Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 781 · 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 median of 38, 33, 21, 32, 37, 24 and 1? (a) 31 (b) 33 (c) 32 (d) 24
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
3. 3.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 80° (c) 100° (d) 105°
4. 4.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
5. 5.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 35 (b) 30 (c) 29 (d) 28
6. 6.In a class of 33 children, 22 like maths, 7 like science and 2 like both. How many like at least one of the two? (a) 29 (b) 33 (c) 27 (d) 25
7. 7.What is the mode of 15, 12, 12, 1, 15, 15 and 19? (a) 19 (b) 1 (c) 12 (d) 15
8. 8.What is the distance between the points (8, 0) and (16, 6)? (a) 14 (b) 100 (c) 10 (d) 11
9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
10. 10.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 85° (d) 95°
11. 11.A bag has 5 blue balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 7 (c) 14 (d) 6
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 6 (b) 4 (c) 7 (d) 5
13. 13.What is the midpoint of the line joining (4, 12) and (8, 0)? (a) (2, 6) (b) (6, 6) (c) (12, 12) (d) (7, 6)
14. 14.What is the median of 14, 3, 24, 22 and 13? (a) 24 (b) 14 (c) 22 (d) 13
15. 15.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 212 (b) 207 (c) 43 (d) 414
16. 16.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 144 (c) 17 (d) 138
17. 17.If a + b = 13 and ab = 42, what is a² + b²? (a) 127 (b) 253 (c) 169 (d) 85
18. 18.In a class of 34 children, 13 like cricket, 26 like football and 8 like both. How many like neither? (a) 4 (b) 11 (c) 8 (d) 3
19. 19.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 42 (d) 14
20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 17 (b) 16 (c) 7 (d) 18
21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 462 (d) 231
22. 22.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 37 (c) 49 (d) 48
23. 23.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
24. 24.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 53 (c) 62 (d) 44
25. 25.In a class of 20 children, 8 like dance, 9 like music and 7 like neither. How many like both? (a) 4 (b) 5 (c) 13 (d) 7
26. 26.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 9) (b) (x + 1)(x + 21) (c) (x − 3)(x − 7) (d) (x + 3)(x + 7)
27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
28. 28.In a class of 20 children, 11 like cricket, 10 like football and 3 like both. How many like at least one of the two? (a) 18 (b) 21 (c) 20 (d) 15
29. 29.A bag has 3 white, 9 green and 5 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 3/14 (c) 3/17 (d) 14/17
30. 30.A bag has 5 black balls and 12 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) 17 (c) 13 (d) 6
31. 31.What is the median of 6, 23, 18, 14 and 11? (a) 18 (b) 15 (c) 14 (d) 11
32. 32.How many prime numbers are there between 70 and 80? (a) 4 (b) 2 (c) 5 (d) 3
33. 33.In a class of 43 children, 20 like maths, 18 like science and 2 like both. How many like neither? (a) 9 (b) 7 (c) 5 (d) 2
34. 34.In a class of 36 children, 22 like maths, 21 like science and 9 like both. How many like only maths? (a) 15 (b) 13 (c) 22 (d) 12
35. 35.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 312 (b) 37 (c) 176 (d) 156
36. 36.If a + b = 3 and ab = 2, what is a² + b²? (a) 9 (b) 7 (c) 5 (d) 13
37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
38. 38.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 15 (c) 20 (d) 10
39. 39.What is the smallest prime factor of 39? (a) 2 (b) 1 (c) 3 (d) 13
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8

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