Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Worked Mathematics Solutions for Nanyang Primary School P5 Second Continual Examination 2009
EXCEL EDUSERVICE Mathematics Paper 2
You’re in good hands when you’re with Excel!
Terms of Use – This copy of Maths worked solutions is distributed FREE OF CHARGE. The user of this copy agrees not to sell this copy or any part of it, in any form, be it in print, digitally or other means. The user of this copy is given permission make copies of this Maths worked solution on condition that it is reprinted and/or digitally copied in its entirety, including Excel Eduservice’s logo, watermarks, headers and footers.
EXCEL EDUSERVICE
No part of this copy is to be amended or omitted.
You’re in good hands when you’re with Excel! --------------------------------------------------------------------------
If you find any mistakes in this copy, please let us know through email so that we would be able to amend the error and give you a new copy. Email:
[email protected] ROAD TO PSLE
Your resource to better PSLE (Primary School Leaving Examination) scores! To view more Free Maths Worked Solutions, please visit the url below. http://road-to-psle.blogspot.com
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
1
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q1
Mr Lim had 1890 twenty-cent coins. Mr Tan had 2
3 of the number 10
of coins that Mr Lim had. How much money did Mr Tan have?
Solution 2
3 x 1890 (coins) Æ 4347 (coins) 10
EXCEL EDUSERVICE
4347 x $0.20 = $869.40 Answer: $869.40
You’re in good hands when you’re with Excel!
____________________________________________________ Q2
Mary bought a TV set. She paid an initial payment of $328. The rest of the amount was paid in month instalments of $80.80 over a period or 24 months. What was the cost of the TV set?
Solution 1st payment Æ $328 Instalments Æ 24 x $80.80 = $1939.20 Total Æ $328 + $1939.20 = $2267.20
EXCEL EDUSERVICE
Answer: $2267.20
You’re in good hands when you’re with Excel! ___________________________________________________
Q3
The interest rate for a fixed deposit account in Bank A is 2.5% per year. If Mr Tan invests $20 000 in such an account, how much will he have in his account after a year?
Solution Interest paid Æ
2.5 x $20 000 = $500 100
Total after 1 year Æ $20 000 + $500 = $ 20 500 Answer: $20 500
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
2
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
1 of 4 the rice in Bag A was transferred to Bag B, both bags had the same amount of rice. How many grams of rice were transferred from Bag A to Bag B?
Q4
Bags A and B contained a total of 78.39 kg of rice. After
Solution Bag A 78.39 kg
EXCEL EDUSERVICE
Bag B
You’re in good hands when you’re with Excel!
6 units Æ 78.39 kg 1 unit Æ 78.39 kg ÷ 6 = 13.065 kg 13.065 kg = 13 065 g Answer: 13 065 g
__________________________________________________ Q5
The ratio of the number of Charlie’s toy cars to the number of 1 Xavier’s toy cars was 9 : 2. After Charlie gave of the toy 3 cars to Xavier, he still had 10 cars more than Xavier. How many toy cars did Charlie give to Xavier?
EXCEL EDUSERVICE
Solution Before Charlie gave 1 x9=3 3 After
You’re in good hands when you’re with Excel!
Charlie
:
Xavier
9
:
2
(9 – 3 = 6) 6
(2 + 3 = 5) :
5
Difference is 1 unit Æ 10 (toy cars) 3 units Æ 3 x 10 = 30 Answer: 30 toy cars You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
3
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q6
A group of boys played only two types of sports during recess. 1 2 of them played badminton and of them played football. 4 3 1 of the boys played both sports and 90 boys did not play 6 any sports at all. How many boys were there?
Solution
EXCEL EDUSERVICE
Badminton Æ
Football Æ
Both Æ
1 3 (or ) 4 12
2 8 (or You’re ) in good hands when you’re with Excel! 3 12
1 2 (or ) 6 12
2 ) 12 Both (
Football (
8 ) 12
EXCEL EDUSERVICE You’re in good hands when you’re with Excel!
Badminton 3 ( ) 12
No sports
3 units Æ 90 1 unit Æ 90 ÷ 3 = 30 12 units Æ 12 x 30 = 360 Answer: 360 boys
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
4
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q7
Mohamed answered 30 quiz questions and scored 54 marks. For each correct answer, 5 marks were given. For each wrong answer, 3 marks were deducted. How many correct answers did Mohamed get?
Solution Difference between right and wrong answer Æ 8 marks -3
EXCEL EDUSERVICE 0
Wrong answer
+5
You’re in good hands when you’re with Excel!
Right answer
If all answers are right Æ 30 x 5 = 150 But he scored 54 marks only Æ 150 – 54 = 96 (marks lost) The 96 marks loss is due to the wrong answers. For every one answer that is wrong, he loses 8 marks (5 marks lost, plus another 3 marks deducted) 96 ÷ 8 = 12 (questions wrong)
EXCEL EDUSERVICE
30 – 12 = 18 (questions right)
You’re in good hands when you’re with Excel! Answer: 18 questions right
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
5
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q8
The ratio of Ahmad’s age to Suri’s age is 5 : 3 now. 4 years ago, the ratio was 7 : 4. How old is Ahmad now?
Solution 4 years ago Ahmad Suri
add 4 years
7 units 4 units
+4 +4
Æ Æ
Now 5 parts 3 parts
(x3)* (x5)*
EXCEL EDUSERVICE
*(x3) and (x5) to common Ahmad’s 5 parts and Suri’s 3 parts. You’re in good hands when you’re with Excel!
Ahmad Suri
21 units 20 units
+ 12 + 20
Æ Æ
(21 units – 20 units) + (12 – 20) Æ 1 unit – 8 Æ 0 1 unit Æ 8
15 parts 15 parts (15 parts) – (15 parts)
Ahmad now Æ 7 units + 4 = (7 x 8) + 4 = 56 + 4 = 60
EXCEL EDUSERVICE
Answer: 60 years old
You’re in good hands when you’re with Excel!
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
6
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q9
Tank A contains 3 times as much water as Tank B. After Dolly adds 680 ml of water into Tank A and 8.36 litres of water into Tank B, the two tanks now contain the same amount of water. How many millilitres of water are in the two tanks now?
Solution Tank A
EXCEL EDUSERVICE
Tank B
You’re in good hands when you’re with Excel!
680
8360
2 units Æ 8360 – 680 = 7680 1 unit Æ 7680 ÷ 2 = 3840 Total now Æ 4 units + 680 + 8360 = (4 x 3840) + 9040 = 15 360 + 9040 = 24 400 Answer: 24 400 ml
EXCEL EDUSERVICE You’re in good hands when you’re with Excel!
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
7
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
5 of the amount of 7 money that Shanil had. If Shanil gave Betty $28, the amount of money that Betty had was 140% of the amount of money that Shanil had. How much money did they have altogether?
Q10 The amount of money that Betty had was
Solution Betty Shanil
5 units + $28 Æ 140% 7 units - $28 Æ 100%
EXCEL EDUSERVICE
Let 100% Æ 5 units 20 % Æ 1 unit 140% Æ 7 units
You’re in good hands when you’re with Excel!
Therefore, Betty 5 units + $28 Æ 140% (or 7 units) Shanil 7 units - $28 Æ 100% (or 5 units) Difference between Betty and Shanil after Shanil gave $28 is, 7 units – 5 units Æ $28 2 units Æ $28 1 unit Æ $28 ÷ 2 = $14 12 units Æ 12 x $14 = $168 Answer: $168
EXCEL EDUSERVICE You’re in good hands when you’re with Excel!
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
8
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q11 Henry received his examination result slip but it was torn.
EXCEL EDUSERVICE You’re in good hands when you’re with Excel!
a) What could be Henry’s highest possible average score, if all the scores are in whole numbers? b) If Henry scored 91 marks for Mathematics and had an average score of 85.5 for the four subjects, how many marks did he score for Science? Solution a) (83 + 85 + 99 + 89) ÷ 4 = 356 ÷ 4 = 89
EXCEL EDUSERVICE You’re in good hands when you’re with Excel!
Answer: 89 marks
b) Average Æ 85.5 Total Æ 4 (subjects) x 85.5 = 342 Science Æ 342 – 83 – 85 – 91 = 83 Answer: 83 marks
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
9
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q12 The figure below is not drawn to scale. Find its area.
EXCEL EDUSERVICE You’re in good hands when you’re with Excel!
Solution
EXCEL EDUSERVICE You’re in good hands when you’re with Excel!
Area of rectangle Æ 84 cm x 15 cm = 1260 cm 2 Area one triangle Æ (
1 )(35)(84) cm 2 = 1470 2
Total Area Æ 1260 cm 2 + 1470 cm 2 + 1470 cm 2 = 4200 cm 2 Answer: 4200 cm 2
10
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q13 A dressmaker had some buttons. She used
1 of them on 7
1 of the remainder on Tuesday. On Wednesday, 11 she bought 255 buttons and then had as many buttons as she had at first. How many buttons did she have at first?
Monday and
Solution (Mon) used
1 7 1 6 Æ = left 7 7 7 7
EXCEL EDUSERVICE
1 6 of remaining 11 You’re in good 7hands when you’re with Excel! 1 6 6 Æ x = 11 7 77 (Tue) used
Total used Æ (Mon) + (Tue) 1 6 17 + = 7 77 77
17 Æ 255 (bought) 77
EXCEL EDUSERVICE
1 Æ 255 ÷ 17 = 15 77
77 Æ 77 x 15 = 1155 You’re in good hands when you’re with Excel! 77 Answer: 1155 buttons
11
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q14 Aunt Rosie bought an equal number of curry puffs and cupcakes for a tea party. The curry puffs were bought at 7 for $2 and the cupcakes were bought at 5 for $3. She paid $33 more for the cupcakes than for the curry puffs. a) How many curry puffs did Aunt Rosie buy? b) How much did Aunt Rosie pay for the curry puffs? Solution
EXCEL EDUSERVICE
Curry Puffs Cupcakes
1 group of 7 Æ $2 (x5)* 1 group of 5 Æ $3
(x7)*
You’re in good hands when you’re with Excel!
*Curry puffs (x5) and cupcakes (x7) to give a common number of 35 for both curry puffs and cupcakes. Curry Puffs Cupcakes
5 groups of 7 = 35 Æ $10 7 groups of 5 = 35 Æ $21
Difference = $11
The difference in price for the curry puffs and cupcakes is $11. To get a difference of $33, multiply the above by 3 to get,
EXCEL EDUSERVICE
Curry Puffs
15 groups of 7 Æ $30
Cupcakes
21 groups of 5 Æ $62
Difference = $33
You’re in good hands when you’re with Excel!
a) Curry Puffs Æ 15 groups of 7 = 15 x 7 = 105 Answer: 105 curry puffs b) In order to pay $33 more for cupcakes, she has to buy 15 groups of 7 curry puffs Æ $30 Answer: $30
12
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q15 Devi went shopping with an equal number of $2 and $5 notes. She spent 20% of her $2 notes. She withdrew some $5 notes from the bank and had 30% more $5 notes than before. In the end, Devi had 15 more $5 notes than $2 notes. a) How many $2 notes did Devid spend? b) How much money did Devi have at first? Solution
EXCEL EDUSERVICE Before
$2 notes $5 note
After
100% - 20% Æ 80% You’re in good hands when you’re with Excel! 100% + 30% Æ 130%
$5 notes more than $2 notes Æ 130% - 80% = 50% 50% Æ 15 notes 10 % Æ 15 notes ÷ 5 = 3 notes 100% Æ 10 x 3 notes = 30 notes a) She spent 20% of her $2 notes Æ 2 x 3 notes = 6 notes Answer: 6 two-dollar notes
EXCEL EDUSERVICE
b) You’re in good hands when you’re with Excel! 100% of all $2 notes Æ $2 x 30 notes = $60 100% of all $5 notes Æ $5 x 30 notes = $150 Total Æ $60 + $150 = $210 Answer: $210
13
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q16 Mrs Lim gave her two daughters, Liming and Lizhen, some money in the ratio of 8 : 9. Liming and Lizhen shared the cost 3 of an electronic game in the ratio of 6 : 7. Liming used of 4 her money to pay for her share of the electronic game. Lizhen was left with $130 after paying for her share. a) How much did Liming get from her mother? b) What was the cost of the electronic game?
EXCEL EDUSERVICE
Solution
Liming
At first
8
Cost shared Left with
:
Lizheng
You’re in good hands when you’re with Excel!
:
9
6*
:
7
2
:
2
*(3/4 of Liming’s original 8 units = 6 units. Since ratio spent between LM and LZ is 6 : 7, the figures can be used to deduct from the original amount they had at first.) a) Lizhen left with $130, 2 units Æ $130 1 unit Æ $130 ÷ 2 = $65
EXCEL EDUSERVICE
You’re in good hands when you’re with Excel! Liming at first 8 units Æ 8 x $65 = $520
Answer: $520 b) Total cost 6 units (from Liming) + 7 units (from Lizheng) = 13 units 13 units Æ 13 x $65 = $845 Answer: $845
14
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q17 A stack of bookmarks was shared among Peter, Tom and Jerry. Peter received 3 more than 50% of the bookmarks. Tom received 5 more than half of the remaining bookmarks. After Peter and Tom had taken their share, Jerry received 50% of the remainder and the last 3 bookmarks. What percentage of the stack of bookmarks did Jerry receive? Solution Peter received Æ 50% + 3 Remaining Æ 50% - 3
EXCEL EDUSERVICE
Tom received 5 more than half the remaining Æ Half of [(50% -3) + 5] = (25% - 1.5) + 5
You’re in good hands when you’re with Excel!
This would mean the remaining amount for Jerry after Tom gets his share is Æ (25% - 1.5) – 5 = 25% - 6.5 Jerry received 50% of the above remainder plus the last 3 bookmarks Æ Half of (25% - 6.5) + 3 = (12.5% - 3.25) + 3 50% of J’s share;
The other 50% of J’s share
EXCEL EDUSERVICE
If Jerry’s (12.5% - 3.25) is 50% of his share, then the other 50% in good hands when you’re with Excel! has to be the last You’re 3 bookmarks Æ 50% = 50% 12.5% - 3.25 = 3 12.5% = 3 + 3.25 12.5% = 6.25 1% Æ 6.25 ÷ 12.5 = 0.5 100% Æ 100 x 0.5 = 50 (bookmarks)
15
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
50 bookmarks
25
25 3 22
EXCEL EDUSERVICE Peter: 50% + 3
You’re in good hands when you’re with Excel!
Tom: 50% of remaining 22 + 5 = 11 + 5 = 16
If Tom gets 16, Jerry gets 22 – 16 = 6 Percentage of Jerry’s stack of bookmarks 6 Æ x 100% = 12% 50
EXCEL EDUSERVICE
Answer: 12%
You’re in good hands when you’re with Excel!
16
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
Excel Eduservice http://road-to-plse.blogspot.com -------------------------------------------------------------------------------------------
Q18 Kailing and Jim had a total of $63. Kailing gave 0.3 of her 1 share to Jim. Jim then gave of the total amount of money 3 he had to his brother. In the end, all the three children had the same amount of money. How much money did Kailing have at first? Solution
EXCEL EDUSERVICE
In the end Kailing
You’re in good hands when you’re with Excel!
Jim Brother
1 of his amount to his brother and after Kailing 3 gave 0.3 of her share to Jim Before Jim gave
0.7 of Kailing’s original share*
Kailing
EXCEL EDUSERVICE $63
Jim
You’re in good hands when you’re with Excel!
Brother *Kailing gave 0.3 of her share and would be left with 0.7 5 units Æ $63 1 unit Æ $63 ÷ 5 = $12.60 2 units (0.7 of K’s share) Æ 2 x $12.60 = $25.20 0.1 of K’s share Æ $25.20 ÷ 7 = $3.60 Whole of K’s share Æ 10 x $3.60 = $36 Answer: $36
17
You’re in good hands when you’re with Excel! Free Copy – STRICTLY NOT FOR SALE This document was created on 22 July 2010 by Excel Eduservice © All rights reserved
