Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 211 · 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 32nd term of the AP 14, 23, 32, 41, …? (a) 302 (b) 293 (c) 279 (d) 288
2. 2.A bag has 7 black balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 2 (c) 8 (d) 10
3. 3.In a class of 34 children, 18 like maths, 19 like science and 5 like both. How many like neither? (a) 3 (b) 5 (c) 7 (d) 2
4. 4.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 631 (d) 595
5. 5.What is the median of 40, 29, 35, 34 and 31? (a) 35 (b) 31 (c) 33 (d) 34
6. 6.In a class of 35 children, 25 like cricket, 17 like football and 12 like both. How many like only cricket? (a) 18 (b) 5 (c) 13 (d) 25
7. 7.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 726 sq cm
8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 24 (c) 48 (d) 16
9. 9.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 45° (d) 120°
10. 10.How many prime numbers are there between 20 and 30? (a) 4 (b) 1 (c) 2 (d) 3
11. 11.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 70° (c) 160° (d) 340°
12. 12.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7³
13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
14. 14.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 17 (c) 57 (d) 66
15. 15.In a class of 20 children, 9 like dance, 14 like music and 4 like both. How many like at least one of the two? (a) 15 (b) 19 (c) 20 (d) 23
16. 16.In a class of 29 children, 8 like cricket, 21 like football and 4 like both. How many like neither? (a) 5 (b) 0 (c) 8 (d) 4
17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
18. 18.If a + b = 15 and ab = 56, what is (a − b)²? (a) 113 (b) 1 (c) 169 (d) 225
19. 19.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 12 (c) 25 (d) 13
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
21. 21.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 600 cu cm
22. 22.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 12 (c) 10 (d) 11
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/36 (d) 5/11
24. 24.What is the 25th term of the AP 15, 19, 23, 27, …? (a) 115 (b) 100 (c) 96 (d) 111
25. 25.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 125° (d) 35°
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
27. 27.In a class of 33 children, 14 like maths, 23 like science and 9 like both. How many like neither? (a) 5 (b) 6 (c) 14 (d) 9
28. 28.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
29. 29.6 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) 12 (b) 24 (c) 8 (d) 18
30. 30.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
31. 31.What is the midpoint of the line joining (2, 6) and (10, 8)? (a) (7, 6) (b) (6, 7) (c) (4, 1) (d) (12, 14)
32. 32.What is the mode of 13, 17, 6, 6, 3, 3 and 3? (a) 13 (b) 3 (c) 6 (d) 17
33. 33.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 325 (c) 351 (d) 338
34. 34.In which quadrant does the point (8, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
36. 36.A bag has 4 yellow balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 5 (c) 6 (d) 10
37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
38. 38.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 70° (c) 140° (d) 71°
39. 39.A bag has 4 blue balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 5 (b) 2 (c) 7 (d) 6
40. 40.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm

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