This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Sunday, August 30, 2009

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

(54 x \$5) + (6 x \$10)
= \$270 + \$60

Wednesday, August 26, 2009

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