Tao Nan School P5 SA2 2007 Math Q37

A book and 3 pens cost $11.25. The book cost twice as much as a pen. Find the cost of 4 books.

Solution

Book ----- 2 units
Pen ----- 1 unit

1 book + 3 pens ----- $11.25
2 units + 3 units ----- $11.25
5 units ----- $11.25
1 unit ----- $11.25 divided by 5 = $2.25

(4 books) 4 x 2 units ---- 8 units
8 units ----- 8 x $2.25 = $18

Answer: The cost of 4 books is $18.

Tao Nan School P5 SA2 2007 Math Q36

A baking machine can bake 20 muffins in 10 minutes. At this rate, how long does this machine take to bake 48 muffins?

Solution

Unit Method
20 muffins ----- 10 min
1 muffin ----- 10 min divided 20 = ½ min
48 muffins ----- ½ min x 48 = 24 minutes


Ratio Method
Muffins : Minutes
20 : 10
2 : 1
48 : 24

Answer: It takes 24 minutes to bake 48 muffins

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.

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!

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

More Holiday posts.

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)

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.

Catholic High Sch 2006 PSLE Math Prelim Q36

There are 45 boys in a campsite. Out of these boys, 17 of them like cycling. 14 of them like swimming and 10 of them like both cycling and swimming. How many boys do not like cycling and swimming?

Solution


Like both ----- 10
Like cycling only ---- 17 – 10 = 7
Like swimming only ----- 14 – 10 = 4
(Total number of boys) like cycling, swimming or both -----
10 + 7 + 4 = 21

(Number of boys) do not like cycling and swimming -----
45 – 21 = 24

Answer: 24 boys do not like cycling or swimming.

Catholic High Sch 2006 PSLE Math Prelim Q29

Alan has enough money to buy either 18 pencils or 15 pens. If he buys 12 pencils, how many pens can be buy with the remaining money?

Solution 

18 pencils ----- 15 pens 

(divided both by 3)

6 pencils ----- 5 pens

If he bought 12 pencils, it means he bought 6 pencils less. This amount of money is equivalent to the price of 5 pens. 

Answer: He could have bought 5 pens with the remaining money.

Catholic High Sch 2006 PSLE Math Prelim Q27

Kenneth wants to rent a bicycle from Jim’s Bicycle Kiosk. The cost (C) of renting a bicycle for d hours is given by C = $(3d + 5). Find the cost of renting the bicycle if Kenneth wants to cycle for 4 hours. 

Solution

d hours ----- $(3d + 5)

1 hour ----- $(3d + 5)/d 

4 hours ----- $4(3d + 5)/d (Answer) 

Catholic High Sch 2006 PSLE Math Prelim Q26

The figure below is made up of a square and three identical semi-circles.
Calculate the perimeter of the shaded region.




= (2 x 3.14 x 5 cm) + 10 cm + 10 cm
= 31.4 cm + 20 cm= 51.4 cm (Answer)

Common Errors and Confusion – “ovary” and “spores”

It is a bit unfortunate that both the reproductive parts of the female human and the female part of the flower have the same name, “ovary”. Because both have the same name, spelling and the same way they are pronounced, some students end up confused.

Ovary in a flower refers to the female reproductive part of the flower. The ovary in this case, will develop into the fruit after fertilization. The ovary of the flower is illustrated as shown below.



Ovary in the human female on the other hand, is the reproductive part of the female where eggs are produced. The ovary in the human female is illustrated as shown below.



Another confusion which is caused by the same term, is “spores”. Spores are produced by ferns and mushrooms for the purpose of reproduction. Again, because of the same name, some students get confused that mushrooms and ferns are plants. This is not correct. Ferns are plants but mushrooms are fungi. Only plants make their own food. Mushrooms feed on dead matter - eg rotting logs.

PSLE Aggregate Score Calculation

Your individual PSLE Aggregate Score depends on your cohort’s performance and how easy or tough the paper is.

Using the individual’s score of Eng 82, MT 89, Maths 87, Science 86, two scenarios are created below.

Example 1 - where it is assumed the cohort is weak, and the paper is assumed “tough”. An average score of 55 is used, and the Standard Deviation of 20 is used.


PSLE Aggregate Score is worked out to be 262.

Example 2 - Using the same individual score, but the cohort is now assumed to be stronger, and the paper is assumed to be “simple”. A higher average of 60 is used, and a higher Standard Deviation of 25 is used.


PSLE Aggregate Score is worked out to be 242.

Rationale for adjustment - If the cohort is strong, it can be assumed that pupils will be able to score a higher average. Conversely, if the cohort is weak, the average of the cohort will drop.

If the paper is “simple and easy”, it is assumed that more students will be able to score "A*"s and "A"s. Hence, an “easy” paper will widen the gap between the brighter and average pupils, giving a larger Standard Deviation.

Likewise, if the paper is "tough", it is assumed that fewer students will be able to score "A*"s and "A"s, narrowing the gap between the brighter and average pupils, giving a smaller Standard Division.

Note - For those who are using the PSLE Aggregate score calculator, using a low average and low Standard Deviation would create a "most liberal scenario" where the PSLE Aggregate Score Calculator will show a high result. Using a high average and high Standard Deviation would create a "most conservative scenario", where the PSLE Aggregate Score will show a much more conservative result.

Related posts
How PSLE Aggregate Score is calculated
Get a free copy of your PSLE Aggregate Score Calculator

Pei Chun Public Sch 2007 PSLE Math Prelim Q48

Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio of 3 : 2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary.

Solution

(Note: The working has been amended (in blue) on 17 Sep 08 to make the working clearer.)

Cost of 1 dictionary ----- 1 unit + $4
Cost of 1 comic ----- 1 unit

Comics ----- 120%
Dictionary ----- 100%
Total 220% ----- $1496

10% ----- $1496 divided by 22 = $68
(Dictionaries) 100% ----- $680 

Comics ----- $1496 - $680 = $816

But we know that the ratio

comics : dictionaries

3 : 2

Comics

3 units ----- $816

1 unit ----- $272

Dictionaries

2 units + ? groups of $4 ------ $680

(2 x $272) + ? grps of $4 ----- $680

? grps of $4 ----- $680 - $544 = $136

? grps ----- $136 divided by 4 = 34 groups of $4

[Every $4 difference ---- 1 dictionary was bought

$136 difference ----- $136 divided by $4 = 34 (dictionaries)]

Dictionaries ----- $680
$680 divided by 34 dictionaries = $20 per dictionary

Answer: One dictionary cost $20.

Pei Chun Public Sch 2007 PSLE Math Prelim Q47

Najip, Kumar and Gurmit started jogging at the same time from the same starting-point round a circular track. Najip and Kumar jogged in a clockwise direction and Gurmit jogged in an anti-clockwise direction. Gurmit took 5 minutes to complete each round. Gurmit met Najip after every 3 minutes. Gurmit met Kumar after every 2 minutes. The jogging speed of each person remained the same throughout.
a) What was the ratio of Gurmit’s speed to Najip’s speed to Kumar’s speed?

b) When Gurmit and Najip met again at the starting-point after 15 minutes, Kumar had already jogged 3.6 km. What is the circumference of the circular track?



b)
(Gurmit)
5 min ----- 1 round
15 min ----- 3 rounds

Kumar (since ratio Gurmit : Kumar is 2:3) ----- 4.5 rounds
3.6 km divided by 4.5 rounds = 0.8 km per round

Answer: The circumference is 0.8 km

======

Update - 1420 hours, 29 Aug 2008

I have relabelled the model to make it clearer.
The model is seen from Gurmit’s perspective.
He was running in the opposite direction as compared to the other two.

In the 5 min cycle, Gurmit will see Kumar after 2 min.
This means G would have covered 2/5 of lap when he met K.
It also means K would have covered 3/5 lap at that point.
Hence, the model shows 2 units for G and 3 for K.

In the same 5 min cycle, G will meet N after 3 min.
This means G would have covered 3/5 lap when he met N.
Of course, N would have covered 2/5 lap.
Hence, 3 units for G and 2 for N.

Pei Chun Public Sch 2007 PSLE Math Prelim Q46

A rectangular tank measuring 60 cm by 40 cm and 20 cm was 1/6 filled with water. At 08 00, Tap A with water flowing out at a rate of 3 litres per minute was turned on. At 08 02, Tap B was turned on to drain water out of the container at a fixed rate. At 08 13, the tank was 75% filled with water. At what time would the tank be filled to the brim?



Solution

Capacity of tank -----
(60 cm x 40 cm x 20 cm) = 48 000 cubic cm or 48 000 ml

1/6 of volume ----- 48 000 ml x 1/6 = 8000 ml

Water flowed for 2 min ----- 3 litres x 2 = 6000 ml

Amount of water in tank at 08 02 -----
8000 ml + 6000 ml = 14000 ml

75% volume ----- 48 000 ml x 75% = 36 000 ml

From 08 02 to 08 13 ----- 11 min

Rate of increase of water level in tank -----
(36 000 – 14 000) ml divided by 11 min
= 2000 ml per min

To be filled to the brim from 75% volume, another 25% volume must be filled.

25% volume ---- 48 000 ml x 25% = 1200 ml
Time needed ----- 12 000 ml divided by 2000 ml per min = 6 min

6 min after 08 13 is 08 19

Answer: It would be 08 19 when the tank is filled to the brim.

Pei Chun Public Sch 2007 PSLE Math Prelim Q45

400 people took part in a camp. 73 of them were adults and the rest were children. 2/5 of the boys and ¼ of the girls were lower primary pupils while the rest of them were upper primary pupils. There were 9 more upper primary girls than upper primary boys.
a) How many upper primary pupils were there?
b) What percentage of the people who took part in the camp were girls?

Solution

400 people – 73 adults ----- 327 children



12 parts + 15 parts ----- 981 + 45
27 parts ----- 1026
1 part ----- 1026 divided by 27 = 38

a)
(Upp Pri Girls) 3 parts ---- 3 x 38 = 114
(Upp Pri Boys) 114 – 9 = 105
Total Upper Pri ----- 114 + 105 = 219
Answer: There were 219 upper primary pupils.

b)
(Total Girls) 4 parts ----- 38 x 4 = 152
Percentage of girls ----- (152/400) x 100% = 38%
Answer: 38% were girls.

Pei Chun Public Sch 2007 PSLE Math Prelim Q44

The figure below is made up of a rectangle, a semi-circle and 4 identical quadrants.
a) What is the total area of the shaded parts?
b) What is the perimeter of the whole figure?


Solution

a) Redrawing


Area of shaded area
= Area of rectangle + Area of quadrant
= (7 cm x 3.5 cm) + (¼ x 22/7 x 3.5 cm 3.5 cm)
= (24.5 + 9.625) square cm
= 34.125 square cm (Answer)

b)
Perimeter -----
Lengths of 4 quarter arcs + 6r
= 4 x (¼ x 2 x 22/7 x 3.5 cm) + (6 x 3.5) cm
= 22 cm + 21 cm
= 43 cm (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q43

Taufik arranged a rectangle and a square and painted them in three colours as shown in the figure below. The ratio of the area of the rectangle to that of the square is 3:1. The ratio of the area of the red part to that of the blue part is 4:1. The length of the square is 9 cm.
a) What is the area of the purple part?
b) What is the ratio of the area of the purple part to that of the figure?






Area of Rectangle : Area of Square
3 : 1
9 units : 3 units

Red Area : Blue Area
4 : 1
8 units : 2 units

a)
(Square) 3 units ----- 81 square cm
(Purple) 1 unit ----- 81 square cm divided by 3 = 27 square cm (Answer)

b)
Purple ----- 1 unit
Whole figure 11 units

Area of purple part : Area of whole figure
1 : 11 (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q42

The figure below shows a park which is made up of a triangular fitness area, a rectangular pond and a field in the shape of a trapezium. The length of the pond is twice its breadth.



a) The cost of fencing material is $3 per meter. How much will it cost to fence up the pond?
b) What is the area of the park?

Solution

a)
Length of pond ----- 2 x 4 m = 8 m
Perimeter of pond ----- 2 x (8 + 4) m = 24 m

1 m ----- $3
24 m ----- $3 x 24 = $72

Answer: It will cost $72 to fence up the pond.

b)
Area of rectangle -----
21 m x 4 m = 84 square m

Area of triangle -----
½ x 14 m x 21 m = 147 square m

Total area of the park ----- (84 + 147) square m = 231 square meters (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q41

The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers was 1 : 5. Then their mother gave Eunice 12 more stickers and Andrew 5 more stickers. The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers became 1 : 4. How many stickers did Andrew have in the end?

Solution

Andrew (before) 1 unit + 5 ----- 1 part (after) (multiply by 4)
Eunice (before) 5 units +12 ----- 4 parts (after)

Andrew (before) 4 units + 20 ----- 4 parts (after)
Eunice (before) 5 units + 12 ----- 4 parts (after)

Comparing Eunice with Andrew -----
(Eunice) 5 units + 12 ----- 4 units + 20 (Andrew)

5 units – 4 units ----- 20 – 12
1 unit = 8

Andrew in the end -----
1 unit + 5
= 8 + 5
= 13

Answer: Andrew had 13 stickers in the end.

Pei Chun Public Sch 2007 PSLE Math Prelim Q40

Kavita had 50% fewer erasers than Mark. After Mark gave 15 of his erasers to Kavita, Kavita had 40% fewer erasers than Mark. How many erasers did Kavita have at first?

Solution



Kativa has 30 more, while Mark has 15 less. Hence, Kativa will have 45 more than Mark.

45 ----- 120% - 100%
45 ----- 20%
10% ----- 45% divided by 2 = 22.5%

Kativa at first ----- 60% -15
= (6 x 22.5) - 15
= 135 – 15
= 120

Answer: Kativa had 120 erasers at first.

Pei Chun Public Sch 2007 PSLE Math Prelim Q38

A rectangular piece of cardboard measures 17 cm by 12 cm. Sushila cuts the greatest number of rectangular pieces, each measuring 3 cm by 2 cm, from the cardboard. What is the total area of all the pieces cut?

Solution
The diagram below is not drawn to scale



34 pieces of small rectangles can be cut without any cardboard left.

Area used ----- 17 cm x 12 cm = 204 square cm (Answer)

Pei Chun Public Sch 2007 PSLE Math Prelim Q39

A group of pupils were asked to choose a co-curricular activity. The pie chart represents their choices. The same number of pupils chose Basketball and Volleyball.
a) 60 pupils chose Table Tennis. How many pupils chose Basketball?
b) The ratio of the number of pupils who chose Basketball to the number of pupils who chose Soccer is 3 : 10. How many pupils chose Scouts?



Solution

a)
Table Tennis (1/4 pie chart) ----- 60
Basketball (1/2 x Table Tennis) ----- ½ x 60 = 30

Answer: 30 pupils chose Basketball.


b)
Soccer + Scouts (1/2 pie chart) ----- 60 x 2 = 120

Basketball : Soccer
3 : 10
30 : 100

If 100 chose soccer, Scouts ----- 120 – 100 = 20

Answer: 20 chose Scouts.

English Oral - relink

PSLE English Oral is just a day away. Here is a link to Paya Lebar MGS's video on English Oral Exam.

Pei Chun Public Sch 2007 PSLE Math Prelim Q37

Mrs Durai wants to buy bookmarks for 3 classes of pupils. There are 35 pupils in each class. For every 4 bookmarks she buys, she gets another one free.
a) How many bookmarks does she need if each pupil gets 1 bookmark?
b) 4 bookmarks cost $2. What is the least amount she needs to pay?

Solution

a) 3 classes x 35 = 105

Answer: She needs 105 bookmarks.

b)
4 bookmarks + 1 free ----- $2
5 bookmarks (total) ----- $2

105 bookmarks divided by 5 ----- 21 (groups of 5 bookmarks)

21 groups of 5 bookmarks ----- 21 x $2 = $42

Answer: She has to pay $42.

Students, watch your handwriting

Fittingly, just before the exams, the Straits Times publishes an article about the atrocious state of handwriting of some students. (The full article can be found at the end of this post.)

For whatever reason, some students never learn. Even after much advice from teachers and nagging from parents, some students simply would not write legibly. They believe that the world is able to read their handwriting, and even will argue with markers that they deserve the marks, after the exam is over.

The rule is simple. If the marker cannot make out what you write, he/she will not be able to give you the marks.

The importance of handwriting cannot be under-emphasized. For example for Science, key words must be spelt correctly. It is useless arguing with markers after the exam that what you wrote is “stomata”, when what it looks like to everybody else, as “stomota”.

The student may argue all he wants that the marker mis-read his writing. From the marker’s viewpoint, the student did not know the correct spelling of the keyword. If the marker awards the student the mark, it would be unfair to students who genuinely got the answer right.

For the PSLE, although there is an avenue for appeal, students will NEVER get to see their papers after the exam. What this means is that if the markers cannot read your handwriting, and if you lose marks for that, you will have no one to blame but yourself.

The saddest part is that you will never know if you lost marks because you got the answers wrong, or because no one understood what you wrote.

From the Straits Times

Wired teens = 'Ant' writing
Students don't see need to improve handwriting because of tech tools but teachers hate it

BLAME technology for 'ants' - or what teachers call bad teen handwriting.

The Straits Times collected samples from 186 teens aged 13 to 17, which threw up 52 scripts covered with 'ants'.

They needed a lot of deciphering, typical of handwriting of the wired generation, said handwriting expert William Pang, 60.

Mr Pang, a handwriting consultant who began studying the science of handwriting analysis in the 1970s, blames this 'degeneration' on the lack of focus on penmanship in classrooms.

Students are not taught to grasp the pen properly, he said. 'Some of them even slump on the table as they write.'

They do not see the need to improve, either. After all, 'technology helps to make homework neater for students', Mr Pang pointed out.

Modern practices like downloading notes from the school's website and submitting typewritten assignments lessen the need for legible handwriting.

Teachers, who have to wade through an average of 100 to 200 scripts each week, say they especially hate the type of handwriting they call 'ants'.

'The tiny, ant-size writing makes it difficult for teachers to read what is written,' lamented Mrs Kang Yeok Lung, 59, a senior teacher at St Andrew's Junior College.

She has been a teacher for 27 years, and points out: 'When students write like that, they don't realise that the teacher's eyesight is affected and it makes marking a chore.'

The cure?

'I think assignments should be handwritten and not sent to the teacher as an e-mail attachment,' Mrs Kang said.

After all, when teachers have to guess what students write, she added, 'the student loses out'.

Especially during examinations, when essays are still handwritten, it can cost them grades. When markers cannot understand the scripts, 'there is a higher risk of misinterpretation'.

Augustus Set, 17, a second-year student at St Andrew's Junior College, said his parents feared his bad writing so much, they bought him handwriting practice books, 'so that I can write more legibly for my A level examinations'.

Still, other students are recalcitrant - they say they are expressing themselves.

Said Sayyed Amir Zaini, 16, a Secondary 4 student at Pasir Ris Secondary School: 'I tried to change my handwriting but I just can't. Anyway, I don't think I should change it just because others say so. I will change my handwriting only because I want to.'

Handwriting in the 1970s was of a better quality, said Mr Pang, who was then studying close to 300 handwriting samples as an amateur analyst. Tidier scripts showed that Singaporeans were more patient and considerate then.

'People were in less of a rush,' he said. 'They took more pains with their handwriting and the letters were more well-formed... to ensure others could read what they had written.'

The Straits Times' survey, on the other hand, revealed that many of the wired generation are disconnected, individualistic, more rebellious and non-conformist than their predecessors.

Mr Pang believes that teens will change their handwriting as they grow older 'to create their own identity'.

But that might not be for the better, he warned: 'A person's handwriting is likely to get worse with age if at work, he types more than he writes.'

Maha Bodhi Sch 2007 PSLE Math Prelim Q48

Two different machines, A and B, were used together at the same time to print a book. It took two hours for the book to be printed. If only Machine A was used, it would have taken another 4 hours. How long would it take to print the same book if only Machine B was used?

Solution

Machine A only ----- 2 hours + 4 hours = 6 hours

6 hours ----- Machine A printed whole book
2 hours ----- Machine A printed 1/3 book

The other 2/3 of the book was printed by Machine B
2 hours ----- Machine B printed 2/3 book
2/3 book ----- 2 hours
3/3 book ----- 3 hours

Answer: It would take 3 hours if Machine B was used only.

Maha Bodhi Sch 2007 PSLE Math Prelim Q47

Ali, Bala and Krishnan went to a shopping centre and bought a present for their friend. They agreed to share the cost of the present equally but Ali did not have any money with him that day and Bala did not bring enough to pay for his share. As a result, the amount of money Bala paid to that paid by Krishnan was 1 : 4. The next day, Bala returned $12 to Krishnan.

Find
a) how much money Bala brought along with him to the shopping centre.
b) the cost of the present.

Solution

Bala : Krishnan
1 : 4

1 + 4 = 5
5 units to be shared by 3 people -----
5 units divided by 3 = 1 and 2/3 units

Each person was expected to pay 1 and 2/3 units.

a)
Bala paid 1 unit the previous day, but paid $12 the next day, hence,

The balance 2/3 unit ----- $12
1/3 unit ----- $12 divided by 2 = $6
1 unit ----- $6 x 3 = $18

Answer: Bala brought along $18.

b)
Total cost ----- 5 units
5 units ----- $18 x 5 = $90

Answer: The cost of the present was $90.

Maha Bodhi Sch 2007 PSLE Math Prelim Q46

Each corner of the floor mat shown above is made up of a quadrant of radius 4 cm. Find the perimeter of the floor mat.

Solution

4 quadrants make 1 full circle
Perimeter of arcs of 4 quadrants above -----
2 x 3.14 x 4 cm = 25.12 square cm

Consider length of mat -----
40 cm – 4 cm – 4 cm = 32 cm

Consider breadth of mat -----
30 cm – 4 cm – 4 cm = 22 cm

Perimeter of mat -----
(25.12 + 32 cm + 32 cm + 22 cm + 22 cm)

= 133.12 cm (Answer)

Maha Bodhi Sch 2007 PSLE Math Prelim Q45

In a frog-leaping competition, for every two leaps made by a big frog, a small frog would have to leap thrice. In a 100-m race, the big frog leapt 50 times.
a) How many times did the small frog leap?
b) How many metres did the small frog move with each leap?

Solution

a)
Big frog ----- small frog
2 leaps ----- 3 leaps
(x 25) 50 leaps ----- 75 leaps (x25)

Answer: The small frog leapt 75 times.


b)
100 m divided by 75 leaps ----- 1 and 1/3 m per leap (Answer)

Free Ai Tong P5 2006 CA2 Maths Section C Worked Solutions

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Ai Tong School P5 CA2 2006 Math Q37

The average length of 2 ribbons is 2 m. One ribbon is 50 cm longer than the other. Find the ratio of the length of the shorter ribbon to that of the longer ribbon.

Solution

Shorter ----- 1 unit
Longer ----- 1 unit + 50 cm
Total Length ----- 2 units + 50 cm

Average length of 2 ribbons ----- 2 m or 200 cm
Total length of 2 ribbons ----- 200 cm x 2 = 400 cm

(Total) 2 units + 50 cm ----- 400 cm
2 units ----- 400 cm – 50 cm = 350 cm
1 unit ----- 350 cm divided by 2 = 175 cm

Shorter ribbon ----- 175 cm
Longer ribbon ----- 175 cm + 50 cm = 225 cm

Ratio
Shorter : Longer
175 : 225
7 : 9

Answer: The ratio of the shorter ribbon to that of the longer ribbon is 7:9.

Ai Tong School P5 CA2 2006 Math Q36

Agnes and Mabel had a total of 720 beads. After Agnes had given Mabel 72 beads, Agnes had 1/5 as many beads as Mabel. How many beads did Mabel have at first?

Solution

(After)
Agnes ----- 1 unit
Mabel ----- 5 units
Total 6 units ----- 720

1 unit ----- 720 divided by 6 = 120

Mabel at first
5 units – 72 ----- (120 x 5) – 72 = 528

Answer: Mabel had 528 at first.

Maha Bodhi Sch 2007 PSLE Math Prelim Q44

Two motorists, X and Y, travelled on the same route from Town A to Town B. They each drove at a uniform speed but started their journey at a different time of the day.

The table below shows some details of their journey.

If Motorist X reached Town B at 1625, find:
a) the distance between the two towns and
b) the speed at which Motorist Y was travelling.

Solution

a)
Consider Motorist X -----
Distance (middle portion) ----- 120 km/h x 2.5 h = 300 km
Total Distance covered ---- 60 km + 300 km + 60 km = 420 km

Answer: The total distance was 420 km.


b)
Motorist Y -----
Middle portion ----- 420 km – 100 km – 100 km = 220 km
Speed ----- 220 km divided by 2.5 hours = 88 km/h

Answer: Speed of Motorist Y was 88 km/h.

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Maha Bodhi Sch 2007 PSLE Math Prelim Q43

Using 3/5 of his money, Derek could buy 8 similar pens. If he was given an extra dollar, he could use it together with the rest of his money to buy another 6 such pens. How much money had Derek?

Solution


3 units ----- 8 pens (multiply by 2)
2 units + $1 ----- 6 pens (multiply by 3)

6 units ----- 16 pens
6 units + $3 ----- 18 pens

$3 ----- 18 pens – 16 pens = 2 pens
2 pens ----- $3
1 pen ----- $3 divided by 2 = $1.50

14 pens ----- $1.50 x 14 = $21
Less $1 he was given ----- $21 - $1 = $20

Answer: He had $20.

Maha Bodhi Sch 2007 PSLE Math Prelim Q42

During a sale, a departmental store offered a storewide discount of a certain fixed percentage. Mrs Goh paid for $16 for a dress during the sale and saved $4.
a) What is the percentage discount?
b) How much did Mrs Goh save if she paid $20 for her purchases during the sale?

Solution

a)
Saved ----- $4
Price before discount ----- $4 + $16 = $20
Percentage discount ----- ($4 / $20) x 100% = 20% (Answer)

b)
Price at 80% ----- $20 (after 20% discounted)
10% ----- $20 divided by 8 = $2.50
20% discount ----- $2.50 x 2 = $5

Answer: She saved $5

Maha Bodhi Sch 2007 PSLE Math Prelim Q41

Tom tied his pen to his pencil as shown in the diagram below to form a toy. The length of the pencil is 3/5 the length of the pen. What is the length of the toy?



Solution


2 units ----- 7 cm
1 unit ----- 7 cm divided by 2 = 3.5 cm
Length of toy ----- pen + 3 cm
5 units + 3 cm
(5 x 3.5 cm) + 3 cm = 20.5 cm

Answer: The length of the toy is 20.5 cm

Henry Park Pri Sch 2007 PSLE Math Prelim Q48

A lorry, a van and a car set off at the same time travelling at a constant speed of 60 km/h, 80 km/h and 120 km/h respectively. The lorry and the van were travelling from Town G to Town H while the car was travelling from Town H to Town G. The car passed the lorry 2 minutes after passing the van.
a) Find the ratio of the distances travelled by the lorry to the van to the car at the moment when the car passed the van.
b) Find the distance between Town G and H.

Solution

a)
Since all of them started at the same time, the distance covered by each vehicle is proportionate to their respective speeds.

Lorry : Van : Car
60 : 80 : 120
3 : 4 : 6 (Answer)

b)
Ratio of the distance covered by the lorry to the distance covered by the car is 3:6 or 1:2. Hence, for every 2 units of distance the car travelled, the lorry travelled 1 unit.

Ratio of distance covered by the van to the distance covered by the car is 4:6 or 2:3. Hence, for every 3 units of distance the car travelled, the van travelled 2 units.



Van covered 2 units for every 3 units car covered.
Hence if the van covered 6 units, the car would have covered 9 units.

Lorry covered 1 unit for every 2 units car covered.
Hence, if the lorry covered 5 units, the car would have covered 10 units.

Distance = speed x time

The speed of the car was 120 km/h.
When the car passed the lorry, it was 2 min after it had passed the van.

Distance covered by the car within those 2 minutes ----
120 km/h x 1/30 h = 4 km

1 unit ----- 4 km

(Total distance)
15 units ----- 4 km x 15 = 60 km

Answer: The distance between Towns G and H is 60 km.

Henry Park Pri Sch 2007 PSLE Math Prelim Q47

At first, Bob had only $5-notes and Chris had only $2-notes. The number of notes Bob had is 80% of Chris’ notes. When Bob gives Chris $100, the number of notes Chris has now is 70% more than Bob.
a) How many notes did Bob have at first?
b) How much money does Chris have at the end?

Solution

a) When Bob gave $100 to Chris, Bob gave Chris 20 notes because Bob had only $5 notes ----- $100 divided by $5 notes = 20 $5-notes.




(Bob) 136% - 34 notes ----- 100% + 20 notes (Chris)
136% - 100% ----- 34 notes + 20 notes
36% ----- 54 notes
1 % ----- 54 divided by 36 = 1.5
80% ----- 1.5 x 80 = 120

Answer: Bob had 120 notes at first.

b) Chris had at the end ----- (100%) + 20 notes

100% ----- 100 x 1.5 = 150 (notes)
150 notes x $2 = $300

20 notes x $5 (given by Bob)
= $100

$300 + $100 = $400

Answer: Chris had $400 in the end.

Henry Park Pri Sch 2007 PSLE Math Prelim Q46

In the figure, ABCD is a square with a perimeter of 84 cm. It is made up of identical squares and quarter-circles.
a) Find the perimeter of the shaded region.
b) Find the area of the shaded region.



Solution

a)
The perimeter of square ABCD is 84 cm.
1 side of square ABCD ----- 84 cm divided by 4 = 21 cm
Radius of the 6 quadrants ----- 21 cm divided by 3 = 7 cm

The shaded area is made up of 6 quadrants -----
6 x ¼ x 2 x 22/7 x 7 cm = 66 cm (Answer)


b) Redrawing the figure….


Area of 1 quadrant -----
¼ x 22/7 x 7 cm x 7 cm = 38.5 square cm

Area of 1 small partially shaded square ----
Area of 1 small square – Area of 1 quadrant ----- (7 cm x 7 cm) – 38.5 square cm = 10.5 square cm

Area of 2 such small partially shaded squares -----
10.5 square cm x 2 = 21 square cm

Area of 3 small shaded squares -----
(3 x 7 x 7) square cm = 147 square cm

Total shaded area ------
(21 + 147) square cm = 168 square cm (Answer)

Henry Park Pri Sch 2007 PSLE Math Prelim Q45

Terrence earns $350 less than Leslie every month. They each spend $800 every month and save the rest of their money.
a) How long does it take for Terrence to save $2100 and Leslie to save $4550?
b) What is Terrence’s monthly salary?

Solution



a) (Leslie's savings) – (Terrence’s savings) -----
$4550 - $2100 = $2450

$2150 divided by $350 (per month) ----- 7 months

Answer: It takes 7 months.

b) In 7 months, Terrence saves $2100
1 month ----- $2100 divided by 7 = $300

Terrence’s salary ----- $800 + $300 = $1100

Answer: Terence’s monthly salary is $1100.

Henry Park Pri Sch 2007 PSLE Math Prelim Q44

Study the diagram below.
a) What is the sum of Angle a, Angle b, Angle c, Angle d, Angle e and Angle f?


Solution

Angles on a straight line = 180 degrees
3 straight lines will have a total of 180 degrees x 3 = 540 degrees
Sum of all Angles a to f -----
540 degrees – sum of angles of triangle
= (540 – 180) degrees
= 360 degrees (Answer)


The figure below shows a rectangle and a triangle.
b) What is the sum of Angle p + Angle q?


Solution

Sum of interior angles of 2 parallel lines ----- 180 degrees (Answer)

Henry Park Pri Sch 2007 PSLE Math Prelim Q43

Four children, Angela, Belinda, Cristobel and Dorothy shared $240. Angela received ½ of the total amount of money received by Belinda, Cristobel and Dorothy. Belinda received 2/3 of the total amount of money received by Cristobel and Dorothy. Cristobel received 3 times as much money as Dorothy.
a) How much money did Dorothy receive?
b) What fraction of Angela’s money is Dorothy’s money if Angela gave $20 to Dorothy?

Solution



10 units ----- $240
1 unit ----- $240 divided by 10 = $24

a) Dorothy
1 unit ----- $24.

Answer: Dorothy received $24.

b) (Angela) 3 1/3 units ----- $24 x 3 1/3 = $80
(Dorothy) 1 unit ----- $24
If Angela gives Dorothy $20,
Angela ----- $80 – $20 = $60
Dorothy ----- $24 + 20 = $44
$44 / $60 = 11/15 (Answer)

Henry Park Pri Sch 2007 PSLE Math Prelim Q42

At first, the total number of sheep in Farm A and Farm B was 980. After 3/5 of the sheep in Farm A and 200 of the sheep in Farm B are sold, the ratio of the number of sheep in Farm A to Farm B becomes 1 : 4.
a) Find the number of sheep in Farm B at first.
b) Find the total number of sheep left in Farm A and Farm B.

Solution


13 units ----- 980 – 200 = 780
1 unit ----- 780 divided by 13 = 60
a) Number of sheep in Farm B at first -----
8 units + 200 ----- (8 x 60) + 200 = 680

Answer: There were 680 sheep in Farm B at first.

b) Total number of sheep left in Farm A and Farm B -----
10 units ----- 10 x 60 = 600

Answer: There were 600 sheep left in both farms.

Vocabulary - illusion ; allusion

What's this video clip have to do with vocabulary?
Play the clip and read later.



Illusion -
1. something that deceives by producing a false or misleading impression of reality.
2. the state or condition of being deceived; misapprehension.
3.an instance of being deceived.
4.Psychology. a perception, as of visual stimuli (optical illusion), that represents what is perceived in a way different from the way it is in reality.
5. a very thin, delicate tulle of silk or nylon having a cobwebbed appearance, for trimmings, veilings, and the like.
6. Obsolete. the act of deceiving; deception; delusion.

Most students do not have problems understanding what "illusion" is.

"Allusion" however, has a different meaning -
1. a passing or casual reference; an incidental mention of something, either directly or by implication: an allusion to Shakespeare.
2. the act of alluding.
3. Obsolete. a metaphor; parable.

As an example, the video clip above is taken from the 1996 movie, "The Thing That You Do!" It is a fictional movie about a boy-band group set in the 1960s.

What is obvious is that the movie (and the boy-band group) is an allusion to the "Beatlemania era" of the sixties.

Beatlemania is a term that was used during the 1960s to describe the intense fan frenzy (particularly demonstrated by young teenaged girls) directed toward The Beatles, particularly during the early years of their success. A portmanteau of "Beatles" and "mania", it is claimed to have been coined in 1963 by Andi Lothian, a Scottish music promoter, although the first printed use of the word is in The Daily Mirror 2nd November 1963 in a news story about the previous day's Beatles concert in Cheltenham. Many fans across the world were known to have Beatlemania (and were thus known as "Beatlemaniacs") which hit the United States hard after The Beatles performed on The Ed Sullivan Show in 1964. 'Beatlemania' was characterised by intense levels of hysteria demonstrated by fans both during the actual concerts played by the band (during which the level of screaming was often so loud as to completely drown out the music) and during the band's arrivals and travels to and from locations. One can envision the dimensions of the original Beatlemania during its peak year in 1964 by looking at the unprecedented sales figures caused by it. During 1964, The Beatles sold over 30 million records in America alone, at one stage holding the top five positions in the singles chart.

Henry Park Pri Sch 2007 PSLE Math Prelim Q41

In the following figures, the area of the biggest equilateral triangle is 64 square cm as shown in Figure 1. A new triangle is formed by connecting the midpoints of the sides of the previous triangle. If the pattern continues, find the area of the smallest triangle in Figure 4.



Solution

The shaded area of Figure 2 is ¼ of the Area of Figure 1 -----
¼ x 64 square cm = 16 square cm

The shaded area of Figure 3 is ¼ of the shaded area of Figure 2 -----
¼ x 16 square cm = 4 square cm

The shaded area of Figure 4 is ¼ of the shaded area of Figure 3 -----
¼ x 4 square cm = 1 square cm (Answer)

Henry Park Pri Sch 2007 PSLE Math Prelim Q40

There were 30 more members in the IT Club than in the Art Club. 15 members left the Art Club for the IT Club. It was then found that the number of members in the IT Club was 5 times as many as the number of members in the Art Club. How many members were there in both clubs altogether?

Solution



4 units ----- 60
1 unit ----- 60 divided by 4 = 15
(Altogether) 6 units ----- 15 x 6 = 90

Answer: There were 90 members altogether.

Common Mistake - Perimeter of Partial Circles