Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 379 · 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.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 80° (d) 145°
2. 2.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 15 (d) 30
3. 3.How many factors does 61 have? (a) 3 (b) 4 (c) 1 (d) 2
4. 4.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
6. 6.What is the 31st term of the AP 2, 9, 16, 23, …? (a) 212 (b) 217 (c) 210 (d) 219
7. 7.If a + b = 12 and ab = 32, what is (a − b)²? (a) 16 (b) 80 (c) 4 (d) 144
8. 8.In a class of 30 children, 16 like maths, 7 like science and 2 like both. How many like neither? (a) 11 (b) 2 (c) 7 (d) 9
9. 9.What is the missing term in the AP 10, 12, 14, ?, 18? (a) 17 (b) 18 (c) 15 (d) 16
10. 10.The mean of 4 numbers is 18. When the number 3 is added to them, what is the new mean? (a) 16 (b) 15 (c) 18 (d) 14
11. 11.What is the median of 2, 18, 33, 7 and 40? (a) 33 (b) 7 (c) 18 (d) 20
12. 12.What is the 14th term of the AP 12, 21, 30, 39, …? (a) 138 (b) 117 (c) 126 (d) 129
13. 13.In a class of 26 children, 15 like cricket, 13 like football and 3 like both. How many like at least one of the two? (a) 26 (b) 28 (c) 22 (d) 25
14. 14.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 91° (d) 135°
15. 15.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 576 (b) 266 (c) 384 (d) 256
16. 16.A bag has 8 blue balls and 9 white 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) 17 (c) 9 (d) 10
17. 17.In a class of 48 children, 24 like tea, 23 like coffee and 6 like both. How many like only tea? (a) 25 (b) 17 (c) 18 (d) 24
18. 18.What is the mean of 5, 5, 5, 16 and 9? (a) 9 (b) 7 (c) 10 (d) 8
19. 19.In a class of 14 children, 8 like cricket, 6 like football and 2 like both. How many like only cricket? (a) 2 (b) 4 (c) 8 (d) 6
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 1/6 (d) 7/36
21. 21.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
22. 22.A bag has 5 black balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 2 (c) 9 (d) 7
23. 23.3 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 18 (c) 30 (d) 8
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/12 (c) 3/11 (d) 1/11
25. 25.The mean of 5 numbers is 23. When the number 5 is added to them, what is the new mean? (a) 21 (b) 14 (c) 23 (d) 20
26. 26.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 28 (c) 11 (d) 35
27. 27.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5 (c) 3³ × 5 (d) 3 × 5²
28. 28.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 156 (c) 91 (d) 169
29. 29.In a class of 24 children, 12 like maths, 12 like science and 6 like both. How many like only maths? (a) 7 (b) 5 (c) 12 (d) 6
30. 30.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 86° (d) 95°
31. 31.A cuboid is 10 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 560 sq cm (b) 200 sq cm (c) 140 sq cm (d) 280 sq cm
32. 32.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
33. 33.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
34. 34.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 120° (d) 65°
35. 35.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 124 sq cm (b) 240 sq cm (c) 496 sq cm (d) 248 sq cm
36. 36.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 3 (d) 2
37. 37.In a class of 26 children, 19 like mangoes, 17 like bananas and 12 like both. How many like neither? (a) 14 (b) 12 (c) 3 (d) 2
38. 38.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 50° (b) 115° (c) 230° (d) 130°
39. 39.What is the 22nd term of the AP 18, 24, 30, 36, …? (a) 126 (b) 144 (c) 150 (d) 132
40. 40.How many prime numbers are there between 10 and 30? (a) 6 (b) 5 (c) 8 (d) 7

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