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.

Monday, October 06, 2008

The Three States of Water

Most PSLE students know that water exists in three states – solid, liquid and gas. Most students also know that the ‘magic numbers’ are ‘0’ and ‘100’ deg Celsius, because that is the temperature at which water changes its state.

Students also know that ice exists at 0 deg C and below, while steam exists at 100 deg C and above.

However, quite a few students get confused, when the temperature is at or between 0 and 100 deg Celsius. Some students get the impression that water exists in liquid form only when the temperature is at or between 0 and 100 deg C. This concept is wrong.

At or between 0 to 100 deg C, water can exist in two forms – liquid (as in lakes, rivers) and gas (water vapour). Below is a diagram to illustrate the states of water, in relation to the temperature.



Simply put,
Solid - At 0 deg C and below.
Liquid – At and between 0 and 100 deg C.
Gas – At 0 deg C and above.


Important and useful point to note

Because water can exist in 2 forms (liquid and gas) from 0 to 100 deg C, we have evaporation, condensation in this world and hence, the very critical Water Cycle, which is so important to life on earth.

If water exists only as liquid between 0 to 100 deg C, it will not evaporate to form water vapour, then condense to form clouds, and eventually fall back to earth as rain.

This wide range of 0 to 100 deg C, where water exists in 2 forms is unique, unlike many other substances, where at a given temperature, it exists only in one form.

Summary – Water exists in two forms (liquid and gas) from 0 to 100 deg C and NOT in liquid form only.

Saturday, October 04, 2008

A Little Breather

It is good to relax for a few moments and take a breather at this stage. 


In May/June, our family took a 2 week break in Canada. I posted a few pics then. Here are a few more shots and a couple of short video clips. 

Niagara Falls!

video

video




In Canada, like the US, it is left-hand drive. 

Friday, October 03, 2008

Catholic High Sch 2006 PSLE Math Prelim Q48

The diagram below shows 3 figures formed by shaded and unshaded triangles.



Solution

Q(a)
Total number of triangles ----- 5 x 5 = 25
Number of shaded Triangles ----- 1, 3, 6, 10, 15

Answer: 25 and 15.

Q(b)
15 x 15 = 225
Answer: 225

Q(c)
There are 30 levels of shaded and unshaded triangles.
At Level 1 (top most) there is 1 shaded triangle.
At Level 2, there are 2 shaded triangles.
At Level 3, 3 shaded……
At Level 30, 30 shaded.

Total shaded triangles -----
1 + 2 + 3 + …….. + 30
= (1 + 29) + (2 + 28) + (3 + 27) + …..+ (14 + 16) + 15 + 30
= 14 groups of 30 + 15 +30
= (14 x 30) + 45
= 420 + 45
= 465 (Answer)

Catholic High Sch 2006 PSLE Math Prelim Q47

Camp A and Camp B had a total of 350 children. Camp A was for girls whereas Camp B was for boys. There were 2/5 as many girls as boys. Midway, more pupils joined both camps and for every 2 additional girls who joined Camp A, 1 additional boy joined Camp B. Given that there is an equal number of boys and girls in the end, how many boys joined Camp B midway?

Solution


At first -----
Girls ----- 2 units
Boys ----- 5 units
Boys more than girls ----- 5 units – 2 units = 3 units

(Total boys and girls) 7 units ----- 350
1 unit ----- 350 divided by 7 = 50

Girls ----- 2 units x 50 = 100
Boys ----- 5 units x 50 = 250
Boys more than girls ----- 250 – 100 = 150

From the above, we conclude that (boys more than girls)
3 units ---- 150

To have equal number of boys and girls in the end, an additional 3 units of boys and 6 units of girls must join, so that both girls and boys will have 8 units each.

(Note that for every 1 additional boy who joined Camp B, 2 additional girls joined Camp A, hence, ratio is 1:2. Likewise, 3 units of boys and 6 units of girls correspond to the ratio 1:2)

Therefore, 3 units of boys joined Camp B midway -----
3 units ----- 150

Answer: 150 boys joined Camp B.

Catholic High Sch 2006 PSLE Math Prelim Q46

Mary and Jane bought some utensils consisting of forks and spoons from a departmental store. Jane bought 2/5 of the total utensils. Altogether, they bought 30 more spoons than forks. Mary bought 2/3 of the spoons and ½ of the forks. How many utensils did Jane buy?

Solution

All utensils ----
Spoons ----- 6 units + 30
Forks ----- 6 units
(6 units is used because 6 it can be split up into thirds and halves – 2/3 spoons, ½ forks)

Mary bought -----
Spoons ----- 4 units + 20 (working; 2/3 x 6u + 2/3 x 30 spoons)
Forks ----- 3 units (working; 1/2 of 6u is 3u)
Altogether for Mary ----- 7 units + 20 (which is 3/5 of utensils)

Jane bought the remaining utensils which is -----
Spoons ----- 6 units + 30 – 4 units – 20 = 2 units + 10
Forks ----- 6 units – 3 units = 3 units
Altogether for Jane ----- 5 units + 10 (which is 2/5 of the utensils)

(Mary) 7 units + 20 ----- 3/5 (x5)
(Jane) 5 units + 10 ----- 2/5 (x7)

(Mary) 35 units + 100 ----- 15/5
(Jane) 35 units + 70 ----- 14/5

(Mary) – (Jane)
35 units + 100 – 35 units – 70 ----- 15/5 – 14/5
30 ----- 1/5 (of utensils)
2/5 of utensils ----- 2 x 30 = 60

Answer: Jane bought 60 utensils.

Catholic High Sch 2006 PSLE Math Prelim Q45

Q45 can be found in the link below.

http://road-to-psle.blogspot.com/2007/11/catholic-high-school-2006-psle-math.html

Catholic High Sch 2006 PSLE Math Prelim Q44

The figure is made up of three squares A, B and C that overlap each other. The area of square A is 20% that of Square B, where the area of square B is 60% of square C. What is the ratio of the shaded area to the unshaded area?


(Shaded area)
B – A ----- 6000 – 1200 = 4800

(Unshaded area)
C – shaded area ----- 10 000 – 4800 = 5200

Shaded Area : Unshaded Area
4800 : 5200
12 : 13 (Answer)

Thursday, October 02, 2008

Catholic High Sch 2006 PSLE Math Prelim Q43

At 7.30 am, Hubert left Johor, travelling towards Kuala Lumpur at a constant speed. 1 hour later, Joshua started travelling from Johor on the same road. Joshua overtook Hubert at 11.30 am. The speed at which Joshua was travelling at was 20km/h faster than Hubert and he arrived at Kuala Lumpur at 12.30pm. Find the distance between Johor and Kuala Lumpur.

Solution

Hubert’ time ----- 7.30 to 11.30 --- 4h
Joshua’s time ----- (1h later) 8.30 to 11.30 --- 3h

At the point where Joshua overtook Hubert, both travelled the same distance. However Joshua’s speed was 20km/h more than Hubert.

Hubert’s distance ----- Joshua’s distance
Hubert’s speed x Hubert’s time ------ Joshua’s speed x Joshua’s time
1 unit x 4 ----- (1 unit + 20) x 3
4 units ----- 3 units + 60
1 unit ----- 60

Joshua’s speed -----
1 unit + 20
60 + 20 = 80

Distance from Johor to KL -----
Joshua’s speed x Joshua’s time
80km/h x 4h (Joshua took from 8.30 to 12.30 to reach KL)
= 320 km (Answer)

Catholic High Sch 2006 PSLE Math Prelim Q42

It takes Martin 5 hours to fix a jigsaw. If Jeremy helps him, they would take 3 hours to fix the jigsaw together. How long will Jeremy take to fix the jigsaw by himself?

Solution


Martin
5h ----- 1 whole
3h ----- 3/5

Jeremy fixed the other 2/5
2/5 ----- 3h
1/5 ----- 3h/2
5/5 ----- (3h/2) x 5 = 7.5h

Answer: It will take Jeremy 7.5h

Catholic High Sch 2006 PSLE Math Prelim Q41

In the figure below, not drawn to scale, the square, ABCD is made up of four rectangles. Given that the area of the square ABCD = 144 square cm, area of rectangle DFHG = 20 square cm and the area of rectangle AEHG = 28 square cm, find the area of rectangle EBIH.




Solution



Area of EBIH ----- 8 cm x 7 cm = 56 square cm (Answer)

PSLE Math Q on ratio

Andrea has $200 more than Bala. Andrea gives 60% of his money to Bala. Bala then gives 25% of his money to Andrea. In the end, Bala has $200 more than Andrea. How much did Andrea have at first? (Nanyang Prelim 2006 Q48)

At first -----
Andrea ----- 1 unit + 200
Bala ----- 1 unit

Andrea gives 60% -----
Andrea ----- 1 unit + 200 – 0.6 unit – 120
Bala ----- 1 unit + 0.6 unit + 120

Andrea ----- 0.4 unit + 80
Bala ----- 1.6 units + 120

Bala gives 25% -----
Bala ----- 1.6 units + 120 – 0.4 unit – 30
Andrea ----- 0.4 unit + 80 + 0.4 unit + 30

Bala ----- 1.2 units + 90
Andrea ----- 0.8 unit + 110

Bala now has $200 more -----
Bala – Andrea ----- 200
1.2 units + 90 – 0.8 unit –110 ----- 200
0.4 unit – 20 ---- 200
0.4 unit ----- 200 + 20 = 220
1 unit ---- 220 divided by 0.4 = 550

Andrea at first -----
1 unit + 200 ----- 550 + 200 = 750

Answer: Andrea had $750 at first.