Worked Mathematics s for Nanyang Primary School P5 Second Continual Examination 2009 Mathematics Paper 2 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. No part of this copy is to be amended or omitted. -------------------------------------------------------------------------- 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: FreeMathSample@gmail.com ROAD TO PSLE Your resource to better PSLE (Primary School Leaving Examination) scores! To view more Free Maths Worked s, please visit the url below. http://road-to-psle.blogspot.com 1
Q1 Mr Lim had 1890 twenty-cent coins. Mr Tan had 2 10 3 of the number of coins that Mr Lim had. How much money did Mr Tan have? 2 10 3 x 1890 (coins) 4347 (coins) 4347 x $0.20 = $869.40 Answer: $869.40 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? 1 st payment $328 Instalments 24 x $80.80 = $1939.20 Total $328 + $1939.20 = $2267.20 Answer: $2267.20 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? 2. 5 Interest paid 100 x $20 000 = $500 Total after 1 year $20 000 + $500 = $ 20 500 Answer: $20 500 2
Q4 Bags A and B contained a total of 78.39 kg of rice. After 4 1 of 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? Bag A Bag B 78.39 kg 6 units 78.39 kg 1 unit 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? Charlie : Xavier Before 9 : 2 Charlie gave 1 x 9 = 3 3 (9 3 = 6) (2 + 3 = 5) After 6 : 5 3 units 3 x 10 = 30 Answer: 30 toy cars Difference is 1 unit 10 (toy cars) 3
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? Badminton 4 1 (or 12 3 ) 2 You re 8 Football (or ) in good hands when you re with Excel! 3 12 Both 6 1 (or 12 2 ) ( 12 2 ) Both Football ( 12 8 ) Badminton No sports 3 ( ) 12 3 units 90 1 unit 90 3 = 30 12 units 12 x 30 = 360 Answer: 360 boys 4
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? Difference between right and wrong answer 8 marks -3 0 +5 Wrong answer Right answer If all answers are right 30 x 5 = 150 But he scored 54 marks only 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) 30 12 = 18 (questions right) Answer: 18 questions You re in right good hands when you re with Excel! 5
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? 4 years ago add 4 years Now Ahmad 7 units + 4 5 parts (x3)* Suri 4 units + 4 3 parts (x5)* *(x3) and (x5) to common Ahmad s 5 parts and Suri s 3 parts. Ahmad 21 units + 12 15 parts Suri 20 units + 20 15 parts (21 units 20 units) + (12 20) (15 parts) (15 parts) 1 unit 8 0 1 unit 8 Ahmad now 7 units + 4 = (7 x 8) + 4 = 56 + 4 = 60 Answer: 60 years old 6
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? Tank A 680 8360 Tank B 2 units 8360 680 = 7680 1 unit 7680 2 = 3840 Total now 4 units + 680 + 8360 = (4 x 3840) + 9040 = 15 360 + 9040 = 24 400 Answer: 24 400 ml 7
Q10 The amount of money that Betty had was 7 5 of the amount of 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? Betty 5 units + $28 140% Shanil 7 units - $28 100% Let 100% 5 units 20 % 1 unit 140% 7 units Therefore, Betty Shanil 5 units + $28 140% (or 7 units) 7 units - $28 100% (or 5 units) Difference between Betty and Shanil after Shanil gave $28 is, 7 units 5 units $28 2 units $28 1 unit $28 2 = $14 12 units 12 x $14 = $168 Answer: $168 8
Q11 Henry received his examination result slip but it was torn. 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? a) (83 + 85 + 99 + 89) 4 = 356 4 = 89 Answer: 89 marks b) Average 85.5 Total 4 (subjects) x 85.5 = 342 Science 342 83 85 91 = 83 Answer: 83 marks 9
Q12 The figure below is not drawn to scale. Find its area. Area of rectangle 84 cm x 15 cm = 1260 cm 2 Area one triangle ( 2 1 )(35)(84) cm 2 = 1470 Total Area 1260 cm 2 + 1470 cm 2 + 1470 cm 2 = 4200 cm 2 Answer: 4200 cm 2 10
Q13 A dressmaker had some buttons. She used 7 1 of them on 1 Monday and 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? (Mon) used 7 1 7 7-7 1 = 7 6 left 1 6 (Tue) used of remaining 11 You re in good 7 hands when you re with Excel! 1 6 6 x = 11 7 77 Total used (Mon) + (Tue) 1 6 17 + = 7 77 77 17 255 (bought) 77 1 255 17 = 15 77 77 77 x 15 = 1155 77 Answer: 1155 buttons 11
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? Curry Puffs Cupcakes 1 group of 7 $2 (x5)* 1 group of 5 $3 (x7)* *Curry puffs (x5) and cupcakes (x7) to give a common number of 35 for both curry puffs and cupcakes. Curry Puffs 5 groups of 7 = 35 $10 Cupcakes 7 groups of 5 = 35 $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, Curry Puffs 15 groups of 7 $30 Difference = $33 Cupcakes 21 groups of 5 $62 a) Curry Puffs 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 $30 Answer: $30 12
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? Before After $2 notes 100% - 20% 80% $5 note 100% + 30% 130% $5 notes more than $2 notes 130% - 80% = 50% 50% 15 notes 10 % 15 notes 5 = 3 notes 100% 10 x 3 notes = 30 notes a) She spent 20% of her $2 notes 2 x 3 notes = 6 notes Answer: 6 two-dollar notes b) 100% of all $2 notes $2 x 30 notes = $60 100% of all $5 notes $5 x 30 notes = $150 Total $60 + $150 = $210 Answer: $210 13
Q16 Mrs Lim gave her two daughters, Liming and Lizhen, some money in the ratio of 8 : 9. Liming and Lizhen shared the cost of an electronic game in the ratio of 6 : 7. Liming used 4 3 of 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? Liming : Lizheng At first 8 : 9 Cost shared 6* : 7 Left with 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 $130 1 unit $130 2 = $65 Liming at first 8 units 8 x $65 = $520 Answer: $520 b) Total cost 6 units (from Liming) + 7 units (from Lizheng) = 13 units 13 units 13 x $65 = $845 Answer: $845 14
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? Peter received 50% + 3 Remaining 50% - 3 Tom received 5 more than half the remaining Half of [(50% -3) + 5] = (25% - 1.5) + 5 This would mean the remaining amount for Jerry after Tom gets his share is (25% - 1.5) 5 = 25% - 6.5 Jerry received 50% of the above remainder plus the last 3 bookmarks Half of (25% - 6.5) + 3 = (12.5% - 3.25) + 3 50% of J s share; The other 50% of J s share If Jerry s (12.5% - 3.25) is 50% of his share, then the other 50% has to be the last 3 You re bookmarks in good hands when you re with Excel! 50% = 50% 12.5% - 3.25 = 3 12.5% = 3 + 3.25 12.5% = 6.25 1% 6.25 12.5 = 0.5 100% 100 x 0.5 = 50 (bookmarks) 15
50 bookmarks 25 25 3 22 Peter: 50% + 3 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 50 6 x 100% = 12% Answer: 12% 16
Q18 Kailing and Jim had a total of $63. Kailing gave 0.3 of her share to Jim. Jim then gave 3 1 of the total amount of money 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? In the end Kailing Jim Brother Before Jim gave 3 1 of his amount to his brother and after Kailing gave 0.3 of her share to Jim - Kailing Jim 0.7 of Kailing s original share* $63 Brother *Kailing gave 0.3 of her share and would be left with 0.7 5 units $63 1 unit $63 5 = $12.60 2 units (0.7 of K s share) 2 x $12.60 = $25.20 0.1 of K s share $25.20 7 = $3.60 Whole of K s share 10 x $3.60 = $36 Answer: $36 17