Rosyth Sch 2007 PSLE Math Prelim Q39

Find the sum of the six marked angles in the diagram.

The sum of the all the angles in the triangle in the centre is 180 degrees. The sum of all the 3 angles outside the centre triangle, in the figure above is therefore also 180 degrees (opposite angles).

The sum of all the six marked angles is hence,

Sum of marked angles in 1 triangle ----- 180 degrees
Sum of marked angles in 3 triangles ----- 180 degrees x 3 = 540 degrees
Sum of 6 marked angles ----- (540 – 180) degrees = 360 degrees

Answer: 360 degrees

Rosyth Sch 2007 PSLE Math Prelim Q38

In the figure not drawn to scale, the ratio of the area of the bigger square to the smaller square is 8:4. If 25% of the larger square is shaded, what percentage of the whole figure is not shaded?


Solution



Portion unshaded ----- 6 units + 2 units = 8 units
Total area ----- 6 units + 2 units + 2 units = 10 units

Percentage of figure that is not shaded
8/10 x 100% = 80%

Answer: 80%

Rosyth Sch 2007 PSLE Math Prelim Q37

A tank with a square base of side 5 m was 1/3 full of water. When another 100 cubic meters of water was poured into the tank, it became 1/2 full. Find the capacity of the tank.

Solution

1/2 capacity – 1/3 capacity = 1/6 capacity

1/6 capacity ----- 100 cubic metres

6/6 capacity ----- 6 x 100 cubic m = 600 cubic m

Answer: 600 cubic metres

Rosyth Sch 2007 PSLE Math Prelim Q36

The average weight of 5 boys is 8w kg. When 2 more children whose weights are 11w kg and 12 w kg respectively joined the group, what is the average weight of the boys now?

Solution

Average weight of 5 boys ----- 8w kg

Total weight of 5 boys ----- 8w kg x 5 = 40w kg

Total weight of 7 boys
(40w + 11w + 12w) kg = 63w kg

Average weight of 7 boys
63w kg divided by 7 = 9w kg

Answer: 9w kg

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Raffles Girls Pri Sch 2007 PSLE Math Prelim Q48

Valley Department Store sold a dress for $585. This was 17% more than the price of a similar dress in Wiki Department Store. During a sale, both stores offered same percentage discount on the dress. Christine bought the dress in Wiki Department Store and found that she paid $68 less than the discounted price in Valley Department Store.

(a) Find the price of the dress in Wiki Department Store before the sale.
(b) What is the percentage discount given during the sale?

Solution

(a)
Valley ----- 100% + 17% = $585
117% ----- $585
1% ----- $585 divided by 117 = $5

(Wiki) 100% ----- 100 x $5 = $500

Answer: $500


(b)
Before discount


$85 is the difference in price between Valley and Wiki before the discount. After the discount, the difference was $68.

$85 - $68 = $17
Discount ----- ($17/$85) x 100% = 20%

Answer: 20%

Raffles Girls Pri Sch 2007 PSLE Math Prelim Q47

Melissa spent 3/8 of her money on 3 pencils and 8 pens, and 4/5 of the remainder on 15 markers. Each pencil cost 2/3 as much as a pen. Each marker cost $0.20 more than a pencil. What is the cost of a pen?

Solution



40 units – 30 units ----- $3
10 units ----- $3
1 unit ----- $3 divided by 10 = $0.30

(Pen) 3 units ----- $0.30 x 3 = $0.90

Answer: $0.90

Raffles Girls Pri Sch 2007 PSLE Math Prelim Q46

At first, the ratio of the number of marbles received by John and Peter was 4:7. The ratio of the number of marbles received by Peter and Sam was 9:5. Then, John gave 1/12 of his marbles to Sam, and Peter gave 1/9 of his marbles to Sam. As a result, Sam had 135 marbles in the end.

(a) Find the ratio of the number of John’s marbles to the number of Sam’s marbles at first.

(b) Find the total number of marbles received by the 3 boys.

Solution


45 units ----- 135 (marbles)
1 unit ----- 135 divided by 45 = 3
134 units ----- 134 x 3 = 402

(a) Answer: 36 : 35
(b) Answer: 402 marbles

Raffles Girls Pri Sch 2007 PSLE Math Prelim Q45

The figure below shows a rectangle PQRS. The lines are extended from point P, Q, R and S and they meet at point Y. The length of QR is 20 cm and the length of XY is 4 cm. Given that QS is a straight line, the area of Triangle PQY is 72 square cm and the area of Triangle SRY is 84 square cm, find the shaded area of Triangle QSY.



Solution

Area of Triangle PQY + Area of Triangle SRY
72 sq cm + 84 sq cm = 156 square cm

Area covered by Triangles PQY and SRY is also 1/2 of area of Rectangle PQRS. This also means that Area of Triangle PQS is also 156 sq cm.

Area of Triangle PSY = 1/2 x 20 cm x 4 cm = 40 sq cm

Area of Triangle PQY = 72 sq cm

Shaded area
Area of PQS – Area of PQY – Area of PSY
=156 sq cm - 72 sq cm - 40 sq cm= 44 square cm

Answer: 44 square cm

Raffles Girls Pri Sch 2007 PSLE Math Prelim Q44

A group of pupils sat for two tests, test A and test B. The number of pupils who failed test A was 1/7 of those who passed test A. Given that there were 20 pupils who failed test A,

(a) How may pupils passed test A?
(b) The number of pupils who failed test B was 1/4 of those who failed test A. What fraction of the pupils passed test B?

Solution



(a)
1 unit ----- 20
7 units ----- 20 x 7 = 140

Answer: 140 pupils

(b)
Failed Test A ----- 20
Failed Test B ----- 1/4 x 20 = 5

(Total number of pupils)
8 units ----- 8 x 20 = 160

Fraction of pupils who failed Test B
5/160 = 1/32

Fraction of pupils who passed Test B
1 – 1/32 = 31/32

Answer: 31/32