Circle P6 2010 SA2 ACS P2 Q14

pi  x  30 = 94.248



180/360  =  1/2

3  -  1/2  =  2 1/2

2 1/2  x  94.248  =  235.62 cm2 (2 dp)

The shaded area is 235.62 cm2.

Percentage P6 2010 SCGS P2 Q13

Terry bought a vase which he decides to sell. If he sells the vase at a discount of 20%, he makes a gain of $150. If he sells it at a 45% discount, he loses $325. How much did Terry pay for his vase? [4 marks][Answer given: $1370]



100%  -  20%  =  80%

80%  -->  Cost  +  $150


100%  -  45%  =  55%

55%  -->  Cost  -  $325


80%  -  55%  -->  150  +  325

25%  -->  $475

80%  -->  80/25  x  475  =  $1520

Cost --> 1520  -  150 =   $1370


The cost of the vase is  $1370.

Circle P6 2010 SA2 SCGS P2 Q18

[2 marks for (a) and 3 marks for (b)]{Answers given: 116 cm and 364.42 cm (correct to 2 decimal places)]


43  x  2 =  86  cm

86  x  2  =  172  cm

28  x  2  =  56  cm

172  -  56  =  116  cm

a) The length of SR is  116  cm.


86  -  56  =  30  cm

pi  x  30  =   94.247 cm 

2  x  pi  x  43  =  20.177  cm 

94.247  +  20.177  =  364.42 cm (2 dp)


The perimeter is 364.42 cm.

MGS 2010 P6 Prelim P2 Q11:

Ellen and Lenny have some sweets. If Ellen gives away 12 sweets, the number of sweets Ellen has is 13/24 of the total number of sweets that both of them have. If Lenny gives away 12 sweets, the number of sweets Lenny has is 3/8 of the total number of sweets that both of them have. How many sweets do they have altogether? [4 marks][Answer given: 156 sweets]


24  -  13  =  11

E  --  13 u  +  12

L  --  11 u


8  -  3  =  5

L  --  3 p  +  12

E  --  5 p


11 u  -->  3 p  +  12

13  u  +  12  -->  5 p


15 p  -->  55 u  -  12 x 5  =  55 u  -  60

15 p  -->  39 u  +  12 x 3 =  39 u  +  36


55 u - 60  -->  39 u  +  36


16 u  -->  36  +  60  =  96

1 u  -->  96 / 16 = 6

24 u  -->  24  x  6  =  144

144  + 12  =  156  sweets

They have  156  sweets altogether.

MGS 2010 P6 Prelim P2 Q17:

A tank contains some water up to a height of 10 cm. When 4 identical marbles are put into the tank, the water level rises by 8 cm. One marble is then removed from the tank and a metal block is put into the tank. The water level increases to 22 cm.
(a) Find the ratio of the volume of 1 marble to the metal block. [2 marks]
(b) If the base area of the tank is 450 cm², how much more is the volume of the metal block than that of two marbles? [3 marks]
[Answer given: (a) 1 : 3   (b) 900 cm³]



4 marbles  -->  8 cm

1 marble  -->  1/4  x  8  =  2 cm

8  -  2  =  6  cm

Metal block  -->  22  -  10  -  6 =  6 cm

2 : 6 = 1 : 3      Since base area of tank is the same

a) The ratio of the volume of 1 marble to the metal block is 1 : 3.


6  -  2 x 2  =  2 cm

450  x  2  = 900 cm3

b) The volume of the metal block is  900 cm3  more than 2 marbles.

An apple a day will keep the doctor away

In the morning, James ate an apple which his mother had just bought from the market. He then complained that the apple was neither sweet nor juicy. So his mother decided to put the remaining apples into the refrigerator.

In the afternoon, when James ate another apple which his mother had bought that morning, do you think he would find the apple sweet or juicy? Explain your answers.

Time P5 2009 SA2 RGS P1 Q26

Ali was given 0.18 litres of cough mixture by the doctor. He had to take 10 ml of it every 4 hours. How many days would he take to finish the cough mixture?


180 / 10 = 18 times

18 - 1 = 17      Exclude the 1st time he took the cough mixture as time is 0 h

17 x 4 = 68 hours

68/24 = 2 5/6 days