side 42 cm has a design formed by a 4-cm wide shaded strip. The outline of the design is made up of quarter circles with centre P and straight lines. All the straight lines meet at right angles. Find the area of the shaded part. (Take π = 3.14) Outer radius = (42 10) 2 = 16 cm Innner diameter = (32 4) 2 = 14 cm Area of 34 outer circle = π x 16 x 16 x 34 = 192 π Area of 34 inner circle = π x 12 x 12 x 34 = 108 π Area of 34 ring = 192 π π = 84 π = 84 x 3.14 = cm 2 Area of horizontal, vertical bar = ( ) x 4 x 2-4 x 4 = 192 cm 2 Shaded area = = cm 2 Ans: cm 2

P6 Maths SA Paper 2 Word Problems Nanyang. Word Problem Worksheet & Solutions Nanyang Paper P6 Mathematics SA2 2017

P6 Maths SA Paper 2 Word Problems Nanyang. Word Problem Worksheet & Solutions Nanyang Paper P6 Mathematics SA2 2017 Word Problem Worksheet & Solutions Nanyang Paper P6 Mathematics SA2 2017 1 Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. Krishnan and