Word Problem Worksheet & Solutions Modelled after Nanyang Paper P6 Mathematics SA1 2016

Transcription

1 Word Problem Worksheet & Solutions Modelled after Nanyang Paper P6 Mathematics SA Mock exam P6, P5 test papers are based on the latest PSLE question format. The test concepts are modelled after CA1, SA1, CA2, SA2 past year papers set by top schools. The degree of difficulty is the same as top school exam papers. The questions and diagrams are uniquely crafted by graduate teachers. Detailed step-by-step exam solutions with bar models or other diagrams are provided for each questions. The papers are ranked by the degree of difficulty, from AAA which is onerous to AA+, AA, AA-, which are challenging. The next levels are A+, A, A- which are demanding, and they are followed by BBB+, BBB, BBB- which are difficult. Intellectual Property Rights The materials here are published by this site. Parents and tutors can download as many files as possible for personal use or for lessons. If teachers or publishers wish to use our question banks for commercial distribution, please write to us for permission. All rights reserved. No part of these pages may be used for any purpose other than personal use. Any reproduction, modification, storage in a retrieval system or retransmission, without prior written permission, is strictly prohibited other than for personal use. This is regardless whether the content is texts or images or whether the media is electronic, mechanical or otherwise. Copyright 2016 by 1

2 Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. Helen ordered 12 cakes for a children s party. Every girl was given a 1 6 slice of cake while each boy was given a 1 slice of cake. After that there were no cakes left. The 3 number of girls were twice the number of boys. Find the number of boys there. Ans: 7. The ratio of the number of coins Marcus had to the number of coins Rachel had is 13 : 5. The same ratio became 5 : 4 after Marcus gave 45 coins to Rachel. Find the number of coins they had altogether. Ans: Copyright 2016 by 2

3 8. A rectangular piece of paper ABCD is shown in Figure 1. In figure 2, corner A of paper is folded along dotted line. Find a. Ans: 9. On the first day of a tour, the tourists were divided into lunch groups of 8 tourists per group. On the second day, 6 more tourists joined the tour group and the tourists were reorganised into new lunch groups. Every lunch group now has 10 tourists and there were one less group than the first day. None of the tourist left the tour on both days. Find the number of tourist in the tour group on the second day. Ans: Copyright 2016 by 3

4 10. A dining table in a canteen has 4 seats as shown in Diagram 1. When more dining tables were joined together, the number of seats increased as shown in Diagram 2 and 3. (a) Find the number of seats when 5 tables are joined together. (b) Find the number of seats when 45 tables are joined together. Ans: (a) (b) 11. A sum of money was shared between Natalie and Zorro. 1 of Natalie s share was $110 3 more than 25% of Zorro s share. The total sum of money was $4670. Find the amount that Natalie had. Ans: Copyright 2016 by 4

5 12. Initially, the ratio of the number of children to the number of adults at a carnival was 1 : 3. When 76 more children and 127 more adults joined the carnival, the same ratio became 2 : 5. Find the number of adults at the carnival at first. Ans: 13. At a DIY store, Larry bought some white and some black cables. The total length of white and black cables was 260m. He used 1 3 of the white cable and 3 of the black 7 cable. After that he had an equal length of white cable and black cables left. Find the number of metres of black cable he bought. Ans: Copyright 2016 by 5

6 14. Aileen had 0.7 as many stickers as Tanya. Aileen gave away 30% of her stickers and Tanya gave away 54 stickers. As such, Aileen had 0.5 as many stickers as Tanya. Find the number of stickers that Tanya had in the end. Ans: 15. Two quadrants join together as shown in the figure below. The contact line between one quadrant and the other is half of the radius. The line of contact is 8cm long. What is the perimeter of the figure? Let π = Ans: Copyright 2016 by 6

7 16. In a survey, 300 students were asked to choose their preferred colour. The survey result is shown on the graph below. Some pupils did not choose any colour at all and the result of the number of students who chose yellow was inadvertently erased. (a) Find the percentage of the students who chose red as their favourite colour. (b) The total number of students who chose green and blue was twice the number of students who chose red and yellow. Find the number of students who did not choose any colour at all. Ans: (a) (b) Copyright 2016 by 7

8 17. The shape of a motor car is printed on a white sheet of paper. The length of the car is 45cm and its height is 20 cm. It consists of 2 protruded semi-circular wheels with hollow semi-circle inside, 2 rectangular shaped body of the car and a triangular shaped windscreen. The hollow circle is half the size of the bigger circle. What is the area of the motor car figure. Let π = Ans: Copyright 2016 by 8

9 18. Joseph used 1 3 of his salary to buy a shirt. He then bought a pair of jeans with 1 8 of the remaining money. He also bought a belt with $135. He than gave 3 of the rest of his 5 money to his father and $90 to his daughter. Finally, he had 1 of his salary left. Find the 5 salary of Joseph. Ans: Copyright 2016 by 9

10 Answer Key Verified by Subject: Primary 6 Maths Word Problem Solutions Paper: SA Grade AAA a) 12 b) $ m cm 16. a) 30 b) cm $4320 Copyright 2016 by 10

11 Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. Fractions Helen ordered 12 cakes for a children s party. Every girl was given a 1 6 slice of cake while each boy was given a 1 slice of cake. After that there were no cakes left. The 3 number of girls were twice the number of boys. Find the number of boys there. Let u = number of boys Number of cakes for boys = 1 3 x u = 1 3 u Number of girls = 2 x u = 2u Number of cakes for girls = 1 6 x 2u = 1 3 u Total number of cakes = 1 3 u u = u = 12 u = 12 x 3 2 = 18 Number of boys = 18 Ans: 18 Copyright 2016 by 11

12 7. Ratios The ratio of the number of coins Marcus had to the number of coins Rachel had is 13 : 5. The same ratio became 5 : 4 after Marcus gave 45 coins to Rachel. Find the number of coins they had altogether. Before Marcus : Rachel 13 : 5 (total 18) 13u : 5u After Marcus: Rachel 5 : 4 10 : 8 (total 18) 10u : 8u Difference between after and before on both sides (13-10), (8-5) 3u 3u 45 1u 45 3 = 15 Total number of coins 10u + 8u = 18u = 18 x 15 = 270 Ans: 270 Copyright 2016 by 12

13 8. Geometry A rectangular piece of paper ABCD is shown in Figure 1. In figure 2, corner A of paper is folded along dotted line. Find a. ADE = = 27 FDE = 27, as it is symmetrical with ADE a = = 36 Ans: 36 Copyright 2016 by 13

14 9. Whole Numbers On the first day of a tour, the tourists were divided into lunch groups of 8 tourists per group. On the second day, 6 more tourists joined the tour group and the tourists were reorganised into new lunch groups. Every lunch group now has 10 tourists and there were one less group than the first day. None of the tourist left the tour on both days. Find the number of tourist in the tour group on the second day. Multiples of 8 tourists: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 Add 6 more tourists: 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94 Multiples of 10 tourists: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140 As 70 is 7 groups of ten as well as 8 groups of 8 plus 6. 7 groups is one less group than 8 groups. There were 70 participants on Day 2 Ans: 70 Copyright 2016 by 14

15 10. Whole Numbers - Patterns A dining table in a canteen has 4 seats as shown in Diagram 1. When more dining tables were joined together, the number of seats increased as shown in Diagram 2 and 3. (a) Find the number of seats when 5 tables are joined together. (b) Find the number of seats when 45 tables are joined together. Number of seats in increasing number of dining tables: 4, 6, 8, 10, 12 = 2 n + 2, n = number of dining tables Number of seats in 5 dining table = 2 x = 12 Number of seats in 45 dining table = 2 x = 92 Ans: (a) 12 (b) 92 Copyright 2016 by 15

16 11. Percentages A sum of money was shared between Natalie and Zorro. 1 of Natalie s share was $110 3 more than 25% of Zorro s share. The total sum of money was $4670. Find the amount that Natalie had. Let u = 25% part of Zorro s share There are 4 parts in Zorro s share and 3 parts in Natalie s share plus excess. Excess = 110 x 3 = 330 3u + 4u = u = = 4340 u = = 620 Natalie s share = 3u = 3 x = $2190 Ans: $2190 Copyright 2016 by 16

17 12. Ratios Initially, the ratio of the number of children to the number of adults at a carnival was 1 : 3. When 76 more children and 127 more adults joined the carnival, the same ratio became 2 : 5. Find the number of adults at the carnival at first. Before Ratio of number of children to number of adults 1 : 3 Let the number of children at first be u The number of adults at first is 3u After Ratio of number of children to number of adults (u+76) : (3u+127) = 2 : 5 5 x (u+76) = 2 x (3u +127) u = 5 x 76 2 x 127 = = 126 Number of adults at first = 3u = 3 x 126 = 378 Ans: 378 Copyright 2016 by 17

18 13. Fractions At a DIY store, Larry bought some white and some black cables. The total length of white and black cables was 260m. He used 1 3 of the white cable and 3 of the black 7 cable. After that he had an equal length of white cable and black cables left. Find the number of metres of black cable he bought. Remainder of white cable = = 2 3 = 4u Remainder of black cable = = 4 7 = 4u Original length of black cable = 7u Original length of white cable = 6u Total length of two cables = 13u = 260 u = = 20 Original length of black cable = 7u = 7 x 20 = 140 m Ans: 140 m Copyright 2016 by 18

19 14. Percentages Aileen had 0.7 as many stickers as Tanya. Aileen gave away 30% of her stickers and Tanya gave away 54 stickers. As such, Aileen had 0.5 as many stickers as Tanya. Find the number of stickers that Tanya had in the end. Let 0.7 7u 30% of 7u = 0.3 x 7u = 2.1u After that, Aileen s stickers = 7u 2.1u = 4.9u In the end, Tanya s stickers are twice of Aileen s = 4.9u x 2 = 9.8u Tanya s stickers given away 10u 9.8u 0.2u 54 stickers 9.8u x 54 = 2646 Ans: 2646 Copyright 2016 by 19

20 15. Measurements - Perimeter Two quadrants join together as shown in the figure below. The contact line between one quadrant and the other is half of the radius. The line of contact is 8cm long. What is the perimeter of the figure? Let π = Length of contact = 8 cm Radius is twice of length Radius = 2 x 8 = 16 cm Perimeter of circular part of 2 quadrants = ½ x 2 π x r = π x 16 = 16 x 3.14 = cm Length of radial lines = 3 x 16 = 48 cm Perimeter of figure = = cm Ans: cm Copyright 2016 by 20

21 16. Data Analysis In a survey, 300 students were asked to choose their preferred colour. The survey result is shown on the graph below. Some pupils did not choose any colour at all and the result of the number of students who chose yellow was inadvertently erased. (a) Find the percentage of the students who chose red as their favourite colour. (b) The total number of students who chose green and blue was twice the number of students who chose red and yellow. Find the number of students who did not choose any colour at all. Percentage of students who like red = x 100 = 20% Number who chose green and blue = = 180 Number who chose red and yellow =180 2 = 90 Number of students who did not choose any colour = = 30 Ans: (a) 20% (b) 30 Copyright 2016 by 21

22 17. Measurements - Area The shape of a motor car is printed on a white sheet of paper. The length of the car is 45cm and its height is 20 cm. It consists of 2 protruded semi-circular wheels with hollow semi-circle inside, 2 rectangular shaped body of the car and a triangular shaped windscreen. The hollow circle is half the size of the bigger circle. What is the area of the motor car figure. Let π = Outer wheel radius = 4 cm Inner radius = 2 cm Area of a circle = π x 4 x 4 = 16 π Area of a inner circle = π x 2 x 2 = 4 π Area of 2 half car tyres = 16 π - 4 π = 12 π = 12 x 3.14 = cm 2 Area of rectangular lower body of car = 8 x 45 = 360 cm 2 Area of rectangular upper body of car = 8 x 24 = 192 cm 2 Area of triangle = ½ x 3 x 8 = 12 cm 2 Total area = = cm 2 Ans: cm 2 Copyright 2016 by 22

23 18. Fractions Joseph used 1 3 of his salary to buy a shirt. He then bought a pair of jeans with 1 8 of the remaining money. He also bought a belt with $135. He than gave 3 of the rest of his 5 money to his father and $90 to his daughter. Finally, he had 1 of his salary left. Find the 5 salary of Joseph. Let u = salary of Joseph = u Fraction of salary to buy shirt = 1 3 u = 4 12 u Fraction of salary to buy jeans = (1-1 3 ) x 1 8 = 2 3 x 1 8 = 1 12 u 2 5 of the rest of money = of salary 5 5 of the rest of money = ½ of salary u u - 1 u = / u = 360 u = $4320 Ans: $4320 Copyright 2016 by 23