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.

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

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

Fraction PSLE 2010 P1 Q24

Mr Tan took his family to the zoo. They were in the zoo from 9.10 a.m. to 3.10 p.m. What fraction of the 24-hour day did Mr Tan and his family spend in the zoo? Give your answer in the simplest form.


              3 h             3 h
    |---------------|--------------|
9.10 am      12.10 pm      3.10 pm




It was 1/4 of the 24-hour day.6/24 = 1/4

Percentage PSLE 2010 P1 Q26

26.  A school conducted checks on its Primary 1 pupils' eyesight from Monday to Thursday. Each of them had their eyes checked on one of the four days. The bar graph below shows the number of pupils that were checked on each day.


Bar graph:

Y-axis: Number of pupils (intervals of 20 and scale from 0 to 200)

X-axis: Monday, Tuesday, Wednesday and Thursday

Monday: 180

Tuesday: 120

Wednesday: 200

Thursday: 100

All columns in the graph are shaded.

What percentage of the Primary 1 pupils had their eyes checked on Monday?



180  +  120  +  200  +  100  =  600


180/600  x  100%  =  30%

Fraction PSLE 2010 P1 Q30

30.  In the diagram below, ACEG and BDFH are squares. AB, CD, EF and GH are of the same length. The ratio of AB: BC is 2:1.

What fraction of the square ACEG is shaded?


3  x  3  =  9

4  x  1/2  x  1  x  2  =  4

9  -  4  =  5

5/9

Whole Number PSLE 2010 P2 Q1

1. Write down all the common factors of 12 and 18.


1 x 12    1 x 18


2 x 6       2 x 9


3 x 4      3 x 6


The common factors are 1, 2, 3, 6.

Compass PSLE 2010 P2 Q2

The square grid below shows the plan of a playground. The bench is north of the toy car.

(a) In what direction is the swing from the see-saw?

(b) The town council wants to plant a tree in the playground.

The location of the tree is to be north of the swing and south-west of the slide. Put a tick (√) in the square where the tree will be planted.


a) West

b) As shown in the diagram √

Decimal PSLE 2010 P2 Q3

Meijun had some money. She used 1/4 of it on a watch and 1/6 of it on a gift. The watch and the gift cost $133.50 altogether.How much money had she left?


1/4 x 3/3 = 3/12

1/6 x 2/2 = 2/12

3 + 2 = 5

12 - 5 = 7

5 u  -->  133.50

7 u  -->  7/5 x 133.50 =  $186.90


She had $186.90 left.

Area & Perimeter PSLE 2010 P2 Q4

In the figure below, AB=7 cm, BC=9 cm, CD=3 cm and DA=11 cm. Angle ABC and Angle CDA are right angles.

Find the area of the figure ABCD.


1/2 x  9 x 7  =  31.5


1/2 x 11 x 3  =  16.5


31.5  +  16.5  =  48  cm2

It is  48  cm2.

Speed PSLE 2010 P2 Q5

Faizal and Gary ran in a race. When Gary had completed the race, Faizal had only run 5/8 of the distance. Gary's speed was 75 m/min faster than Faizal's speed. Both of them did not change their speeds throughout the race. What was Faizal's speed in m/min?


3 u  -->  75 m/min

5 u  -->  5/3  x  75  =  125  m/min

It was  125  m/min.

Algebra PSLE 2010 P2 Q6

6.  Alan had 1.2 m of wire. He used some of it to make the figure shown below.


A pentagon is given, labelled from left to right and base: k cm, k cm, k cm, (k + 8)cm and (2 k - 5) cm.

(a) How much of the wire did Alan use to make the figure?
      Leave your answer in the simplest form in terms of k.

(b) If k=15, how much of the wire was not used to make the figure?


k  +  k  +  k  +  (k + 8)  +  (2 k - 5)  = (6 k  +  3) cm

a) Alan used (6 k + 3) cm.



6 x 15  +  3  =  93


120  -  93  =  27  cm

It was  27  cm.

Average PSLE 2010 P2 Q7

The table below shows the number of books read by each pupil in a class of 30 pupils. One of the numbers in the table is covered by an ink blot.


---------------------------------------------------------------
| Number of books read by each pupil   |   0   |   8   |  ??  |
---------------------------------------------------------------
| Number of pupils                                 |  10  |  15  |   5   |
---------------------------------------------------------------

The average number of books read by the pupils in the class is 6.


What is the number covered by the ink blot?


30  x  6  =  180


15  x  8  =  120


180  -  120  =  60


60  ÷  5  =  12

It is  12.

Decimal PSLE 2010 P2 Q8

8. A jar filled with 40 identical screws weighs 1.4 kg. The same jar when filled with 20 identical nails weighs 500 g. The mass of each screw is twice the mass of each nail. What is the mass of the empty jar?


J + 80 u -- > 1.4


J + 20 u -- > 0.5



60 u --> 1.4 - 0.5 = 0.9


20 u --> 20/60 x 0.9 = 0.3



J  -->  0.5 - 0.3 = 0.2 kg


The mass of the empty jar is 0.2 kg.

Angle PSLE 2010 P2 Q9

9.  In the figure below, ABCD is a trapezium. E is a point on AD such that AB=BE. Angle BCD=62⁰ and angle CDE=110⁰

Find angle EBC.

180  -  110  =  70

180  -  70  -  70  =  40

180  -  62  =  118

118  -  40  =  78°

It is 78°.

Area & Perimeter PSLE 2010 P2 Q10

10. ADEF is a rectangular cardboard with AF = 7 cm. Two quarter circles have been cut from it as shown below. The remaining cardboard, which is the shaded part, has an area of 56 cm².
Using π=22/7, find the length of BC.

1/2  x  22/7  x  7  x  7  =  77

77  +  56  =  133

133/7  =  19

19  -  7  -  7 =  5 cm

It is 5 cm.

Whole Number PSLE 2010 P2 Q11

Sam packed 320 marbles into four boxes, labelled A, B, C and D. Box A had the most number of marbles and box D had the least. The difference in the number of marbles between Box A and the number of marbles in the other three boxes were 8, 13 and 19.
How many marbles were there in Box D?

D []<----- 19 ----->    ]
C [][ 6 ]<-- 13 --->    ]
B [][ 11  ]<-- 8 -->    ] 320
A [][        19        ]   ]

4 u  -->  320  - 6 - 11 - 19 = 284    Small unit -- D

1 u --> 284 / 4 = 71

It is 71 marbles.


Alternative method (model drawing is actually not required)
------------------------
A [                             ]      ]
B [                 ]<-- 8-->      ]
C [             ]<-- 13 --->     ]  320
D [     ]<---- 19 -------->     ]

4 u  -->  320  +  8  +  13  +  19  =  360     Big units -- A 

1 u -->  360 / 4  =  90

90  -  19  =  71

It is  71  marbles.

Whole Number PSLE 2010 P2 Q12

A group of girls shared some sweets among themselves. They tried taking 11 sweets each, but found that the last girl had only 6 sweets. When each girl took 8 sweets, there were 25 sweets left over. How many sweets were there altogether?



                                                            [     ]   -- 1 u
[    ][    ][    ][    ][    ][    ][    ][    ][    ][    ][6][5]
[    ][    ][    ][    ][    ][    ][    ][    ][       25   ]

3 u  -->  25  +  5  =  30

1 u  -->  30/3 = 10

11 u  -->  11 x 10  =  110

110  - 5  = 105  sweets

There are 105  sweets.


Alternative method
-------------------------
11 x (n - 1)  +  6  -->  8  x  n  +  25

3 n  -->  25  -  6  +  11  =  30

n  -->  30/3  =  10

8  x  10  +  25  =  105 sweets

There are  105  sweets.

Angle PSLE 2010 P2 Q13

In the figure below, ABC is a triangle. X, Y and Z are points on the triangle such that AX=AY and YB=ZB.

If angle AYZ=104⁰ and angle XYB=107⁰, find angle ZCX.

180  -  104  =  76

180  -  76  -  76  =  38

180  -  107  =  73

180  -  73  -  73  =  34

180  -  28  -  34  =  118⁰

It is  118°.

Alternative solution provided by P6 pupil

107° + 104°  =  211°

211°  -  180°  =  31°

360°  -  31°  -  107°  -  104°  =  118°