Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 770 · 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.How many factors does 41 have? (a) 4 (b) 3 (c) 1 (d) 2
2. 2.What is the 32nd term of the AP 13, 18, 23, 28, …? (a) 155 (b) 173 (c) 168 (d) 160
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
4. 4.How many factors does 91 have? (a) 4 (b) 2 (c) 5 (d) 3
5. 5.In a class of 39 children, 14 like cricket, 27 like football and 10 like both. How many like at least one of the two? (a) 41 (b) 21 (c) 31 (d) 39
6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 136 (d) 31
7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 100 (d) 55
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
9. 9.In a class of 39 children, 15 like dance, 22 like music and 4 like both. How many like at least one of the two? (a) 29 (b) 37 (c) 33 (d) 39
10. 10.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 726 cu cm
11. 11.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 100° (d) 40°
12. 12.What is the mean of 19, 5, 10, 4, 4 and 18? (a) 12 (b) 11 (c) 10 (d) 9
13. 13.What is the median of 38, 1, 14, 5 and 9? (a) 14 (b) 5 (c) 10 (d) 9
14. 14.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
15. 15.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
16. 16.A bag has 7 blue balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 17 (b) 9 (c) 2 (d) 8
17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
18. 18.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 1 (d) 11
19. 19.What is the midpoint of the line joining (8, 1) and (16, 9)? (a) (24, 10) (b) (4, 4) (c) (5, 12) (d) (12, 5)
20. 20.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
21. 21.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 1332 (c) 666 (d) 630
22. 22.If a + b = 10 and ab = 21, what is (a − b)²? (a) 58 (b) 16 (c) 100 (d) 4
23. 23.In a class of 41 children, 18 like maths, 21 like science and 2 like both. How many like at least one of the two? (a) 35 (b) 41 (c) 37 (d) 39
24. 24.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
25. 25.A bag has 5 black balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 7 (c) 11 (d) 2
26. 26.What is the midpoint of the line joining (10, 12) and (18, 0)? (a) (14, 6) (b) (4, 6) (c) (28, 12) (d) (6, 14)
27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
28. 28.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 125° (d) 305°
29. 29.In a class of 44 children, 29 like mangoes, 21 like bananas and 11 like both. How many like at least one of the two? (a) 28 (b) 39 (c) 44 (d) 50
30. 30.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
31. 31.In a class of 20 children, 9 like dance, 8 like music and 2 like both. How many like neither? (a) 2 (b) 7 (c) 5 (d) 3
32. 32.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 75° (b) 105° (c) 140° (d) 115°
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
34. 34.A bag has 9 white, 2 green and 5 blue balls. One ball is taken out without looking. What is the probability that it is not white? (a) 7/16 (b) 9/16 (c) 1/3 (d) 7/9
35. 35.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/12 (c) 1/11 (d) 2/11
37. 37.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 1 (d) 2
38. 38.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 1)(x + 7) (c) (x + 1)(x + 15) (d) (x + 3)(x + 5)
39. 39.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2178 (c) 2145 (d) 2211

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