Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 145 · 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 median of 39, 38, 33, 36, 10, 37 and 16? (a) 35 (b) 33 (c) 36 (d) 37
2. 2.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1653 (d) 1711
3. 3.A bag has 3 blue, 4 green and 7 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 6/7 (c) 11/14 (d) 3/14
4. 4.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 41 (b) 48 (c) 39 (d) 40
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
6. 6.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
7. 7.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 12 (d) 24
8. 8.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 135° (b) 150° (c) 75° (d) 45°
9. 9.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
10. 10.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 55 (c) 90 (d) 100
11. 11.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 12 (c) 15 (d) 24
12. 12.What is the mean of 10, 9, 7, 15 and 9? (a) 9 (b) 11 (c) 12 (d) 10
13. 13.What is the mean of 9, 2, 18, 7 and 9? (a) 10 (b) 11 (c) 8 (d) 9
14. 14.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 280° (c) 100° (d) 10°
15. 15.How many factors does 119 have? (a) 3 (b) 5 (c) 4 (d) 2
16. 16.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 105° (d) 130°
17. 17.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 57 (d) 171
18. 18.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 196 (d) 182
19. 19.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 35° (c) 55° (d) 125°
20. 20.4 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 10 (c) 28 (d) 24
21. 21.A drawer has lots of red, yellow 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) 2 (b) 3 (c) 6 (d) 4
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 5/36 (c) 1/9 (d) 1/11
23. 23.In a class of 27 children, 12 like cricket, 17 like football and 4 like neither. How many like both? (a) 23 (b) 4 (c) 2 (d) 6
24. 24.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
25. 25.A bag has 9 white, 3 blue and 5 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/17 (b) 13/17 (c) 12/17 (d) 1/3
26. 26.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 20 (c) 8 (d) 16
27. 27.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 282 (c) 316 (d) 306
28. 28.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 35° (b) 215° (c) 145° (d) 70°
29. 29.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
30. 30.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 37 (b) 43 (c) 36 (d) 35
31. 31.What is the median of 22, 12, 21, 2, 13, 4 and 39? (a) 2 (b) 12 (c) 13 (d) 21
32. 32.If a + b = 12 and ab = 35, what is (a − b)²? (a) 2 (b) 74 (c) 4 (d) 144
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 19 (d) 9
34. 34.A bag has 10 blue balls and 5 yellow 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) 15 (c) 6 (d) 11
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 7/36 (c) 1/11 (d) 6/11
36. 36.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
37. 37.What is the prime factorisation of 35? (a) 5 × 7² (b) 5² × 7 (c) 5³ × 7 (d) 5 × 7
38. 38.What is the distance between the points (9, 17) and (18, 5)? (a) 21 (b) 15 (c) 16 (d) 225
39. 39.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 32 (b) 27 (c) 28 (d) 26
40. 40.A cuboid is 8 cm long, 7 cm wide and 5 cm high. What is its volume? (a) 280 cu cm (b) 262 cu cm (c) 56 cu cm (d) 20 cu cm

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