Graph PSLE 2010 P2 Q15

Chris filled a tank with water using two taps. He turned on Tap A first and after 4 minutes, he also turned on Tap B. Both taps were turned off at the same time when the tank was completely filled without overflowing.

The graph below shows the amount of water in the tank over 16 minutes.

(a) What fraction of the tank was filled 4 minutes after Tap A was turned on? Express your answer in the simplest form.

(b) In one minute, how many litres of water flowed from Tap B?

5/35  =  1/7

a) 1/7 of the tank was filled 4 minutes after Tap A was turned on.

35 - 5  =  30

10  -  4  =  6

30/6  =  5

5/4  =  1.25

5  -  1.25  =  3.75 litres


Alternative method
----------------------

10  -  4  =  6

6/4  x  5  =  7.5

35  -  5  -  7.5  =  22.5

22.5/6  =  3.75  litres

b) In one minutes, 3.75 litres of water flowed from Tap B.

Volume PSLE 2010 P2 Q18

Diagram given - Tank A, 60 cm by 10 cm by 40 cm, with a tap above it, was empty.

Diagram given - Tank B, 50 cm by 20 cm by 36 cm, with a tap above it, was filled with water.
At first, Tank A was empty and one third of Tank B was filled with water. Both taps were turned on at the same time and water from both taps flowed at the same rate of 1.2 litres per minute.
How long did it take for the height of the water to be the same in both tanks?
(1 litre = 1000 cm³)


1/3  x  36  =  12

60 x 10 x H  -->  50 x 20 x (H - 12)

1000 H  -  600 H  -->  12 000

H  -->  12 000 / 400  =  30

60  x  10  x  30  =  18 000

18 000 / 1 200  =  15  minutes

It took  15 minutes.


Alternative method
----------------------

60  x  10  :  50  x  20  =  3  :  5

2 u  -->  1/3  x  36  =  12 cm

5 u -->  5/2  x  12  =  30  cm

60  x  10  x  30  ÷  1200  =  15  cm

It took  15  minutes.

Perimeter PSLE 2010 P1 Q28

The shaded figure below is formed using 3 squares and 3 equilateral triangles. The length of the straight line AB is 15 cm. Find the perimeter of the shaded figure.

15 x 3  =  45        Squares


15 x 2  =  30          Triangles


 45 + 30  =  75 cm


Alternative method
----------------------

15  x  5  =  75  cm

Speed PSLE 2010 P1 Q27

Chun and Devi started jogging from the same place in opposite directions along a straight path. They jogged for 40 minutes. At the end of the jog, they were 7 km apart. Chun's average speed was 6 km/h.

What was Devi's average speed?


6  x  40/60  =  4

7  -  4  =  3

3  x  60/40 =  4.5 km/h   or  3/4  x  6  =  4.5 km/h


Alternative method
----------------------

7  ÷  40/60  =  7  x  60/40  =  10.5        Combined speed

10.5  -  6  =  4.5  km/h

Ratio PSLE 2010 P1 Q25

At a fruit stall, the price of a pear is 3/5 the price of an orange. The price of an apple is half the price of a pear. What is the ratio of the price of an orange to the price of a pear to the price of an apple?



3/5  x  2/2  =  6/10

1/2  x  3/3  =  3/6

10 : 6 : 3

Perimeter PSLE 2010 P1 Q13

A floor is covered with a row of equilateral triangular tiles of side 3 cm. The perimeter of the floor covered by the tiles is 93 cm. How many tiles are used to cover the floor?  Ans: 29 (Option 2)

93 / 3 = 31 sides

31 - 2 =  29   Remove the 2 sides to avoid double counting


Alternative method
----------------------

93  -  3  -  3  =  87      Remove the lengths of both sides

87/3  =  29       Divide by the length of each side