Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 763 · 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.If a + b = 15 and ab = 54, what is a² + b²? (a) 333 (b) 117 (c) 225 (d) 171
2. 2.A bag has 7 green balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 15 (b) 8 (c) 9 (d) 2
3. 3.A bag has 6 black balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 7 (c) 2 (d) 13
4. 4.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 120°
5. 5.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
6. 6.If a + b = 7 and ab = 10, what is (a − b)²? (a) 9 (b) 3 (c) 29 (d) 49
7. 7.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
8. 8.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 65° (c) 115° (d) 160°
9. 9.In a class of 27 children, 13 like maths, 13 like science and 7 like both. How many like neither? (a) 8 (b) 7 (c) 15 (d) 1
10. 10.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 5/6 (b) 2/3 (c) 1/4 (d) 1/3
11. 11.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
12. 12.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 26 (b) 18 (c) 20 (d) 19
13. 13.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 42 (b) 38 (c) 41 (d) 40
14. 14.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
15. 15.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 35° (d) 45°
16. 16.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 25 (b) 26 (c) 34 (d) 24
17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
18. 18.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 136° (c) 315° (d) 45°
19. 19.The mean of 4 numbers is 17. When the number 12 is added to them, what is the new mean? (a) 16 (b) 15 (c) 18 (d) 17
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
21. 21.What is the mode of 17, 10, 17, 10, 14, 11 and 10? (a) 17 (b) 10 (c) 14 (d) 11
22. 22.What is the 36th term of the AP 1, 4, 7, 10, …? (a) 108 (b) 106 (c) 109 (d) 105
23. 23.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
24. 24.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 72 (c) 36 (d) 42
25. 25.The mean of 6 numbers is 13. When the number 41 is added to them, what is the new mean? (a) 18 (b) 17 (c) 13 (d) 27
26. 26.In a class of 59 children, 31 like mangoes, 30 like bananas and 12 like both. How many like at least one of the two? (a) 61 (b) 37 (c) 59 (d) 49
27. 27.What is the median of 28, 36, 1, 12, 17, 25 and 8? (a) 17 (b) 18 (c) 12 (d) 25
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 5 (b) 6 (c) 8 (d) 7
29. 29.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 49 (d) 14
30. 30.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 8 (b) 36 (c) 35 (d) 70
31. 31.There are 8 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 16 (c) 24 (d) 32
32. 32.In a class of 36 children, 12 like tea, 21 like coffee and 6 like neither. How many like both? (a) 6 (b) 3 (c) 30 (d) 4
33. 33.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5³
34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
35. 35.Using (a + b)² = a² + 2ab + b², what is 73²? (a) 4489 (b) 5339 (c) 4909 (d) 5329
36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 6 (b) 5 (c) 7 (d) 4
37. 37.A bag has 3 white, 8 yellow and 6 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 12/17 (c) 6/17 (d) 11/17
38. 38.What is the 35th term of the AP 10, 15, 20, 25, …? (a) 185 (b) 170 (c) 175 (d) 180
39. 39.In a class of 34 children, 28 like tea, 12 like coffee and 9 like both. How many like at least one of the two? (a) 40 (b) 31 (c) 22 (d) 34
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 6 (b) 5 (c) 3 (d) 4

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