Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 479 · 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 prime factorisation of 72? (a) 2² × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2⁴ × 3²
2. 2.What is the mode of 17, 17, 10, 2, 20, 2 and 2? (a) 2 (b) 17 (c) 10 (d) 20
3. 3.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 125 cu cm (d) 100 cu cm
4. 4.What is the mean of 6, 11, 6, 10 and 17? (a) 12 (b) 11 (c) 10 (d) 9
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
6. 6.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 12) (b) (x + 4)(x + 9) (c) (x + 1)(x + 36) (d) (x − 4)(x − 9)
7. 7.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 40° (b) 170° (c) 150° (d) 10°
8. 8.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/8 (c) 3/8 (d) 1/4
9. 9.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 375 (b) 225 (c) 625 (d) 235
10. 10.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°
11. 11.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 31 (b) 24 (c) 25 (d) 26
12. 12.Using (a − b)² = a² − 2ab + b², what is 17²? (a) 391 (b) 529 (c) 299 (d) 289
13. 13.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 225 (d) 120
14. 14.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 3 (d) 4
15. 15.In a class of 33 children, 20 like dance, 18 like music and 8 like both. How many like only dance? (a) 15 (b) 12 (c) 20 (d) 10
16. 16.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 2016 (c) 1953 (d) 4032
17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12
18. 18.What is the median of 38, 27, 33, 18, 11, 6 and 19? (a) 27 (b) 19 (c) 18 (d) 20
19. 19.If a + b = 11 and ab = 28, what is (a − b)²? (a) 65 (b) 121 (c) 3 (d) 9
20. 20.How many prime numbers are there between 40 and 70? (a) 9 (b) 6 (c) 8 (d) 7
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/18 (d) 1/12
22. 22.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 50° (c) 110° (d) 130°
23. 23.What is the mode of 7, 17, 7, 13, 17, 7 and 19? (a) 17 (b) 7 (c) 13 (d) 19
24. 24.How many factors does 119 have? (a) 5 (b) 4 (c) 3 (d) 2
25. 25.What is the mode of 15, 20, 20, 2, 20, 2 and 7? (a) 2 (b) 7 (c) 15 (d) 20
26. 26.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 320° (d) 20°
27. 27.How many factors does 67 have? (a) 1 (b) 3 (c) 2 (d) 4
28. 28.How many factors does 76 have? (a) 4 (b) 5 (c) 6 (d) 7
29. 29.The mean of 3 numbers is 24. When the number 16 is added to them, what is the new mean? (a) 24 (b) 22 (c) 20 (d) 23
30. 30.What is the mean of 4, 13, 13 and 14? (a) 12 (b) 11 (c) 10 (d) 13
31. 31.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
32. 32.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
33. 33.In which quadrant does the point (−2, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
34. 34.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
35. 35.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 110° (b) 160° (c) 90° (d) 270°
36. 36.A bag has 12 black balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 20 (b) 2 (c) 13 (d) 14
37. 37.A bag has 8 red, 6 white and 2 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/5 (b) 5/8 (c) 1/3 (d) 3/8
38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
39. 39.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
40. 40.In a class of 25 children, 8 like mangoes, 15 like bananas and 4 like both. How many like only mangoes? (a) 8 (b) 11 (c) 4 (d) 10

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