Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 709 · 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 smallest prime factor of 65? (a) 13 (b) 5 (c) 2 (d) 1
2. 2.A bag has 4 blue, 3 yellow and 7 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 3/14 (c) 11/14 (d) 3/11
3. 3.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
4. 4.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 125° (b) 140° (c) 85° (d) 95°
5. 5.What is the 37th term of the AP 7, 13, 19, 25, …? (a) 222 (b) 216 (c) 229 (d) 223
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 1/11 (d) 5/36
7. 7.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 36 (c) 37 (d) 25
8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 7 (b) 6 (c) 4 (d) 5
9. 9.A bag has 10 black balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 12 (c) 2 (d) 22
10. 10.3 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 7 (c) 24 (d) 12
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
12. 12.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 75 (b) 78 (c) 15 (d) 150
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
14. 14.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 3/8 (d) 1/4
15. 15.What is the median of 21, 18, 6, 13, 17, 20 and 29? (a) 18 (b) 13 (c) 17 (d) 20
16. 16.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
17. 17.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 320° (d) 50°
18. 18.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 4 (d) 3
19. 19.How many factors does 41 have? (a) 2 (b) 1 (c) 4 (d) 3
20. 20.What is the 10th term of the AP 1, 4, 7, 10, …? (a) 31 (b) 28 (c) 30 (d) 27
21. 21.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 160° (b) 110° (c) 90° (d) 70°
22. 22.Which is the correct factorisation of x² + 9x + 18? (a) (x + 3)(x + 6) (b) (x + 1)(x + 18) (c) (x − 3)(x − 6) (d) (x + 1)(x + 8)
23. 23.Which term of the AP 4, 9, 14, 19, … is 189? (a) 39th (b) 37th (c) 38th (d) 40th
24. 24.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
25. 25.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 21 (c) 15 (d) 14
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
27. 27.What is the mode of 3, 15, 5, 1, 1, 5 and 1? (a) 5 (b) 1 (c) 3 (d) 15
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/18 (c) 1/11 (d) 1/36
29. 29.A drawer has lots of green, yellow, black, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 6 (c) 10 (d) 2
30. 30.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120
31. 31.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 3 (d) 4
32. 32.In which quadrant does the point (8, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
33. 33.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 7/36 (d) 1/6
35. 35.What is the midpoint of the line joining (1, 4) and (3, 12)? (a) (1, 4) (b) (8, 2) (c) (4, 16) (d) (2, 8)
36. 36.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
37. 37.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 56° (c) 125° (d) 55°
38. 38.What is the smallest prime factor of 161? (a) 7 (b) 2 (c) 23 (d) 1
39. 39.In a class of 43 children, 31 like tea, 15 like coffee and 12 like both. How many like at least one of the two? (a) 46 (b) 34 (c) 43 (d) 22
40. 40.How many factors does 70 have? (a) 9 (b) 6 (c) 7 (d) 8

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