Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 391 · 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.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 65° (d) 115°
2. 2.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
3. 3.Using (a − b)² = a² − 2ab + b², what is 88²? (a) 8096 (b) 7754 (c) 8464 (d) 7744
4. 4.Which term of the AP 5, 14, 23, 32, … is 239? (a) 26th (b) 28th (c) 27th (d) 29th
5. 5.What is the midpoint of the line joining (8, 5) and (14, 11)? (a) (8, 11) (b) (22, 16) (c) (11, 8) (d) (3, 3)
6. 6.What is the median of 22, 37, 16, 40 and 20? (a) 27 (b) 16 (c) 22 (d) 37
7. 7.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 156 (d) 78
8. 8.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 10 (c) 15 (d) 25
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/12 (d) 1/9
10. 10.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7² (c) 2 × 5 × 7 (d) 2³ × 5 × 7
11. 11.Which term of the AP 12, 14, 16, 18, … is 28? (a) 9th (b) 8th (c) 10th (d) 14th
12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 15 (c) 17 (d) 16
13. 13.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 18 (c) 24 (d) 36
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 15 (b) 14 (c) 3 (d) 13
16. 16.A bag has 5 green, 2 white and 7 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/14 (b) 5/9 (c) 5/14 (d) 1/3
17. 17.Using (a + b)² = a² + 2ab + b², what is 64²? (a) 4096 (b) 3616 (c) 4106 (d) 3136
18. 18.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 15 (c) 36 (d) 30
19. 19.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 80° (c) 55° (d) 125°
20. 20.A bag has 3 white, 5 red and 5 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 8/13 (c) 5/13 (d) 9/13
21. 21.If a + b = 12 and ab = 27, what is (a − b)²? (a) 6 (b) 36 (c) 90 (d) 144
22. 22.A bag has 6 green balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 7 (d) 16
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
24. 24.Which is the correct factorisation of x² + 11x + 24? (a) (x − 3)(x − 8) (b) (x + 1)(x + 10) (c) (x + 1)(x + 24) (d) (x + 3)(x + 8)
25. 25.What is the mean of 11, 6, 15, 11, 3 and 20? (a) 10 (b) 11 (c) 12 (d) 13
26. 26.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 85° (b) 120° (c) 145° (d) 95°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 70° (c) 145° (d) 36°
28. 28.The mean of 6 numbers is 28. When the number 7 is added to them, what is the new mean? (a) 24 (b) 25 (c) 26 (d) 28
29. 29.What is the smallest prime factor of 69? (a) 1 (b) 3 (c) 23 (d) 2
30. 30.What is the midpoint of the line joining (8, 6) and (18, 4)? (a) (13, 5) (b) (5, 13) (c) (5, 1) (d) (26, 10)
31. 31.The mean of 5 numbers is 26. When the number 14 is added to them, what is the new mean? (a) 26 (b) 24 (c) 20 (d) 25
32. 32.A bag has 7 black balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 11 (c) 8 (d) 2
33. 33.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
34. 34.In a class of 39 children, 26 like maths, 19 like science and 10 like both. How many like only maths? (a) 26 (b) 9 (c) 16 (d) 20
35. 35.What is the prime factorisation of 560? (a) 2⁵ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2³ × 5 × 7 (d) 2⁴ × 5 × 7
36. 36.In a class of 34 children, 18 like mangoes, 17 like bananas and 4 like neither. How many like both? (a) 30 (b) 1 (c) 4 (d) 5
37. 37.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
38. 38.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
39. 39.In a class of 44 children, 25 like cricket, 21 like football and 11 like both. How many like at least one of the two? (a) 46 (b) 44 (c) 24 (d) 35
40. 40.In a class of 35 children, 15 like mangoes, 14 like bananas and 4 like both. How many like neither? (a) 10 (b) 6 (c) 4 (d) 14

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