Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q12

20 similar pails of water can fill 5/12 of a container. Another 8 similar pails and 105 similar bowls of water are needed to fill the container to its brim. How many such bowls of water are needed to fill the empty container completely?

Solution

20 pails --> 5/12 of container (x2)

8 pails + 105 bowls --> remaining 7/12 of container (x5)

40 pails --> 10/12 of container (after x2)

40 pails + 525 bowls --> 35/12 containers (after (x5)

From the above we can see that 525 bowls can fill up:-

525 bowls --> 35/12 - 10/12 = 25/12 containers

25/12 --> 525 bowls

1/12 --> 525 divided 25 = 21 bowls

(Full container) 12/12 --> 12 x 21 = 252

Answer: 252 bowls

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q11

James spends 20% of his monthly income on transport, 30% of it on food and 10% of the remainder on clothes. He saves the rest of his income. If his monthly savings is $900, find his monthly income.

Solution






(Saves)
90% of 50% --> $900
(90/100) x (50/100) x 100% --> $900
45% --> $900
1%--> $900 divided by 45 = $20

(Monthly Income)
100% --> 100 x $20 = $2000

Answer: $2000

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q10

The diagrams below show tiling patterns. Each tile is a square of side 1 cm.

What is the perimeter of Pattern 10?

Solution

(Add 6 cm for every new pattern)

Pattern 1 --> 10 cm

Pattern 2 --> 16 cm

Pattern 3 --> 22 cm

Pattern 4 --> 28 cm

Pattern 5 --> 34 cm

Pattern 6 --> 40 cm

Pattern 7 --> 46 cm

Pattern 8 --> 52 cm

Pattern 9 --> 58 cm

Pattern 10 --> 64 cm

Answer: 64 cm

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q9

A snail fell into a well that is 300 cm deep.

In the first hour, it climbed 80 cm up the well.

In the second hour, it climbed 70 cm up the well.

Each hour, it managed to climb 10 cm less than the hour before.

How many hours did it take to climb out of the well?

Solution

1st h --> 80 cm

2nd h --> 70 cm

3rd h --> 60 cm

4th h --> 50 cm

5th h --> 40 cm

(80 + 70 + 60 + 50 + 40) cm = 300 cm

--> 5 hours

Answer: 5 h

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q8

The rectangle ACEG is divided into 4 parts. BCEF is a square. Each part has a different area. Find the area X.

Area of X

--> 4 cm x 3 cm = 12 square cm

Answer: 12 square cm

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q7

The table below shows the rates for water consumption.

a) Find the amount paid for 50 cubic metres of water used.

b) If 7% GST is imposed on the total amount, how much is the GST correct to the nearest 10-cent?

Water Consumption Rates

First 20 cubic metres ----- $1.33 per cubic metre

Next 20 cubic metres ----- $1.46 per cubic metre

Additional amount above 40 cubic metres ----- $1.73 cubic meter

Solution

a)

1st 20 cubic metres --> 20 x $1.33 = $26.60

2nd 20 cubic metres --> 20 x $1.26 = $29.20

Next 10 cubic metres --> 10 x $1.73 = $17.30

Total Amount

--> $26.60 + $29.60 + $17.10 = $73.30

Answer: $73.10

b)

7 % x $73.10 = $5.117

Approximately --> $5.10 (to nearest 10-cent)

Answer: $5.10

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q6

Zen had a piece of rectangular paper. He cut away 1/9 of the breadth and 2/5 of the length. Then he measured the remaining piece of rectangular paper. He found that the breadth to be 16 cm and the length to be 15 cm. Find the area of the original piece of paper.

Solution

Breadth

8/9 --> 16 cm

1/9 --> 16 cm divided by 8 = 2 cm

9/9 --> 9 x 2 cm = 18 cm

Length

3/5 --> 15 cm

1/5 --> 15 cm divided by 3 = 5 cm

5/5 --> 5 x 5 cm = 25 cm

Original area --> 25 cm x 18 cm = 450 square cm

Answer: 450 square cm

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q5

The figure below is made up of 2 squares, A and B. The ratio of Square A to Square B is 1:4. The shaded part is 1/5 of Square A. What fraction of the whole figure is shaded?




Solution

Shaded part --> 1 unit

Area of Square A --> 5 units (shaded area is 1/5 of Area of Square A)
Note that Square A has 4 units of unshaded and 1 unit of shaded area.

Area of Square B --> 4 x 5 units = 20 units (Area of Square B is 4x that of Square A)
Note that Square B has 19 units of unshaded and 1 unit of shaded area.

Total Area

--> 1 unit (shaded) + 4 units (unshaded Square A) + 19 units (unshaded Square B)
= 24 units

Fraction of shaded area to area of whole figure
--> 1/24

Answer: 1/24

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q4

In a right-angled triangle, the two sides which form the right angle are 16 cm by 12 cm respectively. How many such triangles are needed to form the smallest square?

Horizontal --> 4 x 12 cm = 48 cm

Vertical --> 3 x 16 cm = 48 cm

The above figure (not drawn to scale) is therefore a square.

The smallest 1 unit rectangle has 2 triangles.

There are 3 rows and 4 columns of the smallest 1 unit rectangle.

3 x 4 = 12 smallest unit of rectangles

2 triangles x 12 = 24 triangles

Answer: 24 triangles

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q3

The ratio of Paul's age to Sue's age is 4:3. In 8 years' time the sum of their ages will be 86. What is Paul's age now?

Solution

7 units + 8 + 8 --> 86

7 units --> 86 - 8 - 8 = 70

7 units --> 70

1 unit --> 70 divided by 7 = 10

Paul's age now

4 units --> 4 x 10 = 40

Answer: 40 years old

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