RGS Primary 2009 PSLE Math Prelim Paper 2 Q1

Find the value of each of the following expressions when y = 6.
a) 3y - 4
b) y + 2y/3

Solution

a)
3(6) - 4
= 18 - 4
= 14

Answer: 14


b)
(6) + 2(6)/3
= 6 + 4
= 10

Answer: 10

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Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q6

(a) Arif is 2x years old. His father is 4 times as old as he. His mother is 3 years younger than his father. What is their total age in terms of x?

(b) If x is = 4, find their total age.

Solution

(a)
Arif --> 2x
Father --> 4 x 2x = 8x
Mother --> 8x - 3

Total --> 2x + 8x + 8x - 3 = 18x - 3

Answer: (18x - 3) years

(b)
18(4) - 3
= 72 - 3
= 69

Answer: 69 years

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q13

The length of a rectangle is thrice as long as its width. Its perimeter is 16p cm.

a) Find the length of the rectangle in terms of p.

b) Find the area of the rectangle if p = 4.

Solution

Perimeter

--> 3 units + 1 unit + 3 units + 1 unit

= 8 units

8 units --> 16p cm

1 unit --> 16p cm divided 8 = 2p cm

a)

Length

3 units --> 3 x 2p cm = 6p cm

Answer: 6p cm

Answer: 192 square cm

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q2

Each skirt costs $m and 3 blouses cost $62.50. Find the cost of 2 skirts and 6 blouses.

Solution

Skirt --> $m

2 skirts --> 2 x $m = $2m

3 blouses --> $62.50

6 blouses --> 2 x $62.50 = $125

Total --> $2m + $125m

= $(2m + 125) (Answer)

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Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q1

Express the perimeter of the figure below in terms of t.

Solution

Perimeter

--> (6 + t + 5 + 7 +11 + 7 + t) cm

= (2t + 36) cm (Answer)

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Rosyth Sch 2007 PSLE Math Prelim Q36

The average weight of 5 boys is 8w kg. When 2 more children whose weights are 11w kg and 12 w kg respectively joined the group, what is the average weight of the boys now?

Solution

Average weight of 5 boys ----- 8w kg

Total weight of 5 boys ----- 8w kg x 5 = 40w kg

Total weight of 7 boys
(40w + 11w + 12w) kg = 63w kg

Average weight of 7 boys
63w kg divided by 7 = 9w kg

Answer: 9w kg

Rosyth Sch 2006 PSLE Math Prelim Q26

The average mass of 4 girls, Gale, Nancy, Rani and Fiona is 4p. Gale weighs 2p kg, Nancy weighs p kg and Rani weighs 56 kg. What is the mass of Fiona?

Solution

Total of 4 girls ----- 4p kg x 4 = 16p kg

Fiona ----- (16p – 2p – p – 56) kg
= (13p – 56) kg (Answer)

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.

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) 

Henry Park Pri Sch 2007 PSLE Math Prelim Q36

Joseph has $m. Kenny has 3 times as much money as Joseph. Leo has half the amount of money Joseph and Kenny has altogether. How much money do the 3 boys have altogether?

Solution

Joseph ----- $m
Kenny ----- 3 x $m = $3m
Joseph and Kenny ----- $m + $3m = $4m
Leo ----- $4m divided by 2 = $2m

Total ----- $4m + $2m = $6m

Answer: They had $6m altogether.

S’pore Hokkien Huay Kuan 2007 PSLE Math Prelim Q41

Ali had y stamps. His father gave him 20 more stamps. He then shared all his stamps equally with his 2 brothers.
a) How many stamps did each boy get in terms of y?
b) If y = 28, how many stamps did each boy get?

Solution

a)
Number of stamps Ali had at first ----- y
After father gave another 20 stamps ----- y + 20
After sharing with 2 other brothers ----- (y + 20) divided by 3
= (y + 20)/3 (Answer)

b) If y = 28 -----
(28 + 20)/3 stamps
= 48/3 stamps
= 16 stamps (Answer)

Note – “The Singapore Hokkien Huay Kuan 5-School Combined Prelim Maths” is the common Maths Prelim Exam for Tao Nan, Ai Tong, Chongfu, Nan Chiau and Kong Hwa schools.

Tao Nan School P6 Math CA1 2004 (Q46)

A skirt and 3 blouses cost $78. The skirt costs $p more than a blouse.
a) Express the cost of a blouse in term of p.
b) If p=10, how much is the cost of the skirt?

Solution


Skirt ----- 1 unit + $p
Blouse ----- 1 unit

Q(a)
Skirt + 3 blouses ----- $78
(1 unit + $p) + (3 units) ----- $78
4 units + $p ----- $78
4 units ------ $78 - $p
1 unit ----- $(78 – p)/4

Answer: The cost of a blouse is $(78 – p)/4

Q(b)
1 unit ----- $(78 – 10)/4 = $17

Skirt ----- 1 unit + p
= $17 + $10 = $27

Answer: The cost of the skirt is $27

Tao Nan School P6 Math CA1 2004 (Q44)

The figure below is made up of 2 rectangles and a square. Its dimensions are given in cm.

a) Find the perimeter of the figure in terms of n.
b) Find the area of the figure in terms of n.




Solution


Q(a)

Perimeter is (n + 7) cm + n cm + 7 cm + 4 cm + n cm + (n + 4) cm = (4n + 22) cm

Algebra allowed but not encouraged

Using Algebra for PSLE Maths is perfectly legal. The student would not be penalized. However, Algebra taught in P6 is very basic. It is not deep enough to solve many of the Section C questions found in PSLE Maths. As such, teachers usually do not encourage students to use Algebra. Instead, heuristics are encouraged.

In P6, only the 4 operations of Algebra is taught. Students are not taught how to use Algebra to solve Section C type questions, which cognitive skills are needed.

As such, if students were use Algebra without being taught how to apply them in actual Section C questions, they may fumble along the way.

Here is an example how Algebra can be used to solve a P6 question.

Question

Ricci saved $200 from her salary and spent the rest. She spent 1/9 of the expenditure on a blouse, $40 on a scarf and the rest on books. The amount spent on the scarf was $20 less than that spent on the blouse. What was her salary?

Solution

Let $n be her salary

Since she saved $200, she would have $n - $200 left to spend.

Amount spent on blouse was 1/9 x ($n - $200) = $(n – 200)/9

Amount spent on scarf was $40. But we know scarf was $20 less than blouse, which means blouse cost $60.

Cost of blouse….

$(n – 200)/9 = $60
$(n - 200) = $60 x 9
$n - $200 = $540
$n = $540 + $200
$n = $740

Since $n represents her salary, it means her salary was $740.

Note that there are no diagrams or models used. Every step has to be envisioned in the mind. In the above, you must be able to see that 1/9 of the expenditure is equivalent to the cost of the blouse, which is also equivalent to $40 more than the cost of the scarf . P6 students are not trained to do that using Algebra.

P6 students are however trained in heuristics. Now compare how the same question is done, using heuristics, as demonstrated in the link below.

Tao Nan School P5 SA2 2006 Math Question (Q47)

So to answer the question, “Is Algebra allowed in PSLE Maths?”, the answer is yes, it is, but it is not encouraged.