Word Problem Worksheet & Solutions Difficulty: A P6 Mathematics SA2 2016

Transcription

1 Word Problem Worksheet & Solutions Difficulty: A 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 lego chips were kept by Gabriel in 2 boxes C and D. There were 25 more lego chips in box C than box D, after 1 5 of the lego chips in box C were transferred to box D. Find the number of lego chips in box D at first. Ans: 7. Berkeley is 150 km from and Anaheim. Luke and Thomas started driving towards Berkeley at the same time. Thomas reached Berkeley about ½ hour before Luke. Luke was still 25 km away from Berkeley, when Thomas arrived at Berkeley. Find the average speed of Thomas. Ans: Copyright 2016 by 2

3 8. Inside a big circle of radius 15 cm, there are 4 small identical circles each in contact with each other. What is the area of the shaded region? Take π = Ans: 9. Melissa had 30 pieces of $2 notes and some $5 notes. The ratio of number of $2 notes to number of $5 notes was 3 : 10. The ratio of number of $2 notes to number of $5 notes became 5 : 19, after spending an equal number of $2 and $5 notes. Find the total amount spent by Melissa. Ans: Copyright 2016 by 3

4 10. The bar graph shows the number of DVDs sold by a shop. The number of thriller DVDs was 3 4 of the number of drama DVDs. a) How many thriller DVDs were there? b) The table shows the prices of the DVDs. Which type of DVDs did the shop collect the most money from the sale? Type of book Price per DVD Quantity Drama $ Comedy $ Action $ Thriller $12.00? Ans: Copyright 2016 by 4

5 11. Three identical squares are shown in figure below. If DAE is 45, what is the size of angles a) f b) g Ans: 12. School A and School B were participating in flag day for charity. School A collected 3 times as much money as School B, In the first week. School B raised another $371 and School A raised another $325, in the second week. Find the total amount collected by School A over the first 2 weeks, if School A managed to collect twice as much money as School B over the first 2 weeks, Ans: Copyright 2016 by 5

6 13. Julie and Kimberley used crayon for making star shapes using a mold. Each had a piece of crayon of the same mass and each star is of the same mass. Jane made 27 stars and had kg of crayon left. Kitty made 45 stars and had 525 g of crayon left. a) Find the mass of crayon needed for each star. b) With the leftover crayon from both girls, find out the number of stars that can be made. (b) 14. The water level in a rectangular tank is 15 cm when it is 1 4 filled with water. The length of the rectangular tank is 1 ½ times its breadth. Its breadth is 1 5 of its height. a) Find the capacity of the tank. b) If water flows into the tank at 2 l per minute, find the time taken to fill the remaining tank. Ans: Copyright 2016 by 6

7 15. A Samsung smartphone was sold for $390. This price was 25% lower than the price of Apple smartphone. a) Find the price of the Samsung smartphone. b) Both smartphones were offered an equal percentage discounts during a special promotion. Shawn bought the Apple smartphone. He paid $97.5 more than the discounted Samsung price. Find the percentage discount. Ans: (a) (b) 16. A square of side 6 cm and 2 identical quarter circles forms a rugby shape as shown below. a) Find the perimeter of the shaded areas. b) Find the shaded area. and C. (Take π = 3.14) Ans: Copyright 2016 by 7

8 17. Initially Douglas and Edward had the same amount of money. Douglas spent $750 and Eric spent $805, every month. After several months, both had different amount of money left. Douglas has a remaining amount of $1320 while Edward had 5 6 of the money Douglas had left. What was the amount that Edward had at first? Ans: 18. Robert bought some water bottles. The prices were in sets of 3 or 5 as shown in the table. Silver water bottles Yellow water bottles 3 for $ for $3 a) He purchased the same number of silver and yellow water bottles. He paid $39 more for the silver water bottles than for the yellow water bottles. Find the number of water bottles he bought altogether. b) Helen paid an equal amount of money on the silver and yellow water bottles. Find the fraction of the yellow water bottles she bought. (Give your answer as a fraction in the simplest form.) Ans: (a) (b) Copyright 2016 by 8

9 Answer Key Verified by Subject: Primary 6 Maths Word Problem Solutions Paper: SA km/h cm a) 75 b) Thriller 11. a) 45 b) $ a) 50g b) a) cm 3 b) 4.86 minutes 15. a) $520 b) 25 % 16. a) cm b) 0.52 cm $ a) 60 b) 6 25 Copyright 2016 by 9

10 Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. Fractions 255 lego chips were kept by Gabriel in 2 boxes C and D. There were 25 more lego chips in box C than box D, after 1 5 of the lego chips in box C were transferred to box D. Find the number of lego chips in box D at first. At first Box C has 5 units or 5u, Box D units = d Box D = 255 5u 4u u d = 25 3u (255-5u) = 25 3u u = 25 8u = = 280 u = 280 / 8 = 35 Before After Substitute box D from before Box D = 255 5x 35 = 80 Ans: 80 Copyright 2016 by 10

11 7. Measurement Distance Berkeley is 150 km from Anaheim. Luke and Thomas started driving towards Berkeley at the same time. Thomas reached Berkeley about ½ hour before Luke. Luke was still 25 km away from Berkeley, when Thomas arrived at Berkeley. Find the average speed of Thomas. Luke s speed = 25 ½ hour = 25 x 2 = 50 km/h Time taken by Luke = = 3 hr Time taken by Thomas = 3 hr ½ hr = 2 ½ hr Thomas s speed = ½ hr = 150 x 2 5 = 30 x 2 = 60 km/h Ans: 60 km/h Copyright 2016 by 11

12 8. Measurement Area Inside a big circle of radius 15 cm, there are 4 small identical circles each in contact with each other. What is the area of the shaded region? Take π = Area of big circle = π x 15 x 15 = 225 π Radius of small circle = 15 3 = 5 cm Area of one small circle = π x 5 x 5 = 25 π Area of 4 small circles = 4 x 25 π = 100 π Shaded area = 225 π 100 π = 125 π = 125 x 3.14 = cm 2 Ans: cm 2 Copyright 2016 by 12

13 9. Ratios Melissa had 30 pieces of $2 notes and some $5 notes. The ratio of number of $2 notes to number of $5 notes was 3 : 10. The ratio of number of $2 notes to number of $5 notes became 5 : 19, after spending an equal number of $2 and $5 notes. Find the total amount spent by Melissa. 3 : 10 -> 30 : 100 Minus 1 note -> 29 : 99 Minus 2 notes -> 28 : 98 Minus 3 notes -> 27 : 97 Minus 4 notes -> 26 : 96 Minus 5 notes -> 25 : 95 = 5 : 19 Total amount spent = 5 x x 5 = 35 Ans: 35 Copyright 2016 by 13

14 10. Data Analysis The bar graph shows the number of DVDs sold by a shop. The number of thriller DVDs was 3 4 of the number of drama DVDs. a) How many thriller DVDs were there? b) The table shows the prices of the DVDs. Which type of DVDs did the shop collect the most money from the sale? Type of book Price per DVD Quantity Drama $ Comedy $ Action $ Thriller $12.00? a) Number of thriller DVDs = 3 4 x 100 = 75 Type of book Price per DVD Quantity Total Sales Drama $ $790 Comedy $ $360 Action $ $436 Thriller $ $900 b) Thriller DVDs collected the most money. Ans: (a) 75 (b) Thriller Copyright 2016 by 14

15 11. Geometry Three identical squares are shown in figure below. If DAE is 45, what is the size of angles a) f b) g f = 45 g = = 30 Ans: (a) 45 (b) 30 Copyright 2016 by 15

16 12. Measurement Money School A and School B were participating in flag day for charity. School A collected 3 times as much money as School B, in the first week. School B raised another $371 and School A raised another $325, in the second week. Find the total amount collected by School A over the first 2 weeks, if School A managed to collect twice as much money as School B over the first 2 weeks, u = School B 3u = 2 x (u + 371) u = 371 x = 417 School B = u = 417 A = 3 x = = $1576 Ans: $1576 Copyright 2016 by 16

17 13. Measurement Mass Julie and Kimberley used crayon for making star shapes using a mold. Each had a piece of crayon of the same mass and each star is of the same mass. Jane made 27 stars and had kg of crayon left. Kitty made 45 stars and had 525 g of crayon left. c) Find the mass of crayon needed for each star. d) With the leftover crayon from both girls, find out the number of stars that can be made. u = mass of dough for each star 27u = 45u u 27u = u = 900 u = = 50g Remaining dough = = 1950 g Number of stars that can be made from remaining dough = = 39 Ans: (a) 50g (b) 39 Copyright 2016 by 17

18 14. Volume The water level in a rectangular tank is 15 cm when it is 1 4 filled with water. The length of the rectangular tank is 1 ½ times its breadth. Its breadth is 1 5 of its height. a) Find the capacity of the tank. b) If water flows into the tank at 2 l per minute, find the time taken to fill the remaining tank. Height of water tank = = 15 x 4 = 60 cm Breadth = 1 5 x 60 = 12 cm Length = 1 ½ x 12 = 18 cm Capacity of tank = 12 x 18 x 60 = cm 3 Remaining height = = 45 cm Remaining volume = 12 x 18 x 45 = 9720 cm 3 = = 9.72 l Time taken to fill remaining tank = = 4.86 minutes Ans: (a) cm 3 (b) 4.86 minutes Copyright 2016 by 18

19 15. Percentages A Samsung smartphone was sold for $390. This price was 25% lower than the price of Apple smartphone. c) Find the price of the Apple smartphone. d) Both smartphones were offered an equal percentage discounts during a special promotion. Shawn bought the Apple smartphone. He paid $97.5 more than the discounted Samsung price. Find the percentage discount. Price of Samsung smartphone is 75% of Apple smartphone. Price of Apple smartphone = = $520 Price difference = = $130 After discount difference = $97.5 Percent after discount = $ = 75% Discount = = 25 % Ans: (a) $520 (b) 25 % Copyright 2016 by 19

20 16. Measurement Area A square of side 6 cm and 2 identical quarter circles forms a rugby shape as shown below. a) Find the perimeter of the shaded areas. b) Find the shaded area. and C. (Take π = 3.14) Perimeter of 2 quarter circle = 2 x π x r x 2 4 = 6 x π = 6 π = 6 x 3.14 = cm Area of quarter circle = π x r x r 4 = π x 6 x 6 4 = 9 π = 9 x 3.14 = cm 2 Crescent shape =Square minus quarter circle = 6 x = 7.74 cm 2 Rugby shape=square minus 2 crescent shape = 6 x = cm 2 Ans: (a) cm (b) cm 2 Copyright 2016 by 20

21 17. Measurement Money Initially Douglas and Edward had the same amount of money. Douglas spent $750 and Eric spent $805, every month. After several months, both had different amount of money left. Douglas has a remaining amount of $1320 while Edward had 5 6 of the money Douglas had left. What was the amount that Edward had at first? Douglas finally had = $1320 Edward finally had = 5 x 1320 = $ Difference between Douglas and Edward s balance = = 220 Difference between Douglas and Edward s spending = = 55 Number of months of spending = = 4 Amount Edward had at first = 805 x = $4320 Ans: $4320 Copyright 2016 by 21

22 18. Fractions Robert bought some water bottles. The prices were in sets of 3 or 5 as shown in the table. Silver water bottles Yellow water bottles 3 for $ for $3 a) He purchased the same number of silver and yellow water bottles. He paid $39 more for the silver water bottles than for the yellow water bottles. Find the number of water bottles he bought altogether. b) Helen paid an equal amount of money on the silver and yellow water bottles. Find the fraction of the yellow water bottles she bought. (Give your answer as a fraction in the simplest form.) LCM of 5 and 3 = 15 Price of 15 silver water bottles = 5.70 x 5 = $28.50 Price of 15 yellow water bottles = 3 x 3 = 9 Difference of price for each dozen = = No of sets of 15 he bought = = 2 No of water bottles he bought = 2 x 2 x 15 = 60 When she bought 10 sets of silver water bottles costing $57 and 19 sets of yellow water bottles for $57, the price is equal. Number of silver water bottles bought = 10 x 3 = 30 Number of yellow water bottles bought = 19 x 5 = 95 Total = = 125 Fraction of yellow water bottles = 30/125 = 6 25 Ans: (a) 60 (b) 6 25 Copyright 2016 by 22