Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 521 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
2. 2.What is the 16th term of the AP 12, 15, 18, 21, …? (a) 57 (b) 45 (c) 48 (d) 60
3. 3.A bag has 5 red, 2 blue and 2 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 7/9 (c) 2/7 (d) 2/9
4. 4.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 144 (c) 154 (d) 153
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
6. 6.In a class of 32 children, 12 like tea, 25 like coffee and 7 like both. How many like neither? (a) 9 (b) 3 (c) 2 (d) 7
7. 7.How many factors does 33 have? (a) 5 (b) 3 (c) 4 (d) 2
8. 8.How many factors does 89 have? (a) 4 (b) 1 (c) 3 (d) 2
9. 9.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 15 (d) 45
10. 10.How many factors does 73 have? (a) 2 (b) 1 (c) 3 (d) 4
11. 11.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 96 (b) 22 (c) 174 (d) 87
12. 12.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 110° (b) 130° (c) 120° (d) 60°
13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 57 (d) 870
14. 14.What is the 28th term of the AP 7, 15, 23, 31, …? (a) 216 (b) 231 (c) 224 (d) 223
15. 15.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
17. 17.What is the mean of 4, 11, 5, 5, 14 and 15? (a) 9 (b) 8 (c) 11 (d) 10
18. 18.How many prime numbers are there between 60 and 70? (a) 3 (b) 1 (c) 2 (d) 4
19. 19.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/3 (b) 5/6 (c) 1/5 (d) 1/6
20. 20.How many factors does 71 have? (a) 3 (b) 1 (c) 4 (d) 2
21. 21.What is the distance between the points (9, 5) and (16, 29)? (a) 26 (b) 625 (c) 31 (d) 25
22. 22.If a + b = 14 and ab = 45, what is (a − b)²? (a) 16 (b) 196 (c) 106 (d) 4
23. 23.In a class of 23 children, 17 like cricket, 15 like football and 11 like both. How many like at least one of the two? (a) 32 (b) 23 (c) 10 (d) 21
24. 24.A bag has 3 yellow, 6 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 9/11 (b) 2/11 (c) 1/3 (d) 2/9
25. 25.A bag has 5 blue balls and 6 black 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) 7 (c) 6 (d) 11
26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
27. 27.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
28. 28.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 11 cu cm (b) 20 cu cm (c) 40 cu cm (d) 76 cu cm
29. 29.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 16 (c) 12 (d) 24
30. 30.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
31. 31.A bag has 6 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 17 (b) 8 (c) 2 (d) 7
32. 32.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x − 5)(x − 6) (c) (x + 5)(x + 6) (d) (x + 1)(x + 10)
33. 33.In which quadrant does the point (7, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
34. 34.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 100° (d) 80°
35. 35.A bag has 8 yellow balls and 9 red 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) 17 (d) 10
36. 36.A bag has 11 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 14 (b) 12 (c) 2 (d) 13
37. 37.A bag has 5 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 16 (c) 6 (d) 2
38. 38.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 115° (d) 85°
39. 39.In a class of 23 children, 12 like cricket, 17 like football and 2 like neither. How many like both? (a) 8 (b) 2 (c) 21 (d) 6
40. 40.What is the mode of 2, 8, 2, 12, 13, 13 and 2? (a) 2 (b) 8 (c) 13 (d) 12

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