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.

Saturday, February 28, 2009

Nanyang Pri Sch P6 CA1 2008 Math Q45

A faulty weighing machine scale showed a reading of 0.2 kg when nothing was placed on it. A box which contained 21 identical books was placed on the weighing scale. After 5/7 of the books were removed from the box, the weighing scale showed a reading of 32.68 kg. Given that the mass of each book was 0.8 times the mass of the box, find the mass of the box.

Solution


Mass of book is 0.8 that of box -----
Book ----- 8 units
Box ----- 10 units

After 5/7 book removed, 2/7 was left:-

(2/7) x 21 books = 6 books
6 books + box ----- 32 680g – 200g
(6 x 8 units) + 10 units ----- 32 480g
58 units ----- 32 480g
1 unit ----- 32 480g divided by 58 = 560g

(Box) 10 units ----- 10 x 560g = 5600g or 5.6 kg

Answer: The mass of the box was 5.6 kg.

Nanyang Pri Sch P6 CA1 2008 Math Q44

Sandy and Christine went to the bookshop and bought some stationary. Sandy bought 6 pens and 4 exercise books for $6.60. Christine bought 4 pens and 6 exercise books for $5.90. How much does each pen cost?

Solution


(Sandy) 6 pens + 4 books ----- $6.60 (x3)
(Christine) 4 pens + 6 books ----- $5.90 (x2)

(Sandy) 18 pens + 12 books ----- $19.80
(Christine) 8 pens + 12 books ----- $11.80

Difference in price between what Sandy and Christine paid:-
$19.80 - $11.80 = $8

Sandy paid $8 more because she bought 10 more pens than Christine:-
10 pens ----- $8
1 pen ----- $8 divided by 10 = $0.80

Answer: Each pen costs $0.80

Nanyang Pri Sch P6 CA1 2008 Math Q43

The line graph below shows the number of visitors at the zoo from Monday to Saturday.



a) If each visitor paid $12 for a ticket, how much money was collected on weekdays?

b) The number of visitors who visited the zoo on Sunday was 30% more than the number of visitors on Friday. What is the difference in the number of visitors between Saturday and Sunday?

Solution


Between “0” and “2000” on the vertical scale, there are 8 divisions.
8 divisions ----- 2000 (visitors)
1 division ----- 2000 divided 8 = 250 (visitors)

Data from graph above
(Mon) 2000 + 1 division ----- 2000 + 250 = 2250
(Tue) 2000 + 4 divisions ----- 2000 + 1000 = 3000
(Wed) 2000 + 2 divisions ----- 2500
(Thu) 2000 + 4 divisions ----- 3000
(Fri) 4000 + 3 divisions ----- 4750
(Sat) 6000 + 5 divisions ----- 7250

Total no. of visitors (Mon to Fri) ----- 15 500 visitors

a)
15 500 x $12 = $186 000
Answer: The amount collected was $186 000

b)
(Fri) 100% ----- 4750 (visitors)
(Sun) 130% ----- 130% x 4750 = 6175 (visitors)
Sat – Sun ----- 7250 – 6175 = 1075

Answer: The difference in number of visitors is 1075.

Nanyang Pri Sch P6 CA1 2008 Math Q42

Nora bought a bottle of detergent. She used an equal amount of detergent each day. She had 2/3 of the detergent left after 5 days. She had 1.2 litres of detergent left after another 7 days. What was the volume of the detergent at first?

Solution

5 days ----- 1/3 detergent used
1 day ----- 1/3 divided by 5 = 1/15 detergent used

After another 7 days, total no. of days is 12 -----
12 days ----- 12 x (1/15) = 12/15 detergent used

Detergent left after 12 days -----
3/15 of detergent left ----- 1200 ml
1/15 detergent ----- 1200 ml divided by 3 = 400 ml
(Full amount) 15/15 ----- 15 x 400 ml = 6000 ml

Answer: 6000 ml or 6 litres were left.

Nanyang Pri Sch P6 CA1 2008 Math Q41

The cost of a chicken pie is thrice the cost of a muffin. Mrs Seetho paid a total of $40 for 20 muffins and 10 chicken pies. Find the cost of a chicken pie.

Solution


Chicken pie ----- 3 units
Muffin ----- 1 unit

20 muffins + 10 chicken pies ----- $40
(20 x 1 unit) + (10 x 3 units) ----- $40
20 units + 30 units ----- $40
50 units ----- $40
1 unit ----- $40 divided by 50 = $0.80
(Chicken pie) 3 units ----- 3 x $0.80 = $2.40

Answer: The cost of a chicken pie is $2.40

Friday, February 27, 2009

Nanyang Pri Sch P6 CA1 2008 Math Q40

A slice of cake costs $m. Yi Ling bought n such slices of cake. Find the smallest possible sum of m and n if Yi ling paid a total of $24.

Solution


1 slice ----- $m
n slices ----- $m x n = $24
m x n = 24

Factors of 24 ----- Sum of factors
24 x 2 = 24 ----- 24 + 1 = 25
12 x 2 = 24 ----- 12 + 2 = 14
8 x 3 = 24 ----- 8 + 3 = 11
6 x 4 = 24 ----- 4 + 6 = 10

Answer: The smallest possible sum of m and n is 10.

Thursday, February 26, 2009

Nanyang Pri Sch P6 CA1 2008 Math Q39

Jaffa gave 60% of his marbles to his brother and 25% of the remainder to two friends. Each of his friends received 30 marbles. How many marbles did his brother receive?

Solution




(2 friends)
40% x 25% ----- 30 x 2 = 60
10% ----- 60
60% ----- 6 x 60 = 360

Answer: He received 360 marbles.

Tuesday, February 17, 2009

Nanyang Pri Sch P6 CA1 2008 Math Q38

Two identical taps, when turned on at the same time, take 5 minutes to release 10 litres of water. How many such taps, when turned on at the same time, are needed to release 27 litres of water in 3 minutes?

Solution

2 taps, 5 min ----- 10 litres
2 taps, 1 min ----- 10 litres divided by 5 = 2 litres
1 tap, 1 min ----- 2 litres divided by 2 = 1 litre

27 litres, 1 min ----- 27 litres x 1 = 27 litres

27 litres, 3 min (3x slower than 1 min)
----- 27 divided by 3 = 9

Answer: It took 9 taps

Monday, February 16, 2009

Nanyang Pri Sch P6 CA1 2008 Math Q36

The figure below is made up of Triangle FHJ and Trapezium ABDE. Given that GB // FC and BJC is an isosceles triangle, find Angle GHB.



Solution

Angle BCF ----- 106 deg *
Angle BCJ ----- (180 – 106) deg = 74 deg **
Angle BJC ----- 74 deg #
Angle GBH ---- 74 deg *
Angle GHB ----- Angle BGF – Angle GBF ##
= (156 – 74) deg = 82 degrees (Answer)

* corresponding angles
** angles on a straight line
# base angles of isosceles triangle
## exterior angle

Wednesday, February 11, 2009

MOE to recruit another 3,000 teachers this year

From Channel News Asia

SINGAPORE: The Ministry of Education (MOE) is hoping to recruit another 3,000 teachers this year, but if this target could not be met “so be it”, said Education Minister Ng Eng Hen during the Committee of Supply Debate on Tuesday.

“We will... ensure that only those with the passion, aptitude and commitment to teaching are selected,” said Dr Ng. “We would rather hire less to get the type of teachers we want to maintain a quality teaching force.”

He was responding to concerns raised by some Members of Parliament about bumping up recruitment in the education sector in light of the recession.

Senior Minister of State for Education Grace Fu pointed out that only about half of those who had met MOE’s current academic criteria for teacher training passed the selection interviews.

And while the ministry is moving towards all-graduate recruitment for its teaching force, Ms Fu stressed that current non-graduate teachers need not feel “compelled” to upgrade their academic qualifications. “What is more important is how well they perform as educators,” she said.

The MOE is also looking into hiring 500 Allied Educators - who support teachers in areas like counselling and teaching - as well as professionals with strong language skills for a new Language Facilitator Scheme to boost language proficiency among students.

Mid-career professionals with leadership experience can consider applying to be vice-principals, while MOE also hoped to recruit “high-calibre young graduates” to join as education policy analysts, said Dr Ng.

To meet demand in the preschool sector, a new diploma developed by the Singapore Polytechnic will be introduced to provide shorter training duration for kindergarten teachers, at half the time taken to obtain a specialised diploma in early childhood care.

All this will make an estimated 7,500 teaching and teaching-support jobs available in the education sector this year.

Friday, February 06, 2009

Tao Nan School P5 SA2 2007 Math Q48

There are some eggs in 3 baskets, A, B and C. 20% of the number of eggs in A is equal to 10% of the number eggs in B. The number of eggs in C is equal to 50% of the total number of eggs in A and B.

a) Express the number of eggs in C as a fraction of the number of eggs in B. (Leave your answer in its simplest form.)

b) If half of the eggs in B are taken out and placed into C, there will be 50 eggs in C. How many eggs are there in the 3 baskets?

Solution



a)
A + B ----- 15 units
C has 50% of 15 units ----- 15 units x 50/100 = 7.5 units

Fraction of number of eggs in C to B ----
7.5/10
= 75/100
= ¾ (Answer)

b)
If half of the eggs in B transferred to C -----
B ----- 10 units
Half of B ----- 5 units
C now will have, 7.5 units + 5 units ----- 12.5 units

12.5 units ----- 50 eggs
1 unit ----- 50 eggs divided by 12.5 = 4 eggs

Total number of eggs -----
A has 5 units
B has 10 units
C has 7.5 units
Total ----- 22.5 units

22.5 units ----- 22.5 x 4 = 90

Answer: There are 90 eggs in the 3 baskets.

Wednesday, February 04, 2009

Tao Nan School P5 SA2 2007 Math Q47

Kathy had some pocket money. From the pocket money, she spent $35 on food and $65 on transport. After that, she spent 2/7 of the remaining money on 5 books. As for the rest of her money, she gave 2/5 of it to her cousin and had $75 left.

a) How much did each book cost?
b) How much money did she have at first?

Solution


a)
3 units ----- $75
1 unit ----- $75 divided by 3 = $25
(5 books) 2 units ----- $25 x 2 = $50
1 book ----- $50 divided by 5 = $10

Answer: 1 book cost $10


b)
Total amount of money

$35 + $65 + 7 units
= $35 + $65 + (7 x $25)
=$35 + $65 + $175
= $275

Answer: She had $275 at first.

Monday, February 02, 2009

Tao Nan School P5 SA2 2007 Math Q46

The table below shows the rates of charges for water consumption.

First 5 cubic metres ----- $1.50 per cubic metre
Next 5 cubic metres ----- $1.75 per cubic metre
Every additional 1 cubic metre or part thereof ---- $2.00 per cubic metre

a) In the month of June, Family A used 18 cubic metres of water. How much did Family A pay for their water bill?

b) Family A’s water bill for July was $48.25. How much water was used?

Solution


a)
Charges for 18 cubic metres -----

First 5 cubic metres ----- $1.50 x 5 = $7.50
Second 5 cubic metres ----- $1.75 x 5 = $8.75
Last 8 cubic metres ----- $2 x 8 = $16.00

Total charges ----- $7.50 + $8.75 + $16 = $32.25

Answer: The family paid $32.25


b)
First 10 cubic metres cost ----- $7.50 + $8.75 = $16.25

48.25 - $16.25 = $32

$32 was charged at a rate of $2 per metre cube -----
$32 divided by $2 per metre cube = 16 cubic metres

Total consumption ----- 10 + 16 = 26

Answer: 26 cubic metres of water was used.