Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 632 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
2. 2.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 260° (d) 100°
3. 3.What is the missing term in the AP 9, 15, ?, 27, 33? (a) 22 (b) 20 (c) 27 (d) 21
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
5. 5.What is the distance between the points (0, 8) and (8, 14)? (a) 11 (b) 10 (c) 14 (d) 100
6. 6.If a + b = 20 and ab = 99, what is a² + b²? (a) 400 (b) 598 (c) 301 (d) 202
7. 7.A bag has 4 red 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) 2 (b) 10 (c) 5 (d) 7
8. 8.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 130° (b) 135° (c) 95° (d) 85°
9. 9.What is the smallest prime factor of 55? (a) 2 (b) 1 (c) 5 (d) 11
10. 10.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
12. 12.What is the median of 38, 19, 27, 10, 11, 33 and 23? (a) 23 (b) 19 (c) 27 (d) 10
13. 13.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 17 (b) 16 (c) 15 (d) 24
14. 14.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 12 (c) 8 (d) 6
15. 15.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
16. 16.In a class of 51 children, 26 like mangoes, 25 like bananas and 7 like both. How many like at least one of the two? (a) 37 (b) 45 (c) 44 (d) 51
17. 17.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 10 (d) 15
18. 18.What is the prime factorisation of 21? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 17 (b) 16 (c) 7 (d) 18
20. 20.A bag has 9 yellow, 8 green and 3 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 3/5 (b) 2/5 (c) 1/3 (d) 2/3
21. 21.How many factors does 27 have? (a) 4 (b) 2 (c) 3 (d) 5
22. 22.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 423 (c) 432 (d) 360
23. 23.If a + b = 14 and ab = 40, what is a² + b²? (a) 276 (b) 156 (c) 196 (d) 116
24. 24.What is the sum of the roots of x² − 15x + 54 = 0? (a) 54 (b) 14 (c) 15 (d) 16
25. 25.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
26. 26.A bag has 11 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 2 (c) 22 (d) 13
27. 27.A bag has 4 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 9 (c) 2 (d) 6
28. 28.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 15 (d) 14
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
30. 30.What is the median of 12, 7, 39, 34, 15, 33 and 2? (a) 15 (b) 34 (c) 12 (d) 33
31. 31.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
32. 32.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
33. 33.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 8 sq cm (d) 24 sq cm
34. 34.In a class of 30 children, 18 like maths, 10 like science and 3 like both. How many like neither? (a) 2 (b) 5 (c) 8 (d) 3
35. 35.How many factors does 99 have? (a) 7 (b) 6 (c) 4 (d) 5
36. 36.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 1806 (c) 882 (d) 861
37. 37.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x + 5)(x + 6) (c) (x + 1)(x + 10) (d) (x − 5)(x − 6)
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 1/11 (d) 7/36
39. 39.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
40. 40.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7

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