Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 356 · 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.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 18 (c) 6 (d) 54
2. 2.A bag has 8 yellow, 6 red and 4 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 2/9 (c) 7/9 (d) 5/6
3. 3.In a class of 41 children, 20 like cricket, 28 like football and 8 like both. How many like only cricket? (a) 13 (b) 12 (c) 8 (d) 20
4. 4.A bag has 11 red balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 22 (b) 2 (c) 12 (d) 13
5. 5.If a + b = 10 and ab = 24, what is a² + b²? (a) 148 (b) 100 (c) 52 (d) 76
6. 6.If a + b = 9 and ab = 14, what is a² + b²? (a) 53 (b) 109 (c) 81 (d) 67
7. 7.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 96 (c) 106 (d) 114
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
9. 9.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁵ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
10. 10.What is the mode of 11, 13, 7, 2, 13, 7 and 13? (a) 2 (b) 11 (c) 13 (d) 7
11. 11.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
12. 12.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 51 (d) 54
13. 13.A bag has 11 white balls and 12 green 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) 23 (c) 13 (d) 12
14. 14.In a class of 37 children, 26 like maths, 16 like science and 4 like neither. How many like both? (a) 5 (b) 9 (c) 33 (d) 4
15. 15.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 512 sq cm (d) 256 sq cm
16. 16.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
17. 17.A bag has 12 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 4 (d) 13
18. 18.What is the mode of 19, 1, 19, 7, 17, 7 and 19? (a) 7 (b) 1 (c) 19 (d) 17
19. 19.What is the midpoint of the line joining (4, 4) and (14, 10)? (a) (7, 9) (b) (9, 7) (c) (18, 14) (d) (5, 3)
20. 20.What is the mean of 16, 13, 11 and 20? (a) 20 (b) 12 (c) 15 (d) 16
21. 21.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 120 (d) 25
22. 22.If a + b = 17 and ab = 60, what is (a − b)²? (a) 7 (b) 289 (c) 49 (d) 169
23. 23.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 310° (c) 130° (d) 25°
24. 24.How many factors does 47 have? (a) 3 (b) 2 (c) 1 (d) 4
25. 25.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 75° (d) 150°
26. 26.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
27. 27.In which quadrant does the point (−7, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
28. 28.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 494 (b) 404 (c) 484 (d) 324
29. 29.What is the mode of 18, 2, 10, 18, 2, 11 and 18? (a) 18 (b) 2 (c) 11 (d) 10
30. 30.How many factors does 87 have? (a) 4 (b) 5 (c) 3 (d) 2
31. 31.What is the distance between the points (1, 18) and (10, 6)? (a) 225 (b) 21 (c) 16 (d) 15
32. 32.The mean of 3 numbers is 20. When the number 36 is added to them, what is the new mean? (a) 28 (b) 20 (c) 25 (d) 24
33. 33.What is the distance between the points (0, 19) and (16, 7)? (a) 21 (b) 400 (c) 28 (d) 20
34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
35. 35.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
36. 36.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/4 (d) 1/2
37. 37.How many factors does 89 have? (a) 1 (b) 4 (c) 3 (d) 2
38. 38.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 110 (d) 66
39. 39.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
40. 40.A bag has 10 blue balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 17 (c) 2 (d) 8

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