Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 838 · 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 times is the digit 5 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 2 (d) 4
2. 2.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 42 (d) 49
3. 3.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
4. 4.What is the median of 18, 37, 25, 32, 12, 20 and 22? (a) 22 (b) 25 (c) 32 (d) 20
5. 5.What is the distance between the points (2, 9) and (17, 17)? (a) 18 (b) 23 (c) 17 (d) 289
6. 6.What are the roots of x² − 13x + 42 = 0? (a) 2 and 21 (b) 1 and 12 (c) 6 and 7 (d) 1 and 42
7. 7.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2⁴ × 5 (c) 2² × 5 (d) 2³ × 5
8. 8.In a class of 45 children, 27 like maths, 25 like science and 11 like both. How many like neither? (a) 4 (b) 11 (c) 15 (d) 5
9. 9.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/4
10. 10.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
11. 11.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 841 (b) 961 (c) 971 (d) 901
12. 12.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 145° (b) 105° (c) 75° (d) 140°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 140° (d) 80°
14. 14.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) 49 (c) 48 (d) 37
15. 15.If a + b = 16 and ab = 48, what is (a − b)²? (a) 64 (b) 8 (c) 160 (d) 256
16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 7 (b) 14 (c) 15 (d) 12
17. 17.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
18. 18.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3² × 5 (c) 3 × 5 (d) 3 × 5²
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 9 (d) 18
20. 20.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 70° (b) 25° (c) 155° (d) 135°
21. 21.A drawer has lots of green, black, red, yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 10 (c) 5 (d) 2
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 1/11 (c) 7/36 (d) 6/11
23. 23.A bag has 8 black balls and 5 yellow 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) 9 (c) 6 (d) 13
24. 24.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 50° (b) 230° (c) 100° (d) 130°
25. 25.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 21 (c) 19 (d) 18
26. 26.In a class of 28 children, 16 like maths, 11 like science and 5 like neither. How many like both? (a) 5 (b) 4 (c) 3 (d) 23
27. 27.What is the smallest prime factor of 121? (a) 2 (b) 3 (c) 11 (d) 1
28. 28.In a class of 39 children, 24 like mangoes, 21 like bananas and 10 like both. How many like at least one of the two? (a) 35 (b) 39 (c) 45 (d) 25
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
30. 30.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
32. 32.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 15 (c) 30 (d) 18
33. 33.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
34. 34.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
35. 35.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 28 (d) 10
36. 36.How many factors does 36 have? (a) 10 (b) 8 (c) 9 (d) 7
37. 37.What is the distance between the points (0, 7) and (3, 3)? (a) 25 (b) 7 (c) 5 (d) 6
38. 38.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
39. 39.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
40. 40.What is the mode of 5, 18, 18, 5, 9, 13 and 18? (a) 9 (b) 5 (c) 18 (d) 13

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