Primary Mathematics World Contest

We have primary mathematics world contest problems for individual contest and may be usefull for your students.

1. There are four kinds of dollar-notes (or dollar-bills) of value $1, $5, $10, and $50 respectively. There is a total of nine dollar-notes, with at least one dollar-note of each kind. If the total value of these dollar-notes is $177, how many $10 dollar-notes are there ?

2. A bus starts from town A to town B and another bus starts from town B to town A on the same road. They run with constant speed to their destinations and back home without stopping. The buses pass by each other for the first time at 700 km (kilometers) from town A and they pass by each other for the second time on the way back at 400 km from town B. How many km is it from town A to town B?

3. A contractor requests 2 men to build brick walls. One man can build a brick wall in 9 hours, while the other man can do the same job in 10 hours. However, when the two men work together, there will be shortfall of a total of 10 bricks per hour, and it takes them exactly 5 hours to complete the brick wall . Find the total number of bricks used on the wall.

4. Clock A is ten seconds faster than standard time every hour. Clock B is twenty seconds slower than the standard time every hour. If we adjust the two clocks to standard time at the same time, then within 24 hours Clock A shows 7:00 while Clock B shows 6:50. What is the standard time at that moment ?

5. How many different isosceles triangles of perimeter 25 units can be formed where each side is a whole number (integer) of units?

6. There are four kinds of dollar-notes (or dollar-bills) of value $1, $5, $10, and $50 respectively. There is a total of nine dollar-notes, with at least one dollar-note of each kind. If the total value of these dollar-notes is $177, how many $10 dollar-notes are there?

7. Peter begins counting up from 100 by 7’s (100, 107, …) and Mary begins counting down from 1000 by 8’s (1000, 992, …) at the same time. If they count at the same rate, what number will they say at the same time?

8. A bus starts from town A to town B and another bus starts from town B to town A on the same road. They run with constant speed to their destinations and back home without stopping. The buses pass by each other for the first time at 700 km (kilometers) from town A and they pass by each other for the second time on the way back at 400 km from town B. How many km is it from town A to town B?

9. In the figure, MN is a straight line.  The angles a, b and c satisfy the relations, b:a = 2:1 and c:b = 3:1.  Find angle b.

10. A square floor is tiled with congruent square tiles. The tiles on the two diagonals of the floor are black. The rest of the tiles are white. If there are 101 black tiles, what is the total number of white tiles?

11. In trapezoid ABCD, segments AB and CD are both perpendicular to BC. Diagonals AC and BD intersect at E. If AB = 9, BC = 12 and CD = 16, what is the area of triangle BEC?

12.  Refer to the diagram below. In rectangle ABCD, F is the midpoint of AB, BC = 3BE, AD = 4HD. If the area of rectangle ABCD is 300 square-units, how many square-units is the area of the shaded region?

13. I, II, and III are three semi-circles of different sizes. If the ratio of the diameters of I , II and III is 3:4:5, and the area of III is 24cm2, how many cm2 is the sum of the areas of I and II?

14.  Find the value of:

15. Find the fraction with the smallest denominator between 97/36 and 96/35 !

7th Primary Mathematics World Contest

Problems for Individual Contest

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