Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 995 · 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. 1.7 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) 35 (b) 11 (c) 28 (d) 56
2. 2.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
3. 3.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 160° (d) 20°
4. 4.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 478 (c) 609 (d) 600
5. 5.A drawer has lots of red 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) 3 (b) 2 (c) 4 (d) 5
6. 6.A bag has 12 white balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 24 (b) 2 (c) 14 (d) 13
7. 7.Which term of the AP 13, 15, 17, 19, … is 45? (a) 18th (b) 17th (c) 16th (d) 19th
8. 8.What is the 20th term of the AP 6, 8, 10, 12, …? (a) 44 (b) 38 (c) 46 (d) 40
9. 9.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 115° (d) 65°
10. 10.A bag has 8 red balls and 3 green 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) 11 (c) 4 (d) 9
11. 11.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 140° (c) 75° (d) 105°
12. 12.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 2 and 36 (c) 1 and 72 (d) 1 and 16
13. 13.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 21 (b) 192 (c) 186 (d) 372
14. 14.What is the midpoint of the line joining (0, 6) and (2, 18)? (a) (2, 24) (b) (1, 6) (c) (1, 12) (d) (12, 1)
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
16. 16.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 80° (d) 100°
17. 17.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
18. 18.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 85° (c) 150° (d) 95°
19. 19.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 240 (d) 25
20. 20.In a class of 42 children, 16 like dance, 27 like music and 10 like both. How many like at least one of the two? (a) 33 (b) 42 (c) 23 (d) 43
21. 21.What is the smallest prime factor of 299? (a) 1 (b) 2 (c) 23 (d) 13
22. 22.In a class of 24 children, 12 like maths, 18 like science and 7 like both. How many like only maths? (a) 5 (b) 12 (c) 11 (d) 6
23. 23.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 30 (b) 22 (c) 23 (d) 21
24. 24.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
25. 25.What is the 23rd term of the AP 18, 24, 30, 36, …? (a) 132 (b) 156 (c) 138 (d) 150
26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 4 (d) 5
27. 27.What is the midpoint of the line joining (9, 9) and (15, 17)? (a) (13, 12) (b) (12, 13) (c) (3, 4) (d) (24, 26)
28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
29. 29.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
30. 30.What is the midpoint of the line joining (3, 2) and (5, 6)? (a) (1, 2) (b) (8, 8) (c) (4, 4) (d) (5, 4)
31. 31.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 220° (c) 110° (d) 40°
32. 32.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) 6 times (c) 9 times (d) 27 times
33. 33.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 160° (b) 150° (c) 50° (d) 30°
34. 34.What is the distance between the points (1, 6) and (13, 15)? (a) 21 (b) 16 (c) 225 (d) 15
35. 35.A bag has 8 yellow balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 9 (c) 2 (d) 15
36. 36.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2⁵ × 3
37. 37.What is the median of 34, 2, 18, 25, 19, 27 and 33? (a) 25 (b) 26 (c) 19 (d) 27
38. 38.A bag has 7 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 8 (c) 16 (d) 9
39. 39.What is the smallest prime factor of 403? (a) 1 (b) 13 (c) 31 (d) 2
40. 40.A bag has 3 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 4 (c) 7 (d) 5

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