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.

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q42

In the diagram below, 75% of square Z is not shaded. The ratio of the area of square X to the area of square Y is 9:4. The ratio of the area of square Y to the area of square Z is 4:1.
a) What is the ratio of the area of square X to the area of square Z?
b) Find the ratio of the unshaded area of square Y to the unshaded area of square Z.



Solution

a)
X : Y : Z
9 : 4 : 1

X : Z
9 : 1 (Answer)


b)
Total Area
Y : Z
4 : 1
16 : 4

Unshaded Area
Y : Z
15 : 3 * (see explanatory notes below)
5 : 1 (Answer)

* Total Area (ratio) Y:Z is 4:1. 75% of Z is unshaded, hence for Z, 3 units out of 4. This means 1 unit is shaded. For Y, 16 units total less 1 unit shaded = 15 units unshaded. Hence, unshaded area is Y:Z ---- 15:3.

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q40

The number of girls who registered for art class was 20% of the number of boys. On the actual day, 3 more girls and 3 more boys turned up for the class. As a result, there were 1/3 as many girls as boys at the art class. What was the total number of children who came to art class?

Solution

Girls 20% of boys, hence, girls 1/5 of boys

Before

Girls 1 unit
Boys 5 units

After 3 more boys and 3 more girls turned up, there were 1/3 as many girls as boys:

Girls 1 unit + 3 ----- 1 part (x3)
Boys 5 units + 3 ----- 3 parts

Girls 3 units + 9 ----- 3 parts
Boys 5 units + 3 ----- 3 parts

(Boys) 5 units + 3 ----- 3 units + 9 (Girls)
5 units – 3 units ----- 9 – 3
2 units ----- 6
1 unit ----- 3

Total number of students

Girls ---- 3 + 3 = 6
Boys ---- (5 x 3) + 3 = 18

6 + 18 = 24

Answer: 24 students

Rosyth Sch 2006 PSLE Math Prelim Q35 - alternative method

Daniel is thinking of three consecutive odd numbers. The average of the first and second number is 40, while the average of the second and third numbers is 42. List the three numbers.

Solution

Original post to this question can be found here.

Average of 1st and 2nd numbers ----- 40
Total of 1st and 2nd numbers ----- 40 x 2 = 80

1st ----1 unit
2nd ---- 1 unit + 2
Total of 1st and 2nd ---- 2 units + 2 ---- 80


2nd ---- 1 unit + 2
3rd ---- 1 unit + 2 + 2
Total of 2nd and 3rd ---- 2 units + 6

Total of 1st and 3rd is
(2 units + 2) + (2 units + 6)
= 4 units + 8

Average of 1st and 3rd is
(4 units + 8) divided by 2
= 2 units + 4

From Total of 1st and 2nd,
2 units + 2 ----- 80
2 units ----- 80 – 2 = 78
1 unit ----- 78 divided by 2 = 39

Answer:
1st number is 39
2nd is 41
3rd is 43

Mothers know best

Got this video clip from an ex-P6 student. She emailed it to us.

Mothers are designed all to be the same so that children will all grow up to be the same.