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, November 21, 2011

### PSLE Results to be released on Thursday

PSLE results out Thursday
SINGAPORE: The results of the 2011 Primary School Leaving Examination (PSLE) will be released on Thursday.

The Ministry of Education (MOE) said pupils may obtain their result slips from their respective schools from 12noon.

Eligible pupils will also receive from their respective primary schools, their option forms to select secondary schools.

MOE said the results of Secondary 1 postings will be out on 21 December.

Nan Chiau High School, which has been designated a Special Assistance Plan school from January next year, will admit only Express course students offering Chinese or Higher Chinese as a Mother Tongue Language.

And two more schools - Victoria School and Cedar Girls - will take in their first batch of Secondary 1 students in the six-year integrated programme.

- CNA/ck

## Tuesday, September 20, 2011

### Catholic High School 2010 PSLE Math Prelim Paper 2 Q17

Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

Solution

At first

Daniel ---- 100% + 40%
Brandon ---- 100%
Calvin ---- 1 unit

After Daniel and Brandon each gave 20% of their stickers to Calvin…
Daniel ---- 100% + 40% - (28%)*
Brandon ---- 100% - (20%)**
Calvin ---- 1 unit + (28% + 20% of Dan and Bran --> 80% of 1 unit)#
Hence Calvin --- 1 unit + (48% of Dan and Bran --> 80% of 1 unit)

* 20% of 140% = 28%
** 20% of 100% = 20%
# Cal received 28% + 20% = 48% of (Dan + Bran), which is equal to 80% of Cal's original amount of 1 unit.

80% of 1 unit ---- 48% of total of Dan and Bran
0.8 unit ---- 48%
1 unit ---- 48% divided by 0.8 = 60%

In the end Calvin
1 unit + (48% from Dan and Bran)
= 60% + 48%
= 108%

(Daniel) more than (Calvin) in the end
(140% - 28%)## - (108%)
= 112% - 108%
= 4%
## Danile had 140% at first but gave 28% to Calvin

Daniel had 20 more stickers than Calvin in the end
4% ---- 20
1% ---- 20 divided by 4 = 5

Brandon at first
100% ---- 100 x 5 = 500

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## Wednesday, September 14, 2011

### Catholic High School 2010 PSLE Math Prelim Paper 2 Q18

At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference?

Solution

Male ----- 120%
Female ----- 100%

Speakers
Male : Female
8 (parts) : 5 (parts)

Participants
Male : Female
1 (unit) : 1 (unit)

Men ----- 8 parts + 1 unit
Women ----- 5 parts + 1 unit

But since there are 20% more women than men,
Women ----- 5 parts x 120% + 1 unit x 120%
= 6 parts + 1.2 units

Men ----- Women
8 parts + 1 unit ----- 6 parts + 1.2 units
8 parts - 6 parts ----- 1.2 units - 1 unit
2 parts ----- 0.2 unit
1 part ----- 0.1 unit
10 parts ----- 1 unit
or
1 unit ----- 10 parts

(a)
Male Speakers ----- 8 parts
Male Participants ----- 1 unit or 10 parts

Male Speakers : Male Participants
8 : 10
4 : 5

(b)
Speakers
Male : Female
8 (parts) : 5 (parts) -- (altogether 13 parts)

Participants
Male : Female
1 (unit) : 1 (unit)
10 (parts) : 10 (parts) -- (before)
- 40 : + 60 -- (40 males left; 60 females joined)
3 (units) : 4 (units) -- (3/4 as many male as females in the end)

(Male) 3 units ----- 10 parts - 40
(Female) 4 units ----- 10 parts + 60

(Female) - (Male)
4 units - 3 units ----- 10 parts + 60 - 10 parts - (-40)
1 unit ----- 60 + 40
1 unit ----- 100

(Male after)
3 units ---- 3 x 100 = 300

(Male before)
10 parts ---- 300 + 40 (need to add the 40 who left)
10 parts ----- 340
1 part ---- 34

All speakers
13 parts ---- 13 x 34 = 442

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## Wednesday, September 07, 2011

### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q18

The figure below shows 2 completely-filled tanks being emptied of the water from 2 different taps.

The taps at Tank A and Tank B were turned on at 7 am and 8.30 am respectively, until both tanks were completely empty. At 11 am, the water level in both the tanks was the same. At 12.30 pm, Tank B was completely empty and Tank A was only completely empty at 1 pm. If the rate of the flow of water from each tap was constant throughout, what was the height of Tank A?

Solution

** At 11 am, water level in both Tanks were the same.

Note that 3/8 of B's height is the same as 2/6 or 1/3 of A's height.

(3/8) of B ----- (2/6) or (1/3) of A

(1/8) of B ----- (1/3) of A divided 3 = (1/9) of A

(8/8) of B (B's height) ----- 8 x (1/9) = (8/9) of A

* Remaining (1/9) of A ----- 5 cm
(This is the difference in height between Tank A and B)

(9/9) of A (A's height) ----- 9 x 5cm = 45 cm

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q17

The average length of 6 ropes was 80 cm. The average length of 4 ropes of the ropes A, B, C and D was 15 cm more than the average length of the remaining 2 ropes E and F.
a) Find the average length of ropes E and F. Give your answer in metres.
b) If Rope E had been 18 cm shorter and Rope F had been 12 cm longer, they would have been of the same length. Find the actual length of Rope E.

Solution

Total of 6 ropes ----- 6 x 80cm = 480 cm

Average of A, B, C, D (4 ropes) is more than Average of E and F (2 ropes) by 15 cm.
This means each of the 4 ropes (A, B, C, D) has an average length that is 15 cm longer than the average of E and F.

Therefore, total length of A, B, C, D is longer than total length of E and F by
----- 4 x 15cm = 60 cm

a)
3 units ----- 480cm - 60cm = 420 cm
1 unit (E + F) ----- 420cm divided by 3 = 140 cm

Average ----- 140cm divided by 2 = 70 cm or 0.7 m

b)

2 parts ----- 140 - 12 - 28 = 110
1 part ----- 110 divided by 2 = 55

E ----- 55 + 12 + 18 = 85

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q16

Yanling had 60% more stamps than Lena. Tricia had 75% fewer stamps than Yanling. Yanling and Lena gave Tricia some stamps in the ratio 4:1. As a result, Tricia had 2 and 1/2 times as many stamps as before and Yanling had 300 stamps more than Lena in the end. How many sttamps did Lena give to Tricia?

Solution

*** Tricia had 75% fewer stamps than Yanling
----- 25% of 160% is 40%.

# Tricia finally had 2 and half times as many stamps as before
----- 40% x 2.5 = 100%

Tricia's number of stamps increased by
---- 100% - 40% = 60%

Ratio given by Yanling and Lena was 4:1 -----
Y : L
4 : 1
(Total 5 units) ----- 60%

**(Lena gave) 1 unit ----- 60% divided by 5 = 12%
*(Yanling gave) 4 units ---- 4 x 12% = 48%

In the end, Yanling had more than Lena ----- 300
112% - 88% ----- 300
24% ---- 300
1% ---- 300 divided by 24 = 12.5

Lena gave Tricia 12% -----
12 x 12.5 = 150

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q15

A car and a van started travelling from Town X to Town Y at the same time. The distance between the two towns was 225 km. Both vehicles did not change their speed. The car arrived at Town Y 3/4 h earlier than the van. When the car reached Town Y, the van was still 45 km away from Town Y. What was the speed which the car was travelling?

Solution

* When the car reached Town Y, the van was still 45 km away. The car arrived at Town Y 3/4 h earlier than the van.

(Van) speed -----
45 km divided by (3/4) h
= 60 km/h

(Van) time for the whole journey -----
225 km divided by 60 km/h = 3 and 3/4 hours

Therefore, the car travelled in 3 h.

Speed of car -----
225 km divided by 3 h = 75 km/h

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q13

The figure below shows 2 quarter circles and a rectangle. The radius of the big quarter circle is 8 cm. The radius of the small quarter circle is 4 cm. Find the difference in area between the two shaded parts of X and Y. Use the calculator value of pi and give your answer correct to 1 decimal place.

Solution

Area of rectangle ----- 8 cm x 4 cm = 32 square cm

(1/4) x pi x 8cm x 8 cm
= 16(pi) square cm

(1/4) x (pi) x 4cm x 4cm
= 4(pi) square cm

16(pi) square cm - 4(pi) square cm
= 12(pi) square cm

Difference between the two shaded parts X and Y -----
(12 x pi) square cm - 32 square cm
approximately ----- 5.7 square cm

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q9

The number of pens in Box X and Box Y are in the ration of 3:2. All the pens in Box Y are green. The ratio of green pens to blue pens in Box X is 4:5. There are 12 more green pens in Box Y than in Box X. How many blue pens are there?

Solution

Green in Box X
(4/9) x (3/5) = 4/15

There are 12 more blue pens in Box X than in Box Y
(2/5) - (4/15) ----- 12
(6/15) - (4/15) ----- 12
2/15 ----- 12
1/15 ----- 12 divided by 2 = 6

Blue Pens
(5/9) x (3/5)
= 1/3
= 5/15

5/15 ----- 5 x 6 = 30

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q6

Randy brought along a certain amount of money to buy files. If he bought the files at $1.50 each, he would have$17.50 left. If he bought the same number of files at $2.70 each, he would have$9.10 left. How much money did he bring along?

Solution

1 unit x $1.50 +$17.50 ----- 1 unit x $2.70 +$9.10
($2.70 x 1 unit) - ($1.50 x 1 unit) ----- $17.50 -$9.10
($1.20 x 1 unit) -----$8.40
1 unit ----- $8.40 divided by$1.20 = 7

He brought along -----
(7 x $2.70) +$9.10
= $18.90 +$9.10
= $28 Answer:$28

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q5

At a bakery, muffins are sold at $1 each. When a customer buys 5 muffins, she can buy one more at half the price. What is the greatest number of muffins that a customer can buy with$20?

Solution

6 muffins ----- $5.50 (Five at$1; One at $0.50) 3 groups of$5.50 ----- 6 muffins x 3 = 18 muffins

(3 x $5.50 =$16.50) ----- 18 muffins

$20 -$16.50 = $3.50 (remaining) With the remaining$3.50, the customer can buy another three muffins at $1 each. Total muffins ----- 18 + 3 = 21 Answer: 21 muffins Printer Friendly Version ## Thursday, June 09, 2011 ### A time to relax a little Now that school holidays are around, it is time to relax a little. Just a little, not too much, or you will have problems re-adjusting back to school life when the next semester starts. ## Tuesday, May 03, 2011 ### ACS Primary 2010 SA1 Math Paper 2 Q18 Keane bought some marbles and gave half of them to Leon. Leon then bought some stamps and gave half of the to Keane. Keane used 5 stamps and Leon gave away 11 marbles. The ratio of the number of stamps to the number of marbles Keane had left then became 1:7 and the ratio of the number of stamps to the number of marbles Leon had left became 1:5. How many stamps did Leon buy? Solution M ----- Marbles S ----- Stamps Step 1 Keane bought marbles and gave half to Leon, Keane ----- M Leon ----- M Both have same number of marbles. Step 2 Leon bought stamps and gave half to Keane, Keane ----- M , S Leon ----- M , S Now both have same number of marbles and stamps Step 3 Keane used 5 stamps, Leon gave away 11 marbles, Keane ----- M , [S - 5] Leon ----- [M - 11] , S Now Keane has 5 stamps less, and Leon 11 marbles less Step 4 Keane's no. of stamps to no. of marbles now is 1:7, M ----- (7 units) [S - 5] ----- (1 unit) Now Keane has 7 times as many marbles as stamps. Step 5 Leon's no. of stamps to no. of marbles now is 1:5, [M - 11] ----- (5 parts) S ----- (1 part) Now Leon has 5 times as many stamps as marbles. Step 6 1 unit of Keane's stamps + 5 ----- 1 part of Leon's stamps 1 unit + 5 ----- 1 part Keane gave away 5 stamps, so to have an equal no. of stamps as Leon now, we add back the 5 stamps Keane gave away. Step 7 7 units of Keane's marbles ----- 5 parts of Leon's marbles + 11 7 units ----- 5 parts + 11 Leon gave away 11 marbles, so to have an equal no. of marbles as Keane, we add back the 11 marbles Leon gave away. Step 8 Comparing marbles with stamps (Stamps) 1 unit + 5 ----- 1 part (refer to Step 6) (Marbles) 7 units ----- 5 parts + 11 (refer to Step 7) Step 9 Multiply stamps by 5 (Stamps) 5 units + 25 ----- 5 parts (Marbles) 7 units --> 5 parts + 11 (Stamps) 5 units ----- 5 parts - 25 (Marbles) 7 units ----- 5 parts + 11 Step 10 (marbles) - (stamps) 7 units - 5 units --> 5 parts + 11 - 5 parts - (-25) 2 units --> 11 + 25 2 units --> 36 1 unit --> 18 Step 11 1 unit ----- S - 5 (refer to Step 4) 18 ----- S - 5 S ----- 18 + 5 = 23 This is the no. of stamps Leon had after giving half away. Step 12 Leon bought, 2 x 23 = 46 Answer: 46 stamps ### ACS Primary 2010 SA1 Math Paper 2 Q17 The shaded figure below is formed by semicircles, quarter circles and straight lines of 15 cm each. For each of the following, use the calculator value of to find a) the perimeter of the shaded figure, correct to 2 decimal places. b) the area of the shaded figure, correct to 2 decimal places. Solution (a) Circumference of 2 semicircles (1 circle) --> 2r = 2 x 7.5cm = 47.12 cm Circumference of 2 quarter circles (1 semi circle) -->()2r = ()(2)() x 15cm = 47.12 cm Length of vertical line on the left side of figure --> 2 x 15cm = 30cm Perimeter of shaded figure --> 47.12cm + 47.12cm + 30cm = 124.25cm Answer: 124.25 cm (b) Area of 2 quarter circles (1 semi circle) -->() = () x 15cm x 15cm = 353.43 Area of 2 semi circles (1 circle) --> = x 7.5cm x 7.5 cm = 176.71 Area of whole figure --> 30cm x 30cm = 900 Shaded area --> 900 - 353.43 - 176.71 = 369.86 Answer: 369.86 ## Sunday, April 24, 2011 ### ACS Primary 2010 SA1 Math Paper 2 Q16 Mr Wu had some badges and decided to give them to his two sons, Sean and Matthew. Mr Wu gave 1/3 of the badges and 8 more badges to Sean. He then gave 3/4 of the remainder to Matthew but took back 2 badges. Mr Wu was left with 26 badges. How many badges did Mr Wu have at first? Solution Assume all badges --> 1 unit Mr Wu was left with, ----- 1/4 of Remainder + 2 ----- 1/4 x (2/3 unit - 8) + 2 = (1/6 unit - 2) + 2 = 1/6 unit - 2 + 2 = 1/6 unit 1/6 unit --> 26 badges 1 unit ----- 26 divided by 1/6 = 26 x 6 = 156 Answer: 156 badges ### ACS Primary 2010 SA1 Math Paper 2 Q15 Both Joanne and Joseph had an equal amount of money at first. Every month, Joanne spent$850 and Joseph spent $912. After a few months, Joanne was left with$1550 while Joseph had 4/5 as much as Joanne. How much money did Joseph have at first?

Solution

Every month,
Joanne spends $850 Joseph spends$912
Difference every month
--> $912 -$850 = $62 After a few months, Joseph had 4/5 as much as Joanne, 5 units -----$1550
1 unit ------ $1550 divided by 5 =$310
($310 is the difference between Joanne and Joseph after a certain number of months) Number of months to achieve the$310 difference,
$310 divided by$62 = 5 (mths)
It also takes 5 months for Joseph to have 4/5 as much as Joanne.

Amount Joseph has at first,
Joseph ------ 4 units + (5 mths x $912 spent per mth) ----- (4 x$310) + (5 x $912) =$1240 + $4560 =$5800

Answer: $5800 Printer Friendly Version ## Monday, April 18, 2011 ### Another Problem Sum from a reader Received another question from a reader. Can anyone help this reader out Question: Mrs tan bought 4 times as many toys as teddy bears . She spent$1750 altogether . A toy gun cost $10 less than a teddy bear . The total cost of toy guns was$490 more than the total cost of teddy bears .
(a) How much did Mrs tan spend on the teddy bears?

(B) How much did one teddy bear cost ?

## Thursday, April 14, 2011

### ACS Primary 2010 SA1 Math Paper 2 Q14

Tony and Charles took part in a car race. Tony drove at a speed of 90km/h. Both of them did not change their speed throughout the race. When Charles had covered 1/3 the distance, Tony was 15 km in front of him. Tony reached the finishing line at 9.35 a.m. At what time did Charles recah the finishing line?

Solution

* For every 1/3 of the race Charles covered, Tony was 15 km ahead. When Charles completed the whole race, Tony would have been 3 x 15km = 45km ahead of Charles, if we assume Tony continued to travel beyond the finishing line.

Time = 45 km divided 90 km/h
= 0.5 hour

Half hour after 9.35 am ------ 10.05 am

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## Wednesday, April 13, 2011

### ACS Primary 2010 SA1 Math Paper 2 Q12

Weiming had 2/3 as many stickers as Shiyang. After Weiming gave 52 stickers to Shiyang, Weiming had 2/5 as many stickers as Shiyang. How many stickers did Weiming have at first?

Solution

*(x7) and (x5) to give a common total of 35 units for both "At first" and "In the end", since there is no change in the total number of stickers.

Weiming gave
14 units - 10 units ---- 52
4 units ----- 52
1 unit ----- 52 divided by 4 = 13

Weiming at first
14 units x 13 = 182

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### ACS Primary 2010 SA1 Math Paper 2 Q9

The graph below shows the mass of a container when it is empty and when different combinations of objects X, Y and Z are placed in it.

Solution

Empty container --> 80g
Y + Z ----- 140g - 80g = 60g
X + Z ----- 300g - 80g = 220g
X + Y ----- 340 g - 80g = 260g

Total of all objects
----- 60g + 220g + 260g = 540g

Average ----- 540g divided by 6 = 90g

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### ACS Primary 2010 SA1 Math Paper 2 Q6

At first, Matthew has twice as many soccer cards as Ivan. Each of them then bought the same number of cards. As a result, both of the now have 160 cards in total. If Matthew now has 30 more cards than Ivan, find the number of cards each of them bought.

Solution

bought + bought ----- 160 - 30 - 30 - 30 = 70
bought ----- 70 divided by 2 = 35

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## Monday, March 28, 2011

### Math Problem Sum again

To all,
Posted through email from a reader
===================
David and Michael drove from town A to town B at different speeds. Both did not change their speeds throughout their journeys. David started his journey 30 mins earlier thatn micheal. however, micheal reached town B 5o mins earlier than david. when micheal reached town B, david had travelled 4/5 of the journey and was 75 km away from town B.

what was the distance between town a and b?
hown many kilometers did david travel in 1 hour?
what was the time taken by micheal to travel from town a to b?

sry to disturb u again but i really need help cause i dont have tuition at home.
===================

## Saturday, March 19, 2011

### Another Math Problem Sum

I received another request through email from a reader. Anyone willing to help her out?

==========

Alice, Barbie,Cora and Daylia are given some stickers. The number of stickers Alice has is 25% of the number of stickers the other 3 children have. The number of stickers Barbie has is a third of the number of stickers the other children have, while Cora has half of the number of stickers the other children have. If Daylia has 78 stickers, how many stickers does each of the other children have?

Thank You for taking your time to read this. I appreciate it if you could give me a solution to this problem as soon as possible.

==========

## Tuesday, February 15, 2011

======

I am a Primary 6 Student and have been reading your blog since P5. I would like to ask for your help in the 2 questions from Pei Hwa Presbyterian CA1 Math paper:

Paper2
Q18:
7 apples cost $4 9 oranges cost$11
James bought a total of 1000 apples and oranges for \$999.
How many apples and how many oranges did he buy?

Q5:
297 digits are used to print the page numbers of a story book.
What is the number on the last page number of the story book?

Thank you so much and happy new year.

## Friday, January 21, 2011

### PSLE will start a week earlier this year

http://www.straitstimes.com/BreakingNews/Singapore/Story/STIStory_626701.html

THIS year's Primary School Leaving Examination (PSLE) will take place a week earlier to accommodate Children's Day.

The written papers have been scheduled for Sept 29 to Oct 5. Last year, they were held between Oct 6 and Oct 12.

The Ministry of Education (MOE) said in response to queries from The Straits Times that the adjustment was made to avoid disruption to the exam caused by the extended weekend to mark Children's Day.

Children's Day falls on Oct 7, a Friday, and will be celebrated the day before in schools, with many declaring half-days.

If the PSLE were to start in the first week of October, pupils sitting it would not be able to enjoy the long Children's Day weekend.

Last year, the MOE announced that Teachers' Day and Children's Day would be marked on the first Fridays of September and October respectively, starting from this year. This would give children and teachers long weekends in the two months.