ISMC aims to encourage the young students to compete at the international level. It also helps to identify best talents among students. Its syllabus is mainly common with the Singapore Maths (Primary) syllabus. Thus, students can take part in ISMC without advanced beyond-the-grade-level knowledge and marathon of special training trying to learn in hours all topics which are new and unfamiliar to them. (sc : FB ISMC)

1. $2847 was collected from the sale of tickets for a Charity Show. Each ticket costs the same amount in a whole number in dollars. Between 50 and 100 people bought these tickets. How much was a ticket?

2. The horizontal lines below are parallel and equal distance apart.

Express the area of triangle EFG as a fraction of the area of triangle ABC.

3. Mr Tee received an inheritance this year. He intends to spend 10% of the money this year, and then 10% of the remaining amounts every year in the subsequent years. After how many years will more than half of his inheritance be spent for the first time?

4. The ratio of the number of sparrows to pigeons in my garden was 1 : 5. After 6 sparrows and 6 pigeons flew into the garden, the ratio became 1 : 3. How many sparrows are there now?

Ans: ______ sparrows

5. Little Tyler likes to paddle his kick scooter. He can cover 500 m in 10 minutes. What is his average speed in km/h?

6. Julie bought a vase and she wanted to sell it online at 20% profit. After no one had bought it for several months, Julie announced a 10% discount off the price she listed, and it was sold. What was Julie’s percentage profit?

7. Place each number from 1 to 8 into the 8 blank circles such that no consecutive numbers are linked by a line. What is the sum of the numbers in the shaded circle?

8. Wendy walked to school. 20 minutes after she left, William started walking to school from the same place. William walked 3 times as fast as Wendy. How many minutes did it take for William to catch up with Wendy?

9. RS and TU are straight lines.

Which one of the statements below is true?

1) \(∠a = ∠c\)

2) \(∠b + 25°= ∠d + 63°\)

3) \(∠b + ∠c = ∠a + ∠d\)

4) \(∠c + 38° = ∠a\)

5) \(∠d = 38° + ∠b\)

10. Jane had $100. After buying 6 dresses, each at the same price, she had $2a left. How much did a dress cost?

1) \($100 – 12a\)

2) \($ (100 – \frac{𝑎}{3})\)

3) \($ (\frac{100−𝑎}{3})\)

4) \($ (\frac{50−𝑎}{3})\)

5) \($ (50 – \frac{𝑎}{3})\)

11. Sally bought some pens at the bookshop. \(\frac{3}{8}\) of the pens she bought were red pens. Sally then decided to buy another \(6\) red pens. Now \(\frac{1}{2}\) of all the pens she bought were red pens. How many pens did Sally buy altogether?

12. Mohan has 5 times as many mangoes as papayas. He sold \(\frac{1}{4}\) of the mangoes and \(\frac{1}{4}\) of the papayas. What fraction of the total number of mangoes and papayas were not sold?

13. The Muffin Shop only sold two kinds of muffins – blueberry and chocolate. By noon, the shop had sold 270 blueberry muffins and 25% of the muffins sold were chocolate muffins. If the shop had sold 40% of all the muffins and 162 blueberry muffins are left unsold. What percentage of the unsold muffins were chocolate muffins?

14. Pearl made a total of 270 origami cranes out of some gold foil and silver foil. She gave away 40 gold cranes and 40% of the silver cranes. After that, the ratio of the number of gold cranes to silver cranes Pearl had was 1 : 4.

If Pearl had given away twice as many silver cranes as gold cranes, how many more silver cranes than gold cranes had she made?

15. Four men works at a car-wash.

Wong can wash 1 car in 10 minutes. Xavier can wash 2 cars in 30 minutes.

Yazid can wash 3 cars in 40 minutes. Zaw can wash 4 cars in 50 minutes.

If they work together at their respective rates, how many cars can they complete washing in 1 hour?

16. The table below shows the percentage of pupils who visited each one of the six stalls in the canteen. Although the percentages for Dim Sum stall and Thirsty Hippo stall have not yet been calculated, we know that the Dim Sum stall is not the post popular stall. The bar graph shows the number of pupils who visited these six stalls, but the names of the stalls are not stated.

What is the difference in percentage of pupils who visited the Thirsty Hippo stall and the Dim Sum stall?

17. The length and width of a rectangle are \((5 + 3a)\) cm and \((6 – 4b)\) cm respectively.

The perimeter of the rectangle is 38 cm. What is the area of the rectangle if a and b are whole numbers greater than 0?

18. The graph shows the amount of water that flows from a tap.

The water is filling up an empty tank 1.25 m by 1 m by 0.9 m.

What fraction of the tank would be filled after 30 minutes?

(Reduce fraction to its lowest term.)

19. ABCD is a parallelogram.

Which TWO of the following are true?

1) \(∠a + ∠b = ∠e + ∠f\)

2) \(∠a + ∠b = ∠i + ∠j\)

3) \(∠c + ∠d = ∠e + ∠f\)

4) \(∠d + ∠f = ∠c + ∠e\)

5) \(∠e + ∠f = ∠b + ∠h\)

20. Only 1 of the 6 statements below is true. Which is it?

A) All of the below is true.

B) None of the below is true.

C) All of the above is true.

D) One of the above is true.

E) None of the above is true.

F) None of the above is true.

21. There are between 100 to 150 men and women in a two storey building.

The number of men to the number of women on the first storey is 5 : 4.

The number of men to the number of women on the second storey is 5 : 1.

There are 3 times as many people in the second storey as on the first storey.

How many men are there altogether? (6 marks)

22. Mike’s pocket money is made up of 20¢ coins while Michelle’s pocket money is made up of 5¢ coins. Mike has twice as many coins as Michelle. If Mike gives eight 20¢ coins to Michelle and she gives him one 5¢ coin in return, then Michelle will have four times as much money as Mike. How many 20¢ coins do they have altogether? (7 marks)

23. Pupils 1, Pupil 2, Pupil 3 and Pupil 4 each put a donation of $1, $2, $3 and $4 into envelopes marked E1, E2, E3 and E4. Each student gives a number of dollars which was different from his Pupil number, and into an envelope marked with a number different from the amount and the Pupil number.

Pupil 1 put $2 into E4.

Pupil 4 put his donation into E2.

In which envelope was the donation of $3 put? (8 marks)

24. Jacob was given 8 identical large cubes and Grace was given some identical small cubes.

The length of the sides of 2 large cubes is equal to the length of the sides of 3 small cubes, as shown.

Jacob and Grace were told to fit their cubes inside the outline of a given rectangle.

Jacob fitted 1 layer of 8 of his large cubes exactly, as shown.

Grace fitted 1 layer of 18 of her small cubes, also exactly.

If the total volume of the 8 large cubes and the 18 small cubes is 45 000 cm³, what is the length of the side of a small cube? (9 marks)

25. Fayelin has a set of square tiles of different sizes. The length of the sides of each square tile is an exact centimetre. Fayelin chooses some of the tiles and arranged them as shown below:

a) If the area of the smallest square is 4 cm², what is the area of the next square Fayelin will use?

(3 marks)

b) If each side of the smallest triangle is 1 cm, what is the length of the side of the next triangle Fayelin will use? (2 marks)

c) What fraction of the pattern is shaded in Figure X? (5 marks)