1. Suyin is 12 years old this year. Her father is 4 times her age. What is their total age in y years’ time?

1 + 4 = 5

5 x 12 = 60

60 + y + y = 60 + 2y

2. A water bottle contains 2 l of water. If the water bottle is leaking at a rate of 8 ml per second, how long does it take for the water bottle to be emptied?

Give your answer in minutes and seconds.

2000 ÷ 8 = 250 s

= 4 min 10 s

3. Fanny queued in front of Zoee to take part in the “Singapore Has Talent” contest. The sum of their queue numbers is 4291. What is Zoee’s queue number?

4291 + 1 = 4292

4292 ÷ 2 = 2146

4. The statistics below shows the number of live-births registered in Singapore in the months of February and March 2008.

What is the percentage increase in live-births from February to March? Rounded off your answer to 2 decimal places.

3174 – 2981 = 193

193/2981 ≈ 6.47%

5. The diagram below, not drawn to scale, shows a shaded triangle drawn within a rectangle. The ratio of the length AB to the length of the rectangle is 1 : 3. Calculate the area of the shaded triangle.

36 ÷ 3 = 12

1/2 x 12 x 28 = 168 cm

^{2}6. School A has 2/3 as many pupils as School B. School B has 3/5 as many pupils as School C. If School A has 2234 pupils, how many pupils does School C have?

2 u -- > 2234

5 u -- > 5/2 x 2234 = 5585 pupils

School C has 5585 pupils.

7. Cathy has 1250 more stamps than John. After John gave Cathy 68 stamps, she had four times as many stamps as John. How many stamps did John have at first?

[ ][ ][ ][ ]

C [ ][1250 ][68]

J [ ][68] ?

3 u -- > 68 + 1250 + 68 = 1386

1 u -- > 1386 ÷ 3 = 462

462 + 68 = 530 stamps

John had 530 stamps at first.

8. 1 bottle of shampoo and 1 bottle of bath foam cost $15.50 altogether. Mrs Yeo bought 3 bottles of shampoo and 5 bottles of bath foam for $59.70. How much did one bottle of bath foam cost?

1 S + 1 F --> $15.50

3 S + 5 F --> $59.70

3 S + 3 F --> 3 x 15.50 = 46.50

2 F à 59.70 – 46.50 = 13.20

1 F -- > 13.20 ÷ 2 = $6.60

One bottle of bath foam cost $6.60.

9. In the figure below, not drawn to scale, ABCD is a rhombus. /_BAC = 68

**and /_CED = 45**^{o}**.**^{o}a) Calculate /_ABC. [1m]

b) Calculate /_CDE. [2m]

180 – 68 – 68 = 44

a) /_ABC = 44

^{o}68 – 45 = 23

b) /_CDE = 23

^{o}10. The pie chart below shows the results of a survey done on the preferences of 700 movie viewers. Half of the viewers prefer Japanese and Korean movies.

a) How many viewers like to watch Japanese movies? [1m]

b) The ratio of the number of viewers who like American movies to the number of viewers who like Korean movies is 7 : 4. How many viewers like American movies? [2m]

50 – 20 = 30

100% -- > 700

30% -- > 30/100 x 700 = 210

a) 210 viewers like to watch Japanese movies.

7/4 x 20 = 35

35% -- > 35/100 x 700 = 245

b) 245 viewers like American movies.

11. The table below shows the charges incurred when making overseas phone call.

Miss Ong made an overseas phone call which lasted 25 ½ min. How much must she pay for the overseas phone call?

25 ½ - 5 = 20 ½

First 5 min -- > $8.00

Balance 20 ½ min -- > 21 x 0.15 = $3.15

3.15 + 8.00 = $11.15

She must pay $11.15 for the overseas phone call.

12. Mrs Liu spent 1/5 of her monthly salary on a handbag, 4/7 of the remainder on a vacuum cleaner and saved the rest of her monthly salary. If she saved $1890, what was her monthly salary?

1 – 1/5 = 4/5

4/7 x 4/5 = 16/35

4/5 – 16/35 = 12/35

12 u -- > 1890

35 u -- > 35/12 x 1890 = $5512.50

Her monthly salary was $5512.50.

13. At an enrichment camp, the number of boys was 45% of the number of girls. When 20% of the boys left the camp, there were 192 more girls than boys. How many children were at the camp at first?

G -- > 100%

B -- > 45%

20% x 45% = 9%

45 – 9 = 36

100 – 36 = 64

64% -- > 192

145% -- > 145/64 x 192 = 435 children

There were 435 children at the camp at first.

14. Sally had some beads. On Monday, she gave half of her beads to her sister. On Tuesday, she used ¼ of the remaining beads to make a necklace and bought another 426 beads. After that, she had 957 beads. How many beads did Sally have at first?

N S

[ ][ ][ ][ ][ ][ ][ ][ ]

[ 426 ] 957

3 u -- > 957 – 426 = 531

8 u -- > 8/3 x 531 = 1416 beads

Sally had 1416 beads at first.

15. Study the number pattern below.

a) In 5

**what is the sum of the digits in the ones and tens place?**^{6}b) What is the sum of the last three digits in 5

**?**^{15}c) What is the sum of the last four digits in 5

**?**^{210}5

**= 15625**^{6}5 + 2 = 7

a) In 5

**the sum of the digits in the ones and tens place is 7.**^{6}5

**= 78125**^{7}5

**= 390625**^{8}5

**= …3125**^{9}5

**= ..5625**^{10}5

**= ..8125**^{11}5

**= ..0625**^{12}…

5

**= ..8125**^{15}5 + 2 + 1 = 8

b) The sum of the last 3 digits in 5

^{15}^{is 8.}210 ÷ 4 = 52 r 2

5

**= ..5625**^{210}5 + 2 + 6 + 5 = 18

c) The sum of the last 4 digits in 5

**is 18.**^{210}16. Country A and Country B took part in a Youth Game. From Country A, the ratio of the number of male supporters to the number of female supporters is 5 : 6. From Country B, the ratio of the number of male supporters to the number of female supporters was 1 : 3. The total number of supporters from Country A is ¼ of the total number of supporters from Country B.

a) What is the ratio of the number of female supporters from Country A to the number of female supporters from country B? Express your answer in the simplest form.

b) After 4985 male supporters from both countries left, the percentage of the female supporters became 78%. How many more male supporters from Country B than Country A were there at first?

A B

----------------------------

1 : 4 = 11 : 44

M F M F

5 : 6 1 : 3 = 11 : 33

6 : 33 = 2 : 11

a) The ratio of the number of female supporters from Country A to the number of female supporters from Country B is 2 : 11.

6 + 33 = 39

78 ÷ 39 = 2

5 : 6 : 11 : 33 = 10 : 12 : 22 : 66

10 + 12 + 22 + 66 – 100 = 10

10% -- > 4985

12% -- > 12/10 x 4985 = 5982

b) There were 5982 more male supporters in Country B than in Country A at first.

17. At 7 am, a car started travelling from Town A towards Town B at an average speed of 64 km/h. At 10 am, a van started travelling from Town A towards Town B at an average speed of 56 km/h. By then, the car had already covered 2/5 of the entire journey.

a) What was the distance between Town A and Town B?

b) How far from Town A had the van travelled when the car reached Town B?

64 km/h

7 am 3 h

C A [ ][ ][ ][ ][ ] B

V [ ]?

10 am

10 am

56 km/h

2 u -- > 64 x 3 = 192

5 u -- > 5/2 x 192 = 480 km

a) The distance between Town A and Town B is 480 km.

2 u -- > 3 h

3 u -- > 3/2 x 3 = 4.5 h

56 x 4.5 = 252 km

b) The van had travelled 252 km from Town A when the car reached Town B.

18. The shaded part below is made up of a quarter circle and a semicircle which are drawn within the rectangle ACDF. AB = 12 cm.

a) Find the area of rectangle ACDF.

b) What percentage of rectangle ACDF is shaded? Round off your answer to 2 decimal places.

12 ÷ 2 = 6

6 + 12 = 18

18 x 12 = 216 cm

^{2}a) The area of rectangle ACDF is 216 cm

**.**^{2}1/4 x 22/7 x 12 x 12 = 113 1/7

1/2 x 22/7 x 6 x 6 = 56 4/7

113 1/7 – 56 4/7 = 56 4/7

≈ 56.57 cm

^{2}56 4/7 ÷ 216 x 100% = 26.19%

b) 26.19% of rectangle ACDF is shaded.

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