Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 973 · 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 missing term in the AP 18, 22, 26, ?, 34? (a) 30 (b) 31 (c) 29 (d) 34
2. 2.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
3. 3.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 23 (b) 21 (c) 22 (d) 25
4. 4.Which is the correct factorisation of x² + 12x + 27? (a) (x − 3)(x − 9) (b) (x + 3)(x + 9) (c) (x + 1)(x + 11) (d) (x + 1)(x + 27)
5. 5.If a + b = 11 and ab = 30, what is a² + b²? (a) 61 (b) 91 (c) 121 (d) 181
6. 6.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 63 (c) 64 (d) 72
7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
8. 8.3 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 30 (c) 8 (d) 15
9. 9.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/4 (d) 1/8
10. 10.The mean of 8 numbers is 12. When the number 3 is added to them, what is the new mean? (a) 10 (b) 13 (c) 11 (d) 12
11. 11.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2² × 5 × 7
12. 12.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 60 sq cm (b) 56 sq cm (c) 224 sq cm (d) 112 sq cm
13. 13.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 5° (c) 95° (d) 85°
14. 14.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
15. 15.A bag has 12 green balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 18 (b) 2 (c) 13 (d) 14
16. 16.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the product of the roots of x² − 13x + 36 = 0? (a) 37 (b) 13 (c) 36 (d) 35
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
19. 19.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 65° (d) 50°
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/11 (d) 1/12
21. 21.In which quadrant does the point (5, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
22. 22.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 24) (b) (x − 4)(x − 6) (c) (x + 1)(x + 9) (d) (x + 4)(x + 6)
23. 23.The mean of 4 numbers is 15. When the number 20 is added to them, what is the new mean? (a) 18 (b) 17 (c) 15 (d) 16
24. 24.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 105° (b) 95° (c) 160° (d) 75°
25. 25.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
26. 26.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
27. 27.A bag has 12 white balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 14 (c) 13 (d) 16
28. 28.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
29. 29.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
30. 30.What is the distance between the points (0, 9) and (6, 1)? (a) 14 (b) 10 (c) 11 (d) 100
31. 31.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 78 (d) 169
32. 32.If a + b = 19 and ab = 88, what is (a − b)²? (a) 3 (b) 185 (c) 9 (d) 361
33. 33.What is the missing term in the AP 7, 12, 17, ?, 27? (a) 27 (b) 21 (c) 23 (d) 22
34. 34.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
35. 35.How many factors does 79 have? (a) 3 (b) 4 (c) 1 (d) 2
36. 36.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 30° (b) 80° (c) 130° (d) 150°
37. 37.A bag has 7 blue balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 8 (b) 10 (c) 2 (d) 9
38. 38.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 91 (d) 169
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 1/6 (c) 5/11 (d) 5/36
40. 40.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2

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