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top grades in PSLE math.
We are able to help each child use their mindset through
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1. We make learning math fun through games and activities.
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About PSLE Math Series 2013
PSLE Math Series is a must-have resource guide for any student who
is preparing for PSLE Math in 2013.
It consists of examination questions that appeared in top schools’
examination papers in the past 5 years from 2007 to 2011.
All questions are carefully categorized to ensure every learner
understand and apply all the concepts necessary to solve the most
challenging problems.
It follows the MOE syllabus closely to help every child score well in
school exams and PSLE.
Please register at
www.pslemathseries.com
for product updates.
How to Use PSLE Math Series
1. Self study
2. Use it with the support of your tutor/teacher
3. Attend lessons at any centre that uses PSLE Math Series
To gain maximum benefits from PSLE Math Series, download the
‘PSLE Math Series’ app from App Store.
The ‘PSLE Math Series’ app can be used on both the iPhone and the
iPad.
The app will auto check your answers and generate a report which
will be sent to your registered email.
Unit 1 Whole Numbers
1
Unit 2 Patterns
31
Unit 3 Algebra
73
Unit 4 Data Analysis
87
Unit 5 Fractions
126
Unit 6 Percentage
147
Unit 7 Ratio
172
Unit 8 Speed
230
Volume 1
Contents
1.1 Four Operations
1.2 Pairing/Grouping Concept
1.3 Multiple Differences
1.4 Factors and Multiples
1.5 Bonus/Free Concept
1.6 Equal Intervals
1.7 Guess and Check
1.8 Unit/Model Method
1.9 Before-after Difference
Unit 1 Whole Numbers
2007
1. Gerald received 10 hongbaos during Chinese New Year.
Five of them contained $20 each and three of them contained $12 each.
He used the money in the remaining 2 hongbaos to buy 4 t-shirts at $12.50 each. How much money was there in all the hongbaos Gerald received? PH07C37
2. A total of 36 kg of butter is packaged into boxes each containing 4 kg of butter. Each box is then sold for $1.85. What is the total selling price of all the boxes of butter? NH07C40
3. Emily was twice as old as Jimmy 5 years ago. In 10 years’ time, Jimmy will be 32 years old. How old is Emily now? RY07C40
4. The entrance fee to an amusement park was $4.50 for an adult and $2.50 for a child. Mr Lee took some children to the park and paid a total of $19.50 as entrance fee. How many children did he take to the park? HK07P36
5. James used 12 litres of syrup to make fruit punch. For every litre of syrup, he added 3.5 litres of water. The fruit punch was then poured into cups of 200 mℓ for sale.
(a) How many cups of fruit punch did he get?
(b) If each cup of fruit punch was sold for $0.50, how much money would James collect? RG07P39
2008
6. Mary had $50. She can buy either exactly 3 similar wallets and 5 similar combs or exactly 10 such wallets. How many such combs can she buy with $210? NH08C38
7. A necklace cost $160 more than a bracelet. 2 such bracelets cost as much as 3 rings. If each ring cost $100, what was the cost of the necklace? TN08S36
8. Mary and Eliza went shopping. Mary bought 2 compact discs at $8.50 each and a key chain for $6. Eliza spent $3.80 less than Mary. If Eliza bought a story book for $5.40 and 3 similar markers, how much did she pay for each marker? MB08S38
Unit 1.1 Whole Numbers
Four Operations
9. The table shows the sales of flour at ABC’s supermarket.
Type of packet Price per packet Number of packets sold
Total mass of packets sold
Small $2 48 48 kg
Medium $3 30 45 kg
How much money did the supermarket collect from the total sale of all the flour? AT08S37
10. A box weighs 0.55 kg. When 7 packets of salt were placed into it, the total mass became 3.35 kg. When 3 packets of salt were taken out and a tin of milk powder was placed into the box, the mass of the box became 3.65 kg. Find the mass of a tin of milk powder. RY08P37
11. There are 2500 children in a school. 1400 of them enjoy Music lessons. 1500 of them enjoy Art lessons. 450 of them do not enjoy both Music and Art lessons. How many of them enjoy both Music and Art lessons? RY08S36
2009
12. A bar of chocolate is sold at $3.50 each or in packets of 4 at $12 per packet. Alice wants to buy exactly 38 bars of chocolate for a party. What is the least amount of money that Alice could have spent on the chocolate? AC09P07
13. Dennis wanted to buy a toy aeroplane which cost $44.10. He decided to save $2.10 a day to buy it. If the price of the toy aeroplane decreased to $39.90 at a sale, how much did he need to save each day so that he could buy the toy aeroplane after saving for the same number of days? HK09P06
14. In a school science fair, there were exhibits from Primary 4 to Primary 6. Altogether 25 exhibits came from Primary 5 and 6. If 16 exhibits were not from Primary 6 and 15 exhibits were not from Primary 5, how many exhibits were there altogether? HK09P17
15. At a party, a box of candies was divided equally among 114 children. 38 of these children gave up their candies. As a result, there were 228 more candies shared among the remaining children. How many candies were there in the box at first? RS09P06
16. A Chinese medical shop had 50 jars containing the same number of herbs in each jar. During renovation, 15 jars were removed and their herbs were distributed equally amongst the remaining jars. As a result, there were 12 more herbs in each jar than before. How many herbs were in each jar before the renovation? RY09C10
2010
17. A box contained a total of 506 ten-cent coins and five-cent coins. All the ten-cent coins were worth $15. If all the five-cent coins were removed from the box and replaced by twenty-cent coins of the same value as the five-cent coins, how many twenty-cent coins would replace the five-cent coins? SN10C05
18. During a sale, Shop X and Shop Y were selling similar blouses at $28 and $21
respectively. Before this sale, the price of blouses was the same in both shops. A sum of $170 could be saved by buying 2 blouses from each shop during the sale. How much was the discount per blouse in Shop X? AT10C12
19. Carrie had $210. During a moving-out sale, she paid $54 for 3 dresses and 5 T-shirts. She bought another 10 T-shirts and a few dresses with all the remaining money. If each dress cost $6, how many dresses did she buy in all? RY10S07
20. Nancy and Jane baked 1800 muffins altogether. After Nancy sold 680 of her muffins, Nancy still had 20 muffins more than Jane. How many muffins did Nancy bake? NH10S10
21. After giving 22 cards away, Peter put the rest of the cards equally into boxes. He found that he had 7 cards left after putting 25 cards into each box. How many boxes of cards did Peter have if he had 154 cards at first? AT10S07
22. There is a block of 100 flats. Ah Huat, a painter, paints one flat each month from January to November. The flats are painted in the same order and Ah Huat takes a holiday every December. If my flat was painted in May 2004, which month and year will it be painted next? AT10S11
23. A courier company charged $25 for every large parcel and $15 for every small parcel delivered safely. However, a penalty of $50 was charged for every damaged parcel, regardless of size.
This month, the company delivered 120 parcels of which 𝟏𝟒 of them were small parcels. It collected a total of $2000 after paying a penalty for an equal number of large and small parcels. How many large parcels were delivered safely? NY10S12
24. There are some 10-cent coins and 50-cent coins in the piggy bank. The amount of money in the box is $3.40. If the number of 10-cent coins is less than 5, find the total number of coins in the piggy bank. RG10S09
25. The table below shows the number of mobile phones per family in a particular block of flats.
Number of mobile phones 0 1 2 3 4
Number of families 2 24 49 67 28
What is the total number of mobile phones in that block of flats? AC10P08
26. Lindsay and Johanna went shopping. Lindsay bought 7 dresses at $88.90 each and a pair of shoes for $45.70. Johanna bought a camera which was 0.6 of what Lindsay spent altogether. Then she had $22.85 left. How much money did Johanna have originally? SN10P07
27. There are 2 teams of workers at a fast food restaurant. Team G has 30 more members than Team H. Each member in Team G prepares 4 burgers in 1 minute while each member in Team H only prepares 3 burgers in 1 minute. In 1 hour, both teams prepare 36 600 burgers altogether. How many members are there in each team? SN10S15
28. 5 friends were playing Wii games on a Friday afternoon from 3 pm to 6 pm. As there were only 4 consoles, they took turns to play. At any time, 3 of them played while the other 2 friends watched. If each of them had the same amount of playing time, how many minutes did each child play that afternoon? SN10S09
29. At a factory, Jane could assemble 8 toys in a day while Mary could assemble 5 more toys than her in a day. If Mary was absent for 4 days, how many days would she need to assemble 18 more toys than Jane? CH10P10
30. A condominium unit was sold at $810 000, when rounded off to the nearest ten thousand dollars. What was the lowest possible selling price? NY10S02
31. A lemon costs 30₵ more than a lime. Kayee bought 56 limes at 35₵ each. If she were to use the same amount of money to buy only lemons, how many fewer lemons could she buy? SN10P02
32.
Wendy wants to make icy-pop to serve 10 people. Using the recipe above, how much strawberries does she need? HK10P03
33. During an Art lesson, Mrs Choo gave each group 17 pieces of cardboards as shown below on the left to make a structure. John’s group decided to fold each pieces into a prism as shown below on the right:
His group glued all the 17 prisms together to form the structure shown below.
(a) What is the length of the base of the prism? (b) What is the height of the structure? MB10P08
34. The school conducted a survey with some pupils on how they travelled to school. There were twice as many boys as girls who travelled to school by MRT. 15 of those who
travelled by bus were girls. The table below shows the findings.
Study the table and find the number of boys who went to school by MRT. HP10P05
Walk MRT Car Bus Total
Boys 5 ? 24 ? 107
Girls 10 ? 12 8 53
35. Mr Tseng bought a new car. He paid a down payment of $20 000. After paying monthly instalments of $1200 for 41
2 years, he still had $4000 more to pay. What was the cost of
36. During a basketball match, the teacher promised the team of 8 pupils an equal playing time during the 40 minutes match. Given that only 5 players can play at any one time, what is the average playing time for each pupil? CH10P05
37. A number is between 50 and 70. When it is divided by 3, the answer is a whole number. When it is divided by 8, it has a remainder of 5. What is the number? RY10C03
2011
38. Darren used 14 litres of syrup to make fruit punch. He added 2.35 litres of water. The fruit punch was then poured into cups of 250 mℓ for sale.
(a) How many full cups of fruit punch did he get?
(b) Each cup of fruit punch was sold for $0.95. How much would Darren collect if he sold all the full cups of fruit punch? RG11S11
39. Tammy packed 46 kg of chicken wings into 8 packets of equal mass. What was the mass of 1 packet of chicken wings?
Round off your answer to 1 decimal place. NY11C02
40. A factory produced a total of 5000 toy cars for the first 4 days. With the improved
productivity of the workers subsequently, the factory managed to produce 1750 toy cars per day. How many days did the factory take to produce 22500 toy cars? NY11C05
41. The sum of 2 numbers is 121. One of the numbers is a multiple of 9, while the other number is a factor of 12. Find the two numbers. RY11C01
42. Lauren and Jude went shopping and they spent the same amount of money. Lauren bought 6 dresses at $68.90 each and a pair of jeans for $56.60. Jude spent 0.6 of the amount spent by Lauren on a DVD player. After paying for a mobile phone, Jude had $23.85 left. How much did he pay for the mobile phone? SN11C13
43. Kasey needed to make 120 bows for prize giving. She used 12.4 cm to make a bow. She bought 3 rolls of ribbon, each 5 m long. Find the length of ribbon she had left. HK11P03
44. The total mass of a crate and 16 similar bottles of juice is 29.5 kg. If the mass of 5 such bottles of juice is 8.75 kg. Find the mass of the crate. TN11S05
45. Andre, Benny, Chris share a total of $1144. Andre and Benny have $778 and Benny and Chris have $649. How much money does Benny have? HP11P04
46. The number of children in Twinkle Tots Childcare Centre is less than 80. If they are divided into groups of 14, 3 children will be left out. If they are divided into groups of 16, 9 children will be left out. How many children are there in the childcare centre?
47. Ray has more than 10 but less than 60 cards. If he packs them into packets of 6 cards, he will have 3 cards left over. If he packs them into packets of 7 cards, he will be short of 5 cards. How many cards does Ray have? NH11S03
48. Devi bought 2 identical rulers, 3 identical pens and 2 identical notebooks from Pop Bookstore. Her pen leaked and some ink smudge on her receipt. If the cost of each pen was $2 after rounding off to the nearest dollar, what was the highest possible cost of each notebook? NY11C07
49. The table below shows the number of books borrowed by pupils in the month of July.
Number of pupils 4 5 ? 8 3 0
Number of books borrowed by each pupil
0 1 2 3 4 5
The total number of books borrowed by the pupils is 65. How many pupils borrowed 2 books? CH11P05
50. The table shows the number of pets owned by a class of pupils. If the total number of pets owned by the pupils is 82, how many pupils owned 2 pets? NH11P02
Number of pets 0 1 2 3 4
Number of pupils 4 12 ? 10 6
51. Fill in the boxes below with different operators (+ − × ÷) to make the expression correct. (You are allowed to use the same operator twice) RG11P04
52. Write down the decimal that is exactly halfway between 0.36 and 0.94. NH11P05
53. Ann is 8 years old. When she reaches her mother's present age, her mother would be 62 years old. How old is Ann's mother now? MG11P06
54. A 2-digit number when divided by 9 gives a remainder of 5. What is the largest possi ble number? RS11P01
2007
1. One day, during a pet show-and-tell session in class, 8 pupils brought a dog each while the rest of the pupils brought a cat each. If there were 174 legs altogether in the classroom,
(a) how many pupils were there?
(b) how many more cats than dogs were there? RY07C42
2. Andy bought 20 books and pens for $118. One week later, he sold 4 pens. Then he had
the same number of pens and books left. Each book cost $1.00 more than each pen. How much did he pay for the books? NH07C43
3. Each time Ann deposits $4 into her bank account, her father deposits thrice as much as Ann in her account. When Ann has $208 in her bank account, how much did her father deposit in her account? AC07S38
4. Mr. Lee worked out a saving plan for Janet.
For every $4 Janet saved, he would top up $2 into her bank account. After some time, the amount saved in Janet’s account was $252. How much of this amount was contributed by Mr. Lee? NH07P40
5. A grocer packed 252 kg of rice into bags of kg and 2-kg. He has an equal number of 5-kg bags and 2-5-kg bags of rice. How many bags of rice does he have in all? SC07P37
2008
6. Rafi receives $2 from his mother for every $10 he saves. He also receives $3 from his father for every $20 he saves. He has $174 altogether after some time.
(a) How much of the money is from his mother? (b) How much of it is from his savings? MG08C48
7. The cost of 0.5 kg of lady’s fingers is the same as 1.5 kg of carrots. Mrs Devi spent $41.25 for 2 kg of lady’s fingers and 10.5 kg of carrots. What was the cost of 1 kg of carrots? RG08S44
Unit 1.2 Whole Numbers
Pairing/Grouping
8. John saves a fixed amount of money every week. For the amount that he saves each week, his father will contribute 0.6 of that amount to his savings. How much does John save every week if he saves a total of $192 in 15 weeks? NY08P37
9. Wayne had five more 50₵ coins than 20₵ coins. After he used eight 50₵ coins, the
value of 50₵ coins became $1.50 more than that of 20₵ coins. How many coins did he have at first? NY08S42
2010
10. Curry puff is sold at 80 cents each. For every 3 curry puffs, Mrs Lim can buy 1 more
curry puff at a discount of 50%. If Mrs Lim has $50, how many curry puff can she buy? NH10C15
11. The usual selling price of a bottle of vitamins is $63. During the Great Singapore Sale, for every 2 bottles bought, the second bottle can be purchased at a 50% discount. Mrs Lee paid $567 for the vitamins during the sale. How many bottles of vitamins did she buy? MG10S07
12. John has $34 in his piggy bank. There was a mixture of 20-cent and 50-cent coins. There were 5 more 50-cent coins than 20-cent coins in the piggy bank. How many 50-cent coins are there in his piggy bank? CH10S06
13. Rabiah bought a total of 80 stools and chairs for $1780. When 20 stools were removed,
there was an equal number of stools and chairs left. If each chair cost $6 more than each stool, find the cost of each chair. AT10S10
14. At a bakery, muffins are sold at $1 each. When a customer buys 5 muffins, she can buy one more at half the price. What is the greatest number of muffins that a customer can buy with $20? HK10P05
15. At a sale, wet tissues are sold at $1 per packet or 4 packets for $3.50. What is the maximum number of packets you can buy for $100? CH10P04
16. Siva needed to buy some furniture for his new company. He could buy 4 tables and 6 bookshelves with $490. With the same amount of money, he could buy 14 bookshelves too.
(a) How many sets of 4 tables and 6 bookshelves could he buy with $2000?
2011
17. For every $8 Julie saved, Mrs Tang would top up $3 into her bank account. After some time, the amount saved in Julie’s account was $528. How much did Mrs. Tang contribute? AT11C03
18. Jessica and Joe were buying sports gear at a mall where a discount of $8 was given for every $80 spent.
(a) Jessica picked up $572 worth of sports gear. How much did she pay for them after the discount?
(b) If Joe paid the cashier $864, how much discount did he get? AT11C12
19. The table below shows the admission fees to a circus for an adult and a child. There were 50 more children than adults at the circus. If a total of $5614 was collected, how many children were at the circus? CH11S09
Adult $25
Child $8
20. The price of one egg tart is $0.90 from Delicious Bakery. For every 3 egg tarts a
customer buys, he can buy the fourth one at half the price. What is the greatest number of egg tarts that a customer can buy with $72? AC11P11
2007
1. Eddy gets $4 more pocket money than Sam each week. They each spend $11 per week
on food and save the rest. After a few weeks, Eddy managed to save $65 and Sam only managed to save $45. How much pocket money does Sam get each week? RY07C46
2. For every $20 Jason saved, his brother saved $35. If his brother had saved $90 more than Jason, find out how much Jason had saved. RG07S41
3. Terrence earns $350 less than Leslie every month. They each spend $800 every month and save the rest of their money.
(a) How long does it take for Terrence to save $2100 and Leslie to save $4550? (b) What is Terrence’s monthly salary? HP07P45
2008
4. Alvin’s monthly income is $250 more than Clayton but their monthly expenditures are
the same. Over a certain period of time, Alvin has saved $1350 but Clayton has only saved $600. Given that each of them spends $500 a month,
(a) How long does Clayton take to save the $600? (b) What is Alvin’s monthly income? AC08S42
5. Meili received $2.50 more than Sandy in their daily allowance. Each of them spent the same amount each day and saved the rest. When Meili saved $31.50, Sandy saved only $24. How much was Meili’s daily savings? NY08S39
2010
6. Both Joanne and Joseph had an equal amount of money at first. Every month, Joanne
spent $850 and Joseph spent $912. After a few months, Joanne was left with $1550 while Joseph had 𝟒𝟓 as much as Joanne. How much money did Joseph have at first? AC10S15
7. Darren saves $1.40 daily and Sonia saves $1.10 more than him daily. Although Sonia
started saving one week later than Darren, she now saved $2.30 more than him. How many days has Darren been saving? NY10S06
Unit 1.3 Whole Numbers
Multiple Differences
2011
8. Macy and Kathdu were given equal amount of pocket money each day. Macy and Kathdu started saving on the same day. After saving for a certain number of days, Macy and Kathdu had $11.20 and $12.80 in their savings respectively. Macy spent $0.20 more than Kathdu every day. How many days had they been saving? NY11S01
9. Jeanne earns $22 more than Caleb every week. Each of them spends $110 per week
and saves the rest. When Jeanne has saved $1056, Caleb has only saved $880. (a) How long does Jeanne take to save $1056?
2008
1. Mrs Ming has some party lights. The red light flashes every 4 seconds, the blue light
flashes every 5 seconds while the purple light flashes every 6 seconds. If all 3 colour lights flash together at 9 p.m. what is the very next time on the clock that they will flash together again? AT08S40
2. Mrs Smith has drawn up a schedule to have her home cleaned by 3 part-time workers.
The cleaner goes to her home once every 3 days, the sweeper once every 4 days, and the gardener once every 6 days. If the 3 workers first met on 28 July, when was the earliest date (in July) the cleaner had to start work? NY08P36
3. Mrs Wong bought an equal number of toy dinosaurs and teddy bears at a fun fair. The
toy dinosaurs were sold at 3 for $2 and the teddy bears were sold at 4 for $3. She paid $4 more for the teddy bears than for the toy dinosaurs. How much did she pay for all the items? RY08P44
4. There was a total of 200 blue, red and green balls. There were twice as many red balls as blue balls. There were fewer green balls than red balls. The number of blue balls and red balls in each group was less than 100 and divisible by 3 and 4. How many green balls were there? NY08P41
5. 390 marbles were placed into 3 boxes according to their colours. The number of blue marbles is twice the number of red marbles, and the number of green marbles is less than the number of blue marbles. The number of marbles in each box is less than 200. The number of marbles in each box is divisible by both 6 and 5.
How many green marbles were there? MG08P40
2009
6. There are three bulbs in a shop. One lights up every 4 minutes, another bulb lights up
every 8 minutes and the third bulb lights up every 11 minutes. All the bulbs light up together when Ali walked into the shop. How many times will he see at least 2 bulbs light up together if he was in the shop for 𝟑𝟒 hour? SC09S13
Unit 1.4 Whole Numbers
Factors and Multiples
2010
7. Once a computer program is executed, 3 chipmunks will appear on the screen. One minute later, the 3 chipmunks will yawn at the same time. After that, Chipmunk Alwin will yawn at intervals of 60 seconds, Chipmunk Simmon will yawn at intervals of 75 seconds and Chipmunk Tadore will yawn at intervals of 100 seconds. When the 3 chipmunks yawned at the same time for the third time, how many minutes has the program been running? NY10P02
2011
8. Mrs Ronald has 3 sacks of coffee beans weighing 56 kg, 96 kg and 120 kg. She wants to repack all the coffee beans into smaller packets of equal mass. Without mixing the coffee beans from the three sacks and without any leftover or wastage,
(a) what is the greatest possible mass of each packet?
(b) How many packets of coffee beans will she get in all? SN11C06
9. There are two metal bars of length 72 cm and 96 cm. Short bars of equal length are cut from the two metal bars without any remainders. What is the largest possible length of each short bar? NH11P04
10. One side of a garden was double-fenced. The outer fencing had 3 wooden spokes
along a length of 0.4 m and the inner fencing had 9 metal spokes along a length of 180 cm as shown in the diagram below.
There were 198 more wooden than metal spokes. How many wooden and metal spokes were there altogether? HP11P11
2007
1. Mr Lim earned $3 for each gift hamper he sold. For every 12 hampers sold, he earned an extra $5.
(a) How much money would Mr Lim earn if he sold 85 hampers? (b) How many hampers must he sell in order to earn $194? NY07C43
2. Wendy bought CDs at $3 each and sold them at $8 each. To promote sales, all customers who bought two CDs were given one free CD. After she had sold all the CDs, Wendy made a gain of $1235 despite giving away 150 CDs to her customers. How many of Wendy's customers bought only one CD? HP07S48
3. Mrs Durai wants to buy bookmarks for 3 classes of pupils. There are 35 pupils in each class. For every 4 bookmarks she buys, she gets another one free.
(a) How many bookmarks does she need if each pupil gets 1 bookmark?
(b) 4 bookmarks cost $2. What is the least amount she needs to pay? PC07P(1)37
2008
4. John is paid $3 for every file he sells. He receives a bonus of $20 for every 75 files he sells. How many files must he sell to earn $1249? RG08S38
2009
5. For every 200 books Johnson sells, he earns $8. He will receive an additional bonus of $20 for every 3000 books sold. How many books must he sell to earn $700? AT09C14
6. John earns a commission of $2.20 for every magazine he sells. He also receives an additional bonus of $5 for every dozen magazines he sells. How many magazines must he sell to earn $325? SN09C16
2010
7. One box of greeting cards costs $3.75. Mandy needs 120 boxes of such cards. For every 4 boxes of cards she buys, she gets 1 box free of charge. How much does Mandy have to pay for 120 boxes of such cards? SN10S10
Unit 1.5 Whole Numbers
Bonus/Free Concept
8. A shopkeeper sells a packet of 10 candies for $4. He gives away 2 free candies for every 2 packets of candies purchased. Diana needs 131 candies for her birthday party. What is the least amount of money that she has to pay? NH10P09
9. Mr Lim bought 320 doughnuts for a party at a shop with the following promotions:
What was the least amount of money that Mr Lim could have paid for the doughnuts? NY10P07
2007
1. Mr Lim planted some cherry trees in a circle with the same distance apart. The
distance between the first and the fourth tree was 60 m. (a) Find the distance between the first and the tenth tree.
(b) If 50 trees were planted and Mr Lim tied a rope to fence up the area, find the length of the rope needed. PH07C48
2. Emily had a rod. She marked it in three different ways. First, she marked the rod into
ten equal parts. Without erasing the first set of markings, she then marked the rod into 12 equal parts. Finally, she added another set of markings by marking the rod into 15 equal parts. If she cut the rod according to the markings she had made, how many parts would she get? PH07S48
2008
3. There were 9 chairs in each row. 8 rows of chairs were rearranged, equally spaced, to
form the perimeter of a square. There were same numbers of chairs on each side of the square. How many chairs were there on each side of the square? SC08P43 2009
4. Jason planted 20 mango trees in a row at equal distance apart. The distance between
the first and the fifth tree was 28.4 m. Find the distance between the first and the last tree. HP09S06
2010
5. The Tampines Expressway (TPE) measures 13 892 metres long. Trees were planted
from the beginning to the end along the expressway at an equal distance of 4 m apart. How many trees were planted along the expressway? (Assume the width of the tree is insignificant.) RY10P05
Unit 1.6 Whole Numbers
Equal Interval
6. Mary arranged some round buttons in a straight line at equal intervals. The distance
between the centre of the 1st button and the centre of the 4th button was 24 cm. What was the distance between the centre of the 1st and the centre of the 40th button? NH10P03
7. 125 sticks are placed at equal distance apart along one side of a straight road. The
distance between the first stick and the last stick is 1550 m. What is the distance between the 4th and 8th stick? RS10P02
2011
8. One part of a car wheel was stained with paint of its surface. The diagram below showed the tyre marks made by the car wheel when the vehicle moved through a certain
distance. Find the circumference of the car wheel. RG11P14a
9. It takes Mr. Adams 20 minutes to saw a pole into 5 equal pieces. How many minutes
would it take him to saw another similar pole into 10 equal pieces? HK11P02
10. 35 pupil leaders from a primary school were asked to welcome visitors during the
school's opening ceremony. They were stationed in a row from one end of the school's entrance to the other end at an equal spacing of 1.3 m apart. On the day of the
opening ceremony, 8 pupils did not turn up. As a result, the remaining pupil leaders were restationed at a new equal spacing. What was the new spacing between 2 pupil leaders? RY11S13
11. In a hall, there are 16 rows of 19 chairs each. Mr Wong wishes to rearrange these
chairs into a square with the same number of chairs on each side. There are no chairs inside the square. How many chairs will there be on each side of the square? AC11P13
2007
1. There are 30 problem sums in a test. 4 marks are given for each correct answer and 1 mark will be deducted for each incorrect answer. Joshua obtained 85 marks. How many problem sums did he answer incorrectly? AC07S39
2. There were 20 questions in a Mathematics Quiz. 5 marks were given for each correct answer. 2 marks were deducted for each wrong answer. Cindy answered all the questions and scored 65 marks. How many questions did she answer correctly? NH07S43
3. There were 10 word problems in a Mathematics Competition. 5 points were awarded for each correct answer and 3 points were deducted for each incorrect answer. If Amy answered all 10 word problems and scored 26 points, how many word problems did she answer correctly? NH07P39
4. Mrs Samy made a deal with her son, Raju, that for every night he spent reading, he would get 2 stickers. For every night that he did not read, he would give her back 1 sticker. The deal lasted 30 days and Raju collected 24 stickers in all. How many nights did Raju spend reading? NY07P41
5. Debra played a computer game in which she fired rockets at planes. For every rocket that hits an enemy plane, she gets 7 points. For every rocket that hits one of her own planes, she loses 2 points. When a rocket does not hit any plane, she does not get or lose any point. Debra fired 392 rockets. 65 of them did not hit any plane. At the end of the game, she scored a total of 1650 points. How many enemy planes did she hit? PC07P(2)45
6. In Semester One, Kelly earned a total of 150 silver and gold stars. Ali earned 55 silver stars and 15 gold stars. Each silver star was worth 3 points. Each gold star was worth 5 points each. Kelly scored 390 more points than him.
(a) How many points did Kelly score?
(b) How many silver stars did Kelly earn? RY07C45
7. A boy bought 20 stamps. Some were 50-cent stamps and some were 40-cent stamps. The cost of the 50-cent stamps was $4.60 more than the 40-cent stamps. How many 50-cent stamps did he buy? NH07C37
Unit 1.7 Whole Numbers
Guess & Check
8. There are 60 shirts and pants in a stall. Each shirt costs $9 and each pair of pants costs $7. If the total cost of the shirts is $188 more than the total cost of the pants, how many shirts are there in the stall? RY07S41
2008
9. A salesman delivered 30 vases to his customers. On the way, he had a minor accident and broke some of the vases. For every unbroken vase delivered, the salesman was paid $40. As a penalty, he had to pay the customer $10 for every broken vase. In the end, the salesman earned $1000 for the sale of the vases. How many vases were not broken? NH08S43
10. Mr Loo had to deliver 800 hampers in May. He received $4 for every hamper that was delivered successfully and $7 would be deducted from his salary for every hamper that was damaged. If his salary in May was $2430, how many hampers did Mr Loo deliver successfully? NY08S43
11. A small egg cost 10₵ while a large egg cost 5₵ more. Mrs Lee paid $6.70 for 50 eggs. How many large eggs did she buy? MB08S39
12. Ann bought 10 magazines from the news stand. She paid $5 each for some of the magazines and $7 each for the rest. If Ann spent $56 altogether, how many magazines cost $5? MG08S42
13. A baker puts cupcakes into boxes of two different sizes. 5 cupcakes fill one small box while 12 cupcakes fill one big box. If the baker has 99 cupcakes, how many boxes of each size does he need to contain all the cupcakes with no leftover? AT08S36
2009
14. Wei Qing played with Ravi in a game of chess for twelve rounds. In each round, the winner scored 5 points while the loser scored 2 points. At the end of the game, Ravi’s total score was 45 points. How many rounds did Wei Qing win? HP09P09
15. The table below shows the scoring system at a basketball tournament. A team is awarded 5 points for a win, 2 points for a draw and no point for a loss.
Win Draw Loss
5 points 2 points 0 point
At the end of the tournament, Team Alpha played a total of 36 matches (won, drew or lost) and accumulated 120 points. How many matches did Team Alpha win if they had lost 9 matches? RS09P18
16. Jeneen sat for a quiz that had 70 questions. 3 marks were awarded for each correct answer and 1 mark was deducted for each wrong answer. Jeneen answered all the questions and scored 146 marks for the quiz. How many questions did he answer correctly? SC09S08
17. Mr Lim paid $134.40 for some jackfruits and pomeloes. The cost of the pomelo was 0.8 that of a jackfruit. A pomelo cost $5.60. If all the pomeloes cost $22.40 more than the jackfruits, how many fruits did he buy? NY09C14
2010
18. On a farm, there are some chickens and goats. A boy counts the animals and finds that they have 220 eyes and 360 legs. What fraction of the total animals are goats? NH10C14
19. Grandpa had a farm. He kept 89 goats and chickens. The total number of legs the animals had was 264 legs. How many chickens did Grandpa have? RG10P07
20. In an online quiz, 30 points are awarded for every correct answer. For each wrong answer, 10 points are deducted. Muthu was awarded 2570 points after answering 103 questions.
(a) How many points will be awarded if all 103 questions are answered correctly? (b) How many questions did Muthu answer wrongly? PC10P07
21. Joanne had a total of 36 wires and strings. Each wire is 4 cm long and each string is 3 cm long. The total length of the wires is 25 cm longer than the total length of the strings. How many more wires than strings did she have? AT10C13
2011
22. A test consists of 25 questions. A correct answer is worth 4 marks. An incorrect answer will result in a deduction of 2 marks. Li Meng scored 70marks. How many questions did Li Meng answer incorrectly? MGS11P01
23. A farm has some ducks and cows.
The ratio of the number of animals to the total number of legs is 8 : 23. Express the number of ducks as a fraction of the cows.
Give your answer in the simplest form. NH11C15
24. In a game, you will score 200 points if you win but will have 150 points deducted if you lose. Muthu played 10 games and scored 950 points. How many games did he lose? TN11S08
25. Letchmi attempted all the 70 questions in an online game and scored 224 marks. Given that 5 marks were awarded for each correct answer but 2 marks were deducted for each wrong answer, how many questions did Letchmi answer correctly? RY11S06
26. David bought 120 purple and green pencil cases. Each green pencil case cost $2.50 and each purple pencil case cost $1.75 each. If the total cost of the pencil cases was $246, how many green pencil cases did he buy? MG11S10
2007
1. Shirley paid $120 for 8 bags and 6 T-shirts. Each bag cost 3 times as much as a T-shirt. Find the difference in price between a bag and a T-shirt. NH07C36
2. Baker Tan and Baker Lim bought the same number of eggs. Baker Tan used 240 eggs and Baker Lim used 165 eggs. After that, Baker Lim had four times as many eggs as Baker Tan. How many eggs did each of them have at first? PH07C43
3. Anne and Sally had 1436 beads altogether. After receiving 376 beads from Anne, Sally had thrice as many beads as Anne. How many beads did Sally have at first? RY07C39
4. Deming had $100 more than Ali at first. After Deming spent $120 and Ali received $200,
Ali had 3 times as much money as Deming. How much did Deming have at firs t? AT07S37
5. The total mass of three boxes X, Y and Z is 16 kg. X is 0.7 kg heavier than Y and 0.25 kg heavier than Z.
(a) How much heavier is Z than Y? (b) What is Y’s mass? AT07S38
6. Alan and Benny had equal number of stamps. Alan lost 36 of his stamps. Then Benny had 5 times as many stamps as Alan. How many stamps had Alan at first? NH07S36
7. Alex has $1.50 more money than Betty, and three times as much money as Colin. The 3 of them have $9.70 altogether. How much does Colin have? AC07P41
8. When Mrs Lee was 40 years old, her son was twice her daughter’s age. Mrs Lee will be
twice her son’s age when her daughter is 28 years old. How old will Mrs Lee be when her daughter is 20 years old? SC07P45
2008
9. Each pen cost $1.50 more than each eraser. Each file cost $2.40 more than each pen. Hassan bought 2 of each item and paid $14.40. How much did he pay for each file?
Unit 1.8 Whole Numbers
Unit/Model Method
10. Mandy, Nancy and Oliver have a total height of 5.08 m. Nancy is 7 cm taller than Mandy. Oliver is 0.21 m taller than Mandy. Find the height of Oliver. AT08C41
11. There are 1928 red and green buttons in a box. The number of red buttons is 246 fewer than the number of green buttons. How many green buttons are there? HK08P36
12. The total cost of a chicken pie is thrice the cost of a muffin. Mrs Seetho paid a total of $40 for 20 muffins and 10 chicken pies. Find the cost of a chicken pie. NY08C41
13. Mr Thomas bought 5 note books and 2 exercise books. Each note book cost twice as much as each exercise book. The total cost of a note book and an exercise book was $2.40. How much did Mr Thomas pay altogether? SN08C37
14. A fruit seller started his day with the same number of apples and oranges. After he sold 435 apples and 120 oranges, the number of oranges was 4 times the number of apples. What was the total number of apples and oranges at first? MB08S36
15. A box containing 3 files weighed 8.8 kg. Later, Keith added 2 more files and 2 books
into the box and the mass of the box with the contents became 16 kg. If the mass of one file was 3 times the mass of a book,
(a) find the mass of the book.
(b) Keith could only carry up to a mass of 13 kg. What was the least number of files that he should remove from the box so that he would be able to carry the box and files? MB08S46
16. A box and 4 similar files weighed 7.6 kg. Tom added 2 more such files and 5 identical books into the box and the total weight became 14.2 kg. Each file weighed 3 times as much as a book.
(a) What was the weight of the empty box in kg?
(b) If Tom could only lift 12 kg, what was the least number of files that he should remove from the box so that he could lift the box and its contents? AC08P42
17. Matthew, Neena and Osman shared $157.
Matthew had $8 less than Neena and Osman had three times as much as Neena. How much did Osman have? MG08S39
18. Mother bought a total of 12 books and files for $93. She bought 2 more books than files. A book cost $3 more than a file. How much did she pay for the files? SC08P38
19. An equal number of men and women turned up for an audition. After 74 men and thrice as many women were rejected, the number of men was 5 times that of the women. How many people turned up for the audition? SN08P39
2009
20. 12 athletes ran a total of 21600 m. Each male athlete ran 300 m more than each
female athlete. There were 4 more male athletes than female athletes. What was the total distance ran by the male athletes? RY09C18
21. Alex, Ben and David went for a run but none of them completed the run. Ben ran 5 times as far as Alex before he stopped. David stopped 1 km before the finishing line and he ran 3 km less than twice the distance Ben ran. The three of them ran 21 km. How long was the run? RG09S12
22. Alice, Beth and Claire had 600 stamps altogether. After Beth had given 30 stamps to Alice, Beth had twice as many stamps as Claire and Alice had 20 stamps more than Claire. How many stamps did Claire have? RG09P06
23. The mass of a box containing 3 files was 10.2 kg. Later, Ali added 2 more files and 3 books into the box and the mass of the box and its contents became 19 kg. If the mass of one file was four times the mass of a book, find the mass of the box when empty (leave your answer in kg). HP09S10
24. Jason had $78 and Ben had $25. After Jason and Ben spent $53 altogether on some games, Jason had 3 times as much money as Ben. How much did Ben spend on the games? RG09S08
25. At present, Ronald is 3 times as old as his sister. In 22 years’ time, Ronald’s age will be
19 years less than twice his sister’s age. How old is Ronald now? HP09S08
26. Mrs Sim bought 15 handbags for $267.30. 35 of these handbags cost the same price. Each of the remaining handbags cost 3 times as much. Find the difference in the price of the 2 types of handbags. HP09P07
2010
27. At first, Joe had $177 and Chris had $129. Each of them bought a pair of jeans and a shirt at the same price. The shirt cost three times as much as the jeans. In the end, Joe had 3 times as much money as Chris. What was the cost of the shirt? AC10P07
28. A company paid a total of $23 600 in salaries to 17 female and some male employees.
Each male employee received $500 more than each female employee. There were 14 more female employees than male employees. Find the difference in the total amount of money received by the male employees and the female employees. AT10C18
29. In a fun fair, Matthew and John sold 368 balloons. John and Keith sold 112 balloons altogether. Matthew sold 9 times as many balloons as Keith. How many balloons did the three boys sell altogether? RY10C10
30. Casey and Sherman went to the Information Technology Fair with the same amount of money each. Casey spent $900 on a computer while Sherman spent $300 on a printer. After that, Sherman had thrice as much as money as Casey. How much money did each of them bring to the Information Technology Fair? AT10S06
31. At a sale, Lydia paid $350.40 for 3 blouses, a pair of pants and 3 T-shirts. A blouse cost twice as much as a T-shirt and a pair of pants cost 11
2 times as much as a blouse. How
much money would Lydia have saved if she were to buy 2 blouses, a pair of pants and a T-shirt instead? SN10S12
2011
32. There were 76 more apples than oranges in a fruit stall. After 68 apples and 227
oranges were sold, the number of apples left was 6 times that of the number of oranges left. What was the total number of apples and oranges at the fruit stall at the start? HP11P06
33. Minah paid $2 more for a chocolate cookie than a strawberry cookie. She paid $17 for 4 chocolate cookies and 2 strawberry cookies. How much did she pay for a strawberry cookie? TN11S06
34. A jacket cost 4 times as much as a skirt. The skirt cost $12.60 more than a shawl. If Susie paid $171 for these 3 items, how much did the shawl cost? AC11S02
35. Alan and Dave spent a total of $462. Dave and Martin spent $288 altogether. Alan spent thrice as much as Martin. How much did Dave spend? TN11S10
36. In a game, Parisse scored 240 more points than Max at first. After Parisse lost 332 points to her friend, Fendi, Max had 3 times as many points as Parisse. How many points did Parisse have at first? SN11S08
37. Rubber hose X is 3.5 m longer then Rubber hose Y. Rubber hose Z is 8.74 m shorter than Rubber hose X. The total length of the three hoses is 168.66 m. Mr Garden buys Rubber hose Y at 40⊄ per metre. How much must he pay for Rubber hose Y? SN11C03
38. There were a total of 4540 passengers onboard 4 ships, labelled A, B, C and D. All the
ships were travelling on different sea routes. Ship A had the most number of passengers onboard and Ship D had the least. The difference in the number of passengers onboard Ship A and the other three ships was 139, 363 and 618. (a) How many passengers were on board Ship D?
(b) Each ship was required to load sufficient lifeboats to carry all its passengers onboard in case of emergency. Each lifeboat could take up to 30 passengers. Find the total minimum number of lifeboats to be loaded on Ship A and Ship D.
NY11S16
39. A confectionery factory baked a total of 3 123 cupcakes in 4 different flavours,
Strawberry, Chocolate, Vanilla and Blackforest. The Blackforest flavour was the most popular and Vanilla was the least popular flavour with a difference of 528. The difference in the number of cupcakes between Strawberry flavour and Blackforest flavour was 351. The difference in the number of cupcakes between the Chocolate flavour and Blackforest flavour was 190.
(a) How many Blackforest-flavour cupcakes were baked?
(b) The cupcakes were packed into boxes for delivery. Each box can hold up to 20 cupcakes. What is the minimum number of boxes needed to pack all the Strawberry-flavour and Vanilla-flavour cupcakes? RY11P13
40. Mary and Ben took 49 hours to complete their Science project. They worked
separately on their own project. If Mary had worked 5 hours less and Ben had worked 6 hours more, Mary would have put in 2 hours more than Ben. How many hours did Mary put in for the Science project? RG11S13
2007
1. Andrew has 70 more stamps than Basil. If Basil gives Andrew 40 stamps, the number of stamps Andrew has will be 6 times that of Basil’s.
(a) How many stamps does Andrew have? (b) How many stamps does Basil have? AC07S42
2. In a Mathematics Test, the number of passes is 164 more than the number of failures.
If 6 more pupils passed the test, the number of passes will be 9 times the number of failures. Find the total number of pupils who took the test. SC07S37
3. There were 30 more members in the IT club than in the Art Club. 15 members left the
Art Club for the IT club. It was then found that the number of members in the IT club was 5 times as many as the number of members in the Art Club. How many members were there in both clubs altogether? HP07P40
2008
4. Amy, Beth and Carrie have some money. If Amy gives $3.50 to Beth, the two girls will
have an equal amount of money. If Beth gives $3.50 to Amy, Amy will have thrice as much money as Beth. Carrie’s share is the sum of the other two girls. How much money do they have altogether? NH08P44
2009
5. Container A has 150 more marbles than Container B. If 30 marbles are being
transferred from Container B to Container A, there will be thrice as many marbles in Container A as Container B. How many marbles are there in Container A in the beginning? AC09P11
6. Cathy has 1250 more stamps than John. After John gave Cathy 68 stamps, she had 4
times as many stamps as John. How many stamps did John have at first? PL09P07
Unit 1.9 Whole Numbers
Before-After Difference
2010
7. Ashley has 120 more stamps than Brandon. If Brandon gives 25 stamps to Ashley, the
ratio of the number of stamps he has to the number of stamps Ashley has will be 3 : 5. How many stamps do they have altogether? RV10P02
8. Xavier, Yati and Zul each had a certain number of stamps. At first, Yati had 200 stamps
more than Xavier and Zul had 𝟑
𝟒 the number of stamps Yati had. After Yati gave away 𝟏 𝟖 of her stamps to Xavier, she had 60 fewer stamps than Xavier. What was the ratio of the number of stamps Xavier had to the number of stamps Yati had to the number of stamps Zul had at first? Give your answer in the simplest form. RY10P18
2011
9. Bee Leng had $960 less than Kerri. After Bee Leng gave $2400 to Kerri, the ratio of Bee Leng’s money to to Kerri’s money became 1 : 3. How much did BeeLeng have in the end? AT11C01
10. Valerie has 1764 more stickers than Mark. After Mark gave Valerie 128 stickers, she had five times as many stickers as Mark. How many stickers did Mark have at first? RY11C09
11. Velu and Rosie had some stamps. If Velu gave Rosie 52 stamps, she would have the
same number of stamps as Rosie, If Rosie gave Velu 34 stamps, the ratio of the number of stamps Rosie had to the number of stamps Velu had will be 3 : 7. How many stamps did Velu have at first? RY11P06
12. Packet A, Packet B and Packet C each contained some salt. At first, there were 200g
more salt in Packet A than Packet B. Packet C had 𝟑
𝟒 of the amount of salt in Packet A. After 𝟏
𝟖 of the amount of salt in Packet A was transferred to Packet B, there was 82.15g of salt in Packet B. How many percent less salt were there in Packet C than Packet A at first? NY11P17
13. Eugene, Freddy and George had some playing cards. Freddy had 200 more playing
cards than Eugene. George had 𝟑
𝟒 the number of cards Freddy had. After George lost 𝟏 𝟔 of his cards to Eugene, he had 320 fewer cards than Eugene. What was the ratio of the number of cards Eugene had to the number of cards Freddy had to the number of cards George had in the end? RS11P15
2.1 Multiple and Constant
2.2 Square Numbers
2.3 Triangle Numbers
2.4 Sum of Numbers
2.5 Number Puzzles
2.6 Number Patterns
Unit 2 Patterns
2007
1. The figure below shows the number of toothpicks used to form different number of triangles. Study it carefully and answer the following questions:
(a) Complete the following table:
Number of triangles 1 2 3 4 5 6 … 10
Number of toothpicks 3 5 7 9 11 (i)____ … (ii) ____ (b) How many toothpicks are needed to form 100 triangles?
(c) How many triangles can you form with 101 toothpicks? AC07S48
2. Look at the patterns shown below. They are made up of 2-cm coloured and plain tiles.
Complete Pattern 5 in the table below.
Pattern Number of coloured tiles Total area of coloured tiles
1 8 32 cm2
2 12 48 cm2
3 16 64 cm2
5 (a) (b)
(c) Which pattern number will have 176 cm2 as the total area of coloured tiles? HP07S37
Unit 2.1 Patterns
Multiple and Constant
3. In the following figures, the area of the biggest equilateral triangle is 64 cm2 as shown in Figure 1. A new triangle is formed by connecting the midpoints of the sides of the
previous triangle. If the pattern continues, find the area of the smallest triangle in Figure 4. HP07P41
4. Study the following sequence of patterns consisting of triangles and circles. The first three patterns are shown below.
(a) Complete the table below.
Pattern 1 2 3 4 5 6 7
Number of triangles 1 2 3 4 5 6 7
Number of circles 4 6 ( ) 10 12 ( ) 16
(b) How many circles are there in the Pattern 15?
5. Chun Ying used 2-cm square tiles to make rectangles as shown below.
The table shows the number of tiles used for each pattern.
Pattern Number of tiles
1 2
2 8
3 18
4 5
(a) Complete the table above for Pattern 4 and Pattern 5.
(b) The length of the rectangle of a certain pattern is made up of 50 tiles. Find the perimeter of this rectangle.
(c) What is the area of the rectangle formed in Pattern 96? PC07P(2)48
6. The patterns below consist of shaded and unshaded rectangles. Study the patterns carefully before answering the following questions.
(a) What is the total number of rectangles in Pattern 10?
(b) If the pattern has 127 rectangles, how many unshaded rectangles are there? RG07S38
7. The figures below are made up of squares and triangles formed by lines. Study the table below carefully and then answer the questions that follow.
Figure 1 Figure 2 Figure 3 Figure 4
Figure 1 2 3 4 5 … 20
Number of lines 9 17 25 33 (a) (b)
(a) How many lines are there in Figure 5? (b) How many lines are there in Figure 20?
(c) How many lines would there be in the figure that has 150 squares? RG07P42
8. The shapes in the table are made up of 1-cm squares. Study the pattern carefully and answer the questions that follow.
Shape 1 Shape 2 Shape 3
Area (cm2) 5 9 13
Perimeter (cm) 12 20 28
(a) What is the perimeter of Shape 15?
2008
9. To pin up 1 poster on the board, 4 pins are required. To pin up 2 posters, 6 pins are needed.
(a) How many pins are needed to pin up 50 posters?
(b) How many posters are pinned up if Mary uses 86 pins? RG08S43
10. The pattern below is made up of circles and sticks.
Fig. 1 Fig. 2 Fig. 3
(a) Complete the following table.
Figure Number Number of circles Number of sticks
1 1 4 2 2 6 3 3 8 4 4 10 (i) 10 22 100 100 (ii)
(b) How many circles are needed to complete a pattern if the number of sticks used is 502? AC08S46
11. Study the series of figures below and answer the questions that follow.
(a) How many dots will there be in Figure 5? (b) How many dots will there be in Figure 31? (c) Which figure will have 221 dots? NY08S48
12. Some 1 cm squares are arranged in the following pattern as shown in the table. (Diagrams are not drawn to scale)
(a) Study the pattern carefully and complete the table.
Pattern Figure Number of
squares Perimeter (cm) 1 1 4 2 2 ( ) 3 3 8 4 4 ( ) . . . . . . . . . . . . 10 ( ) ( )
(b) How many squares are needed to form a figure with a perimeter of 142 cm? NH08S45
13. The figure is made up of identical triangles.
(a) Following this pattern, how many triangles will there be in the 5th layer and 10th layer? (b) If each small triangle has a base of 3 cm and a perpendicular height of 4 cm, find the
area of all the triangles in the 30th layer. HK08P45
2009
14. The shapes in the table are made up of circles, triangles and straight lines. Study the pattern carefully and answer the questions that follow.
Pattern number 1 2 3 … 25 100
Number of triangles 4 6 8 … 202
Number of straight lines
4 7 10 … 76
(a) How many triangles are needed to form the shape in Pattern 25?
15. Each of the figures in the table below is made up of 3-cm squares. Study the pattern carefully and answer (a) and (b).
Figure 1 Figure 2 Figure 3
Area (cm2) 45 81 117 Perimeter (cm) 36 60 84
(a) What is the area of Figure 9?
(b) Find the perimeter of the figure which has an area of 405 cm2. SN09P14
16. The diagrams below show tiling patterns. Each tile is a square of side 1 cm.
Pattern Number 1 2 3 … 10
Number of squares 4 9 16 … 121
Perimeter (cm) 10 16 22 … ?
17. The table below shows the number of matchsticks used to make the following patterns.
Figure Pattern Number of matchsticks
1st 6
2nd 11
3rd ?
(a) How many matchsticks are needed to make the 3rd pattern? (b) How many matchsticks are needed to make the 10th pattern?
2010
18. A series of figures is formed by using 1-cm squares as shown in the table below. Figure Perimeter of figure
(cm) Area of figure (cm2) Figure 1 6 Figure 2 18 10 Figure 3 22 16 Figure 4 26 24
(a) Draw Figure 1 in the table above.
(b) Write down the perimeter of Figure 1 in the table above. (c) Find the area of Figure 100. HK10P12
19. Study the pattern below carefully and complete the table below. Figure Number 1 2 3 … 8 … (b)____ Number of rectangles 1 2 3 … Number of triangles 4 7 10 … (a) ___ Total number of rectangles and triangles 5 9 13 … 193
(a) Find the number of triangles in Figure 8.
(b) Find the Figure Number that would require a total number of 193 rectangles and triangles altogether. RY10P12
20. Observe the patterns carefully.
(a) How many dots are there in Pattern 5?
2011
21. Each of the figures below is made up of 1-cm sticks.
The table below shows the number of sticks used for each figure and the perimeter of each figure.
Figure Number Number of 1-cm sticks Perimeter (cm)
1 12 6
2 23 10
3 34 14
4
(a) Complete the table for Figure 4.
(b) Which Figure Number will have a perimeter of 1298 cm? HP11P08
22. David used coins to form a series of L-shaped patterns. The first three patterns are shown below.
(a) Complete the table below.
L-shaped pattern Number of coins
1st 3 2nd 5 3rd 7 4th 5th 6th
(b) Write down the number of coins that David would need to form the 100th pattern? (c) A pattern is formed by 601 coins. Which pattern would it be? AC11S15
23. The sequence of patterns is formed with squares. The first three patterns are shown below.
(a) How many squares are needed in Pattern 10?
(b) Which pattern number contains 669 squares? CH11S13
24. Study the figures carefully.
Each figure is made up of sticks, circles and triangles.
(a) How many circles will there be in Figure 38? (b) In which figure will there be in 123 triangles?
25. Jake used sticks to form cubes and arranged them to form a pattern as shown below. How many sticks are required to form Figure 5? Which figure will require a total of 145 sticks to form?
Figure Number of cubes Number of sticks
1 1 12
2 2 20
3 3 28
4 4 33
5 5 (a) __________
(a) How many sticks are required to form Figure 5?
(b) Which Figure will require a total of 145 sticks to form? AT11S13
26. The following figures are made up of sticks. Look at the figures below and answer the following questions.
Figure number Number of sticks Number of rectangular faces
1 9 3
2 14 5
3 19 7
4
(a) Complete the table for figure 4.
27. Each pattern in the sequence below is made up of square tiles. Look at the patterns below and answer the following questions.
(a) How many square tiles are there in the 25th pattern? (b) In which pattern would 399 square tiles be used? RS11S14
28. The rhombuses below are formed by using matchsticks. Each rhombus has an equal number of matchsticks on its sides.
(a) Complete the following table.
Pattern 1 2 3 4 5 30
Number of
matchsticks 4 12 20 ( ) ( ) ( )
2007
1. Look at the patterns below. They are made up of shaded and plain tiles.
(a) Complete Pattern 4 in the table.
Pattern Number of shaded tiles Number of plain tiles
1 8 1
2 12 4
3 16 9
4
(b) What is the total number of shaded and plain tiles in Pattern 9? AT07S44
2. Study the patterns formed by black and white tiles below and answer the following questions.
(a) Using the series of patterns above, complete the table below.
Pattern No. of Black Tiles No. of White Tiles Total No. of Tiles
1 3 1 4
2 6 3 9
3 9 7 16
4 12 13 25
5
(b) Find the total number of tiles in Pattern 10. NH07P47
Unit 2.2 Patterns
Square Numbers
3. The figure below shows a multi-level pyramid. Each level is formed by identical small triangles.
(a) How many small triangles are needed to form Level 6?
(b) If 1137 small triangles are needed to form a particular level, which level would that be?
(c) What is the total number of small triangles that are needed to build a 25-level pyramid? NY07C46
2008
4. Nathan saved one cent coin on the first day. The next day he put aside two more 20-cent coins as his savings. Each day, he saved two 20-20-cent coins more than the previous day.
(a) Complete the following table.
Day Number of coins saved each day Total number of coins
1 1 1 2 3 4 3 4 5 6
5. Matthew put aside one 20-cent coin as his savings on the first day. The next day, he put aside three 20-cent coins as his savings. Each day he put aside two 20-cent coins more than the previous day.
(a) Complete the table below.
Day Number of coins saved each day Total number of coins
1 1 1
2 3 4
3 5 9
4
5
(b) How many 20-cent coins did Matthew save by the 25th day?
(c) When Matthew had saved 121 coins altogether, what day would it be? NH08P47
2009
6. Study the patterns formed by black and white tiles below and answer the following questions.
(a) Using the series of patterns above, complete the table below. Pattern No of
Black Tiles
No of White Tiles
Total No. of Tiles
1 3 1 4
2 6 3 9
3 9 7 16
4 12 13 25
5 15 36
(b) Find the total number of tiles in Pattern 110.
7. Study the pattern below.
Line Numbers Sum
1 1 1 2 1 + 3 4 3 1 + 3 + 5 9 4 1 + 3 + 5 + 7 16 5 (a) _________________ (b) … (c) … 6400
(a) Write down number sequence for the 5th line in the box above.
(b) Write down the sum of all the numbers in the 5th line in the box above. (c) Which line has a sum of 6400?
(d) The sum of all the numbers on two consecutive lines is 221. Which are the two lines? NH09C18
8. Ashley used dots and sticks to make the following pattern below. Complete the table.
Pattern Number Number of Dots
Pattern 1 4 Pattern 2 9 Pattern 3 16 Pattern 4 (a) Pattern 128 (b)
(c) If Ashley counted 256 dots in her final pattern, which pattern number had she made? AT09S13
9. The figures below are made up of coloured dots. Look at the figures below and answer the following questions.
Figure 1 Figure 2 Figure 3
(a) Calculate the number of dots in figure 4. (b) Calculate the number of dots in figure 20.
(c) Which figure contains 1123 coloured dots? CH09P14 2010
10. The following figures are made of ovals.
Figure Number of ovals
1 1
2 5
3 13
4 25
5
(a) Complete the table above for Figure 5. (b) How many ovals will there be in Figure 87? (c) Which figure will have 5305 ovals? PC10P18
11. The following figures are made up of dots. Look at the figures below and answer the following questions.
Figure Number 1 2 3 4
Number of dots 3 7 13 21
(a) How many dots are there in the Figure 50? (b) In which figure can 651 dots be found? CH10P12
12. The following figures are made up of small squares and dots. Look at the figures below and answer the following questions.
Figure 1 Figure 2 Figure 3
Figure Number Number of small squares
Number of dots
1 1 4
2 4 9
3 9 16
(a) Calculate the number of small squares for figure 4. (b) Calculate the number of dots for figure 10.
