A bus was travelling at a constant speed from Town A to Town B. It passed a car travelling at a constant speed of 90 km/h in the opposite direction. 1 and 1/2 hours later, the bus reached Town B but the car was still 25 km away from Town A. If the bus took 4 hours to complete the whole journey, what is the distance between the two towns?
Solution
Answer: 256 km
Monday, September 28, 2009
Rosyth Sch 2007 PSLE Math Prelim Q48
Rosyth Sch 2007 PSLE Math Prelim Q47
The perimeter of a rectangle to that of a square is in the ratio of 11:6. If the square has an area of 144 square m and the length and breadth of the rectangle are in the ratio of 6:5, find the length and breadth of the rectangle.
Solution
Perimeter
(6 + 6 + 5 + 5) units ----- 88 m
22 units ----- 88 m
1 unit ----- 88m divided by 22 = 4 m
(Length) 6 units ----- 6 x 4 m = 24 m
(Breadth) 5 units ----- 5 x 4 m = 20 m
Answer: Length = 24 m; Breadth = 20 m
Rosyth Sch 2007 PSLE Math Prelim Q46
The total cost of 28 textbooks and workbooks is $784.
3/4 of the books are textbooks and the remaining books are workbooks. A workbook cost half as much as a textbook. Find the difference in the price of a textbook and a workbook.
Solution
Workbook ----- 1 unit
Textbook ------ 2 units
3/4 of the books are textbooks ----- 3/4 x 28 = 21
Workbooks ----- 28 – 21 = 7
21 textbooks + 7 workbooks ---- $784
(21 x 2 units) + 7 units ----- $784
42 units + 7 units ----- $784
49 units ----- $784
1 unit ------ $784 divided 49 = $16
Answer: $16
Friday, September 25, 2009
Rosyth Sch 2007 PSLE Math Prelim Q45
The figure shows a cube with 3 painted parts A, B and C. These painted parts are of the same area and they are touching the midpoints of the sides of the cube. The total area of the painted parts is 54 square cm. Find the volume of the cube. 
3 painted parts on 3 faces of the cube ----- 54 square cm
1 painted part on 1 face of the cube
54 square cm divided by 3 = 18 square cm
Area of 1 triangle is 18 square cm divided by 2
= 9 square cm
For area of triangle to be 9 square cm, the base has to be 6 cm and height has to be 3 cm as worked out below
(1/2 x 6 cm x 3 cm = 9 square cm)
1 side of the cube is therefore 6 cm as seen from above diagram.
Volume of cube
(6 x 6 x 6) cubic cm = 216 cubic cm
Answer: 216 cubic cm
Rosyth Sch 2007 PSLE Math Prelim Q44
The figure is not drawn to scale. What fraction of the figure is the total area of the shaded regions A, B, C, D, E, F, G and H? 
Solution
The base of the whole figure is (4 + 3 + 6 + 3 + 2) cm = 18 cm
1st row from the top
Fig A has a base of 6 cm.
2nd row
The sum of the bases of Figs B and C is 6 cm.
3rd row
The sum of the bases of Figs D and E is 6 cm.
4th row
The sum of the bases of Figs F and G is 6 cm.
5th row
Fig H has a base of 6 cm.
The average length of the bases of all shaded figures is 6 cm.
The length of the base of the whole figure is 18 cm.
Therefore, the fraction of whole figure that is shaded is
6 cm divided by 18 cm = 1/3
Answer: 1/3
Note that the above method can be used because the vertical columns also correspond to the 6 cm shaded out of the 18 cm total vertical length of the figure.
Rosyth Sch 2007 PSLE Math Prelim Q43
The area of the figure ABCD is 48.5 square cm . Find the length of BE.
(Give your answer to the nearest tenth)
Solution
Area of ACD
1/2 x 18 cm x 10.4 cm = 93.6 square cm
Area of ABC
93.6 square cm - 48.5 square cm = 45.1 square cm
Area of Triangle ABC ----- 1/2 x base x height
45.1 square cm = 1/2 x 18 cm x height
height = (45.1 sq cm x 2 ) divided by18 cm
= 5.01 cm ~ 5.0 cm (to the nearest tenth)
Answer: 5.0 cm
Rosyth Sch 2007 PSLE Math Prelim Q41
The table below shows the rates at which a construction worker is being paid daily. 
How many hours must he work in a day to earn $140?
Solution
First 8 hours of work ----- $10 x 8 = $80
To earn $140, he needs another $60.
Overtime rate is ----- $10 per hour x 1.5 = $15 per hour.
For overtime pay to be equal to $60, he must work
$60 divided by $15 per hour = 4 hours
Total time he needs to work
8h + 4h = 12h
Answer: 12 hours
Thursday, September 24, 2009
Rosyth Sch 2007 PSLE Math Prelim Q40
Machine A can do a printing job in 2 hours. Machine B can do the same job in 3 hours. If both machines are used at the same time, how long would it take to complete half the printing job?
Solution
Since Machine A takes 2 hours and Machine B takes 3 hours, Machine A will be able to get more work done than Machine B, if both are used at the same time, in the ratio of 3:2 as shown below.
(Machine A)
Whole job ----- 2 hours
3/5 of job ----- 3/5 x 2 hours = 6/5 hours
Time taken if both machines are used at the same time is 6/5 hours because while Machine A completes 3/5 of the job, Machine B completes the remaining 2/5 of the job.
Time taken for whole job done if both machines are used at same time is therefore 6/5 hours
Time taken for half the job done if both machines are used at the same time is
1/2 x 6/5 hours = 3/5 hour.
Answer: 3/5 hour
Rosyth Sch 2007 PSLE Math Prelim Q39
Find the sum of the six marked angles in the diagram.
The sum of the all the angles in the triangle in the centre is 180 degrees. The sum of all the 3 angles outside the centre triangle, in the figure above is therefore also 180 degrees (opposite angles).
The sum of all the six marked angles is hence,
Sum of marked angles in 1 triangle ----- 180 degrees
Sum of marked angles in 3 triangles ----- 180 degrees x 3 = 540 degrees
Sum of 6 marked angles ----- (540 – 180) degrees = 360 degrees
Answer: 360 degrees
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