Anglo Chinese School 2007 PSLE Math Prelim Q45

The figure is made up of three circles and two semi-circles. O is the center of the circle. AB is 42 cm. Find the total area of the shaded part.





Area of 1 square ----- (10.5 x 10.5)square cm = 110.25 square cm

Area of 2 squares ----- 2 x 110.5 square cm = 220.5 square cm

Area of shaded area is ---- Area of whole figure – area of 1 small circle – area of 4 small quadrants – area of 2 squares

(1386 - 346.5 - 346.5 - 220.5) square cm = 472.5 square cm

Answer: 472.5 square cm

Anglo Chinese School 2007 PSLE Math Prelim Q44

Marvin bought a box of fruits. 30% of the fruits are apples and the rest are oranges. He realized that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found that there were 52 more fruits in the box. How many fruits were there in the box at first?

Solution

At first
Apples ----- 30%
Oranges ----- 70%

Threw half apples away, bought 40% more oranges,
Apples ----- 1/2 x 30% = 15%
Oranges ----- 70% + (40/100 x 70%) = 98%

Total ----- 15% + 98% = 113%

113% - 100% = 13% (increase in number of fruits)
13% ----- 52 fruits
1 % ----- 52% divided by 13 = 4

Number of fruits at first,
100% ----- 4 x 100 = 400

Answer: 400 fruits

Anglo Chinese School 2007 PSLE Math Prelim Q43

Derrick had 2/3 as many stickers as Benedict. After Derrick bought another 8 stickers and Benedict lost 5 stickers, Derrick now has 4/5 as many stickers as Benedict. Find the number of stickers Derrick and Benedict had at first.

Solution



(Derrick after)
4 parts ----- 2 units + 8
2 parts ----- 1 unit + 4
2 parts ----- 1 part + 13 + 4
2 parts – 1 part ----- 17
1 part ----- 17

1 unit – 13 ----- 17
1 unit ----- 17 + 13 = 30
5 units ----- 30 x 5 = 150

Answer: 150 stickers

Anglo Chinese School 2007 PSLE Math Prelim Q41

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?

Solution



7 units - $1.50 ----- $9.70

7 units ----- $9.70 + $1.50 = $11.20

1 unit ----- $11.20 divided by 7 = $1.60


Answer: $1.60

Anglo Chinese School 2007 PSLE Math Prelim Q40

Fara started collecting stamps in January. In each month from February to May, she collected 30 stamps more than the month before. She saved a total of 750 stamps from January to May. How many stamps did she collect in January?

Solution



5 units + 10 groups of 30 ---- 750

5 units + 300 ---- 750

5 units ---- 750 – 300 = 450

1 unit ---- 450 divided by 5 = 90

Answer: 90 stamps

Anglo Chinese School 2007 PSLE Math Prelim Q38

In the figure not drawn to scale, ABCD is a square. BDE and BCF are equilateral triangles. What is Angle FGE?




Solution

Angle BCF ---- 60º (Triangle BCF is an equilateral triangle)

Angle CBD ---- 45º

Angle CBG ---- 60º - 45º = 15º

Angle BGC ---- 180º - 60º - 15º = 105º (sum of angles in a triangle)

Angle FGE ---- 105º (opposite angles)


Answer: 105º

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q48

At a farm, 40% of the animals are cows, 90% of the remainder are sheep and the rest are ducks. There are 56 more sheep than cows. After some cows died, 20% of the remaining animals at the farm are cows. How many cows are there left at the farm?

Solution

Cows ---- 40%
Remainder (sheep + ducks) ---- 100% - 40% = 60%

Sheep ---- 90% (remainder) x 60% = 54%

Sheep more than cows ---- 56
(Sheep) – (Cows) ---- 56
54% - 40% ---- 56
14% ---- 56
1% ---- 56 divided by 14 = 4

(Total) 100% ---- 100 x 4 = 400
(Sheep + ducks) ---- 60%
60% ---- 60 x 4 = 240

After some cows died 80% were sheep and ducks
80% ---- 240
1% ---- 240 divided by 80 = 3

(Cows left) 100% - 80% = 20%
20% ---- 20 x 3 = 60

Answer: There were 60 cows left.

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q47

Mary had some $5 and $10 notes in her wallet. There was a total of 60 pieces of notes at first. She used half of the number of $5 notes and received another twelve $10 notes from her mother. After that, the number of $10 notes she had was 2/3 of the remaining number of $5 notes she had left. How much money did she have at first?

Solution

After she used half of her $5 notes and mother gave her twelve $10 notes:



8 units - 12 ---- 60
8 units ---- 60 – 12 = 72
1 unit ---- 72 divided by 8 = 9

($5 notes) 6 units ---- 6 x 9 = 54
($10 notes) 2 units – 12 = (2 x 9) – 12 = 6

She had -----
(54 x $5) + (6 x $10)
= $270 + $60
= $330 (Answer)

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q44

Andrew left Town X for Town Y which was 500 km apart. He travelled at an average speed of 90 km/h for 3/5 of the journey. He then increased his speed by 30 km/h for the rest of the journey and reached Town Y at 2 pm. Richard also left Town X for Town Y at the same time as Andrew and he drove at an average speed of 100 km/h for the whole journey.

a) What time did Andrew leave Town X?
b) How far apart were they at 1 pm?

Solution



5 units ---- 500 km
1 unit ---- 500 km divided by 5 = 100 km
Every 1/5 of journey ----- 100 km

(a)
Andrew’s Time (1st 3/5 of journey) ---- distance divided by speed
= 300 km divided by 90 km/h
= 3 and 1/3 hours

Andrew’s Time (last 2/5 of journey)
= 200 km/h divided by 100 km/h
= 1 and 2/3 hours

Total time taken by Andrew ----
(3 and 1/3 hours) + (1 and 2/3 hours) = 5 hours

He reached Town Y at 2 pm.
5 hours before 2 pm is 9 am.

Answer: Andrew left Town X at 9 am.


(b)
At 1 pm, both of them travelled for 4 hours.

Richard’s distance ----- speed x time
= 100 km/h x 4 h
= 400 km


Andrew’s distance at 1 pm was ----

For the 1st 3 and 1/3 hours, he travelled 3/5 of journey ---- 300 km.

For the next 2/3 hour he travelled ---- speed x time
= 120 km/h x 2/3 h
= 80 km

Andrew’s total distance in 4 hours ----
300 km + 80 km
= 380 km


They were apart by ----
400 km (Richard’s distance) – 380 km (Andrew’s distance)
= 20 km

Answer: They were 20 km apart.

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q43

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 number of chairs on each side of the square. How many chairs were there on each side of the square?

Solution

Total number of chairs ---- 8 x 9 = 72
No. of chairs less 4 corners ---- 72 - 4 = 48
No. of chairs per row less 4 corners ---- 68 divided by 4 = 17
No. of chairs on 1 side ---- 17 + (2 corner chairs) = 19

Answer: 19 chairs per side.