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

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1 Word Problem Worksheet & Solutions Difficulty: AAA 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 examinationsolutions.com 1

2 Show your working clearly in the space provided for each question and write your answers in the spaces provided 6. There were 140 more boys than girls in a school. 40% of the pupils were girls. Find out the number of boys in the school. Ans: 7. Analyse the pattern given below and find the symbols in questions (a) & (b). Pattern < Δ π < Δ π < Δ π < Δ Postion (a) Draw the symbol in Position 2. (b) Draw the symbol in Position 103. Ans: (a) (b) Copyright 2016 by examinationsolutions.com 2

3 8. To prepare for an outdoor event, Mrs Tanya bought red, blue, yellow, green and orange umbrellas. The number of umbrellas of each colour is shown in the graph below. (a) (b) Find out the total number of umbrellas Mrs Tanya bought? Mrs Tanya altogether spent $58.50 on orange and green umbrellas. Each orange umbrella cost $0.50 more than green umbrella. How much does each orange umbrella cost? Ans: (a) (b) Copyright 2016 by examinationsolutions.com 3

4 9. One rectangle and one square join together to form the shape below. What is the area of the shaded part. Ans: 10. A right-angled isosceles triangle ABC is combined with a square and a semi-circle to form the shape below. The diameter of semi-circle is the same as the side of the square and the area of the triangle is 36 cm 2. (a) How many similar sized right-angled isosceles triangles can you find in the figure. (b) What is the area of the semi-circle. Leave your answer in terms of π. Ans: Copyright 2016 by examinationsolutions.com 4

5 11. Jimmy bought a fish tank measuring 40 cm by 30 cm by 20 cm. He filled the tank with water and positioned 4 identical 10-cm cubes at the bottom of the tank. He poured out ml of water. Find out the height of the water in the tank at the end. Ans: 12. PQRS is a rhombus divided by straight line QTS. Triangle QRT is an isosceles triangle with QT = QR. TQR is 45 less than QTR. Find TRS. Ans: Copyright 2016 by examinationsolutions.com 5

6 13. Sally had in her pencil bag as 5 3 as many paper clips as Adeline. Sally gave 1 5 of his paper clips to Adeline. Adeline then gave 1 2 of her paper clips to Sally. Finally, Sally had 240 more paper clips than Adeline. Find the number of paper clips Sally had at first. Ans: 14. Analyse the number series below. 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 86, 88 Only 2-digit whole numbers are used in the pattern. The numbers in the ones and tens place are even numbers. (a) Find out the total count of numbers in the series. (b) What is the sum of all the numbers in the pattern. Ans: (a) (b) Copyright 2016 by examinationsolutions.com 6

7 15. Mark started driving at 60 km/h from Airport to Brighton City from 9 am. At 9:20 am Allan began travelling from Balestier Road to Airport at 40 km/h. Throughout the journey Mark and Allan were travelling at constant speeds. They met each other two third of the way from Airport. What is the distance between Airport and Brighton City. Ans: 16. The 3 friends Vivian, John and Zoro shared the cost of a dinner. 1/2 of Zoro s portion was the same as 1/3 the total of John s and Vivian s share. 1/3 John s portion was equivalent to 1/6 the sum of Zoro s and Vivian s share. Vivian paid $30 less than Zoro. Find the cost of the dinner? Ans: Copyright 2016 by examinationsolutions.com 7

8 17. The breadth of rectangle WXYZ is three times the breadth of rectangle PQRS. The ratio of the length of rectangle WXYZ to that of rectangle PQRS is 11 : 15. Rectangle WXYZ and rectangle PQRS have the same perimeter. The breadth of rectangle WXYZ is 25 cm shorter than its length. What is the area of rectangle PQRS? Ans: 18. The money that Aileen had was a whole number. She wished to buy a guitar but was short of $ Bob wanted to purchase the same guitar using all his money but was short of $2.50. If they pooled their money together, the sum was still insufficient to buy the guitar. Find the the price of the guitar. Ans: Copyright 2016 by examinationsolutions.com 8

9 Answer Key Verified by Subject: Primary 6 Maths Word Problem Solutions Paper: SA (a) Δ (b) π 8. (a) 30 (b) $ cm π cm cm (a) 25 (b) km 16. $ $ Copyright 2016 by examinationsolutions.com 9

10 Show your working clearly in the space provided for each question and write your answers in the spaces provided 6. Percentages There were 140 more boys than girls in a school. 40% of the pupils were girls. Find out the number of boys in the school. Ans: 420 Copyright 2016 by examinationsolutions.com 10

11 7. Patterns in Sequences Analyse the pattern given below and find the symbols in questions (a) & (b). Pattern < Δ π < Δ π < Δ π < Δ Postion (c) Draw the symbol in Position 2. (d) Draw the symbol in Position 103. The repetitive pattern is < Δ π which starts from positions 1 to 5, then again in position 6 to 10. (a) The symbol in Position 2 is Δ. (b) Position = 20 remainder 3, or 3 rd in pattern The symbol in Position 103 is π. Ans: (a) Δ (b) π Copyright 2016 by examinationsolutions.com 11

12 8. Data Analysis To prepare for an outdoor event, Mrs Tanya bought red, blue, yellow, green and orange umbrellas. The number of umbrellas of each colour is shown in the graph below. (a) Find out the total number of umbrellas Mrs Tanya bought? (b) Mrs Tanya altogether spent $58.50 on orange and green umbrellas. Each orange umbrella cost $0.50 more than green umbrella. How much does each orange umbrella cost? (a) Total number of umbrella = = 30 (b) u = price of green umbrella 11u = = 55 u = $5 Orange umbrella = = $5.5 Ans: (a) 30 (b) $5.5 Copyright 2016 by examinationsolutions.com 12

13 9. Measurement Area One rectangle and one square join together to form the shape below. What is the area of the shaded part. Full area = 8 x x 4 = 128 Area of top unshaded triangle = 1 2 x 8 x 14 = 56 Area of bottom unshaded triangle = 1 2 x 4 x 18 = 36 Shaded area = = 36 cm 2 Ans: 36 cm 2 Copyright 2016 by examinationsolutions.com 13

14 10. Measurement - Area A right-angled isosceles triangle ABC is combined with a square and a semi-circle to form the shape below. The diameter of semi-circle is the same as the side of the square and the area of the triangle is 36 cm 2. (c) How many similar sized right-angled isosceles triangles can you find in the figure. (d) What is the area of the semi-circle. Leave your answer in terms of π. (a) There are 9 right-angled isosceles triangles (b) Area of each small right-angled isosceles triangles = 36 9 = 4 cm 2 Area of triangle = 1 2 x 2r x r = r x r = 4 cm2, radius of semi-circle = r Area of semi-circle = 1 2 x π x r x r = 1 2 x π x 4 = 2 π cm2, substitute r x r with 4. Ans: 2 π cm 2 Copyright 2016 by examinationsolutions.com 14

15 11. Measurement - Volume Jimmy bought a fish tank measuring 40 cm by 30 cm by 20 cm. He filled the tank with water and positioned 4 identical 10-cm cubes at the bottom of the tank. He poured out ml of water. Find out the height of the water in the tank at the end. Volume of water in the full tank = 40 x 30 x 20 = ml Volume of 4 cubes = 10 x 10 x 4 = 400 ml Area of base = 40 x 20 = 800 cm 2 Volume of water & cubes at the end = = ml Height of water at the end = = 13 cm Ans: 13 cm Copyright 2016 by examinationsolutions.com 15

16 12. Geometry PQRS is a rhombus divided by straight line QTS. Triangle QRT is an isosceles triangle with QT = QR. TQR is 45 less than QTR. Find TRS = 90, 45 is the additional angle of QTR and QRT TQR = 90 3 = 30 PQR = 30 x 2 = 60 QRS = SPQ = = 120 TRQ = = 75 TRS = = 45 Ans: 45 Copyright 2016 by examinationsolutions.com 16

17 13. Fractions Sally had in her pencil bag as 5 3 as many paper clips as Adeline. Sally gave 1 5 of his paper clips to Adeline. Adeline then gave 1 2 of her paper clips to Sally. Finally, Sally had 240 more paper clips than Adeline. Find the number of paper clips Sally had at first. At the end difference between Sally and Adeline is the blue bar, Adeline s two halves have been minus off. u = 1 portion of blue bar 4u = 240 1u = 60 5u = 60 x 5 = 300 At first Sally had 300 paper clips Ans: 300 Copyright 2016 by examinationsolutions.com 17

18 14. Whole Numbers Patterns in sequences Analyse the number series below. 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 86, 88 Only 2-digit whole numbers are used in the pattern. The numbers in the ones and tens place are even numbers. (c) Find out the total count of numbers in the series. (d) What is the sum of all the numbers in the pattern. (a) There are 5 set of 5 numbers. Total count = 5 x 5 = 25 (b) Average = 1 2 x ( ) = 54 Sum of all numbers = average x 25 = 54 x 25 = 1350 Ans: (a) 25 (b) 1350 Copyright 2016 by examinationsolutions.com 18

19 15. Measurement Distance Mark started driving at 60 km/h from Airport to Brighton City from 9 am. At 9:20 am Allan began travelling from Brighton City to Airport at 40 km/h. Throughout the journey Mark and Allan were travelling at constant speeds. They met each other two third of the way from Airport. What is the distance between Airport and Brighton City. At 9:20am Mark travelled 20/60 x 60 = 20km, Mark travelled for 20 minutes u = time between 9:20 am and time they met 2 x 40u = 60u u = 20 u = 1 hour Distance travelled by Allan = 40 x 1 = 40km Distance travelled by Mark = 60 x = 80 km Total distance = = 120 km Ans: 120 km Copyright 2016 by examinationsolutions.com 19

20 16. Ratios The 3 friends Vivian, John and Zoro shared the cost of a dinner. 1/2 of Zoro s portion was the same as 1/3 the total of John s and Vivian s share. 1/3 John s portion was equivalent to 1/6 the sum of Zoro s and Vivian s share. Vivian paid $30 less than Zoro. Find the cost of the dinner? Z = Zoro s share, J = John s share, V = Vivian s share 1/2 Z = 1/3 (J + V) 3 Z = 2 (J + V) Z : (J + V) -> 2 : 3 Z = 2/5 of dinner As per diagram 1/3J = 1/6 (Z + V) 2 J = (Z+V) J : (Z+V) -> 1 : 2 Z+V = 2/3 of dinner As per diagram V = Z 30 Z + V = 2/3 of dinner Z + Z 30 = 2/3 of dinner Substitute V = Z Z 30 = 2/3 of dinner 2 x 2/5 of dinner 30 = = 2/3 of dinner Substitute Z = 2/5 of dinner 4/5 of dinner 2/3 of dinner = 30 12/15 10/15 of dinner = 30 2/15 of dinner = 30 dinner = 30 x 15/2 = $225 Ans: $225 Copyright 2016 by examinationsolutions.com 20

21 17. Ratios The breadth of rectangle WXYZ is three times the breadth of rectangle PQRS. The ratio of the length of rectangle WXYZ to that of rectangle PQRS is 11 : 15. Rectangle WXYZ and rectangle PQRS have the same perimeter. The breadth of rectangle WXYZ is 25 cm shorter than its length. What is the area of rectangle PQRS? Length WXYZ: Length PQRS 11 : 15, Breadth WXYZ: Breadth PQRS 3 : 1 or 6 : 2 normalised so that perimeter of both are equal Perimeter WXYZ: Perimeter PQRS 2(11 + 6) = 2(15 + 2) Length WXYZ: breadth ABCD : 11 : 6 Length PQRS: Breadth PQRS 15 : 2 Length WXYZ - breadth WXYZ = 11 6 = 5u = 25 u = 5 Area of PQRS = (15 x 5) x (2 x 5) = 750 Ans: 750 Copyright 2016 by examinationsolutions.com 21

22 18. Measurement Money The money that Aileen had was a whole number. She wished to buy a guitar but was short of $ Bob wanted to purchase the same guitar using all his money but was short of $2.50. If they pooled their money together, the sum was still insufficient to buy the guitar. Find the the price of the guitar. Aileen must have only $2 as adding that to Bob s money is still not enough to buy the guitar. The guitar cost = $ $2 = $ Ans: $ Copyright 2016 by examinationsolutions.com 22