Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 606 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.What is the midpoint of the line joining (3, 8) and (11, 16)? (a) (7, 12) (b) (14, 24) (c) (12, 7) (d) (4, 4)
2. 2.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 150° (d) 60°
3. 3.The mean of 5 numbers is 21. When the number 15 is added to them, what is the new mean? (a) 18 (b) 21 (c) 19 (d) 20
4. 4.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 24 (d) 37
5. 5.In a class of 42 children, 14 like mangoes, 22 like bananas and 2 like both. How many like neither? (a) 10 (b) 8 (c) 6 (d) 2
6. 6.What is the mode of 2, 2, 4, 15, 2, 19 and 4? (a) 4 (b) 2 (c) 19 (d) 15
7. 7.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 155° (d) 45°
8. 8.What is the median of 22, 39, 27, 30 and 21? (a) 28 (b) 30 (c) 22 (d) 27
9. 9.What is the mean of 8, 16, 19, 14 and 3? (a) 13 (b) 10 (c) 12 (d) 15
10. 10.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 217 cu cm (c) 144 cu cm (d) 18 cu cm
11. 11.How many factors does 26 have? (a) 5 (b) 4 (c) 3 (d) 2
12. 12.What is the 31st term of the AP 10, 18, 26, 34, …? (a) 258 (b) 240 (c) 250 (d) 248
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
14. 14.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 15 (d) 25
15. 15.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 126 (c) 14 (d) 45
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
17. 17.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 6 (c) 8 (d) 12
18. 18.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 30 (d) 33
19. 19.What is the midpoint of the line joining (3, 0) and (9, 6)? (a) (3, 3) (b) (3, 6) (c) (6, 3) (d) (12, 6)
20. 20.A bag has 5 red balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 12 (d) 16
21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
22. 22.What is the midpoint of the line joining (5, 9) and (9, 1)? (a) (5, 7) (b) (7, 5) (c) (2, 4) (d) (14, 10)
23. 23.In a class of 30 children, 11 like maths, 20 like science and 6 like both. How many like at least one of the two? (a) 30 (b) 19 (c) 25 (d) 31
24. 24.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 25 (d) 20
25. 25.What is the median of 33, 26, 21, 28, 3, 6 and 22? (a) 21 (b) 26 (c) 22 (d) 28
26. 26.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 2 (d) 7
27. 27.A cuboid is 6 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 236 cu cm (b) 19 cu cm (c) 240 cu cm (d) 30 cu cm
28. 28.A bag has 8 red balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 18 (c) 11 (d) 2
29. 29.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 48 (c) 24 (d) 10
30. 30.In a class of 44 children, 15 like maths, 30 like science and 10 like both. How many like at least one of the two? (a) 25 (b) 45 (c) 44 (d) 35
31. 31.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
32. 32.In a class of 31 children, 9 like dance, 23 like music and 4 like both. How many like only dance? (a) 19 (b) 5 (c) 8 (d) 9
33. 33.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 21) (b) (x + 3)(x + 7) (c) (x − 3)(x − 7) (d) (x + 1)(x + 9)
34. 34.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 150° (d) 60°
35. 35.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 55° (d) 125°
36. 36.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 5 (d) 4
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
38. 38.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 75° (c) 210° (d) 30°
39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
40. 40.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2

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