Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 239 · 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 how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
2. 2.In a class of 25 children, 12 like tea, 11 like coffee and 4 like both. How many like at least one of the two? (a) 15 (b) 25 (c) 23 (d) 19
3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
5. 5.A cuboid is 7 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 42 cu cm (b) 21 cu cm (c) 12 cu cm (d) 82 cu cm
6. 6.A bag has 10 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 11 (c) 12 (d) 15
7. 7.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 30° (c) 150° (d) 15°
8. 8.What is the midpoint of the line joining (10, 9) and (20, 1)? (a) (30, 10) (b) (5, 4) (c) (5, 15) (d) (15, 5)
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
10. 10.If a + b = 15 and ab = 54, what is (a − b)²? (a) 225 (b) 9 (c) 117 (d) 3
11. 11.What is the mode of 12, 2, 12, 15, 12, 5 and 2? (a) 12 (b) 5 (c) 2 (d) 15
12. 12.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/8 (c) 1/4 (d) 1/7
13. 13.How many factors does 87 have? (a) 5 (b) 2 (c) 4 (d) 3
14. 14.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2⁴ × 7 (c) 2 × 7⁴ (d) 2³ × 7
15. 15.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 10 (d) 15
16. 16.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 3/8 (d) 1/4
17. 17.If a + b = 15 and ab = 50, what is a² + b²? (a) 175 (b) 225 (c) 325 (d) 125
18. 18.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2² × 3⁴ (c) 2⁵ × 3² (d) 2³ × 3²
19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
20. 20.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 10° (b) 85° (c) 105° (d) 170°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 100° (c) 130° (d) 50°
22. 22.What is the product of the roots of x² − 11x + 18 = 0? (a) 19 (b) 11 (c) 18 (d) 17
23. 23.What is the 16th term of the AP 18, 23, 28, 33, …? (a) 93 (b) 80 (c) 98 (d) 75
24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
25. 25.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/8 (c) 7/8 (d) 1/4
26. 26.In a class of 28 children, 14 like mangoes, 19 like bananas and 6 like both. How many like neither? (a) 1 (b) 7 (c) 6 (d) 2
27. 27.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 60° (c) 330° (d) 30°
28. 28.In a class of 42 children, 28 like dance, 18 like music and 10 like both. How many like only dance? (a) 18 (b) 24 (c) 8 (d) 28
29. 29.What is the midpoint of the line joining (3, 19) and (15, 9)? (a) (14, 9) (b) (6, 5) (c) (9, 14) (d) (18, 28)
30. 30.In a class of 37 children, 11 like tea, 21 like coffee and 3 like both. How many like at least one of the two? (a) 26 (b) 32 (c) 37 (d) 29
31. 31.There are 5 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) 20 (b) 15 (c) 10 (d) 7
32. 32.In a class of 36 children, 12 like dance, 24 like music and 6 like both. How many like neither? (a) 0 (b) 6 (c) 12 (d) 7
33. 33.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 41 (b) 376 (c) 208 (d) 188
34. 34.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 217 sq cm (d) 144 sq cm
35. 35.In a class of 32 children, 20 like cricket, 7 like football and 4 like both. How many like only cricket? (a) 20 (b) 16 (c) 25 (d) 3
36. 36.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 7) (b) (x + 1)(x + 15) (c) (x + 3)(x + 5) (d) (x − 3)(x − 5)
37. 37.In a class of 49 children, 25 like cricket, 29 like football and 11 like both. How many like at least one of the two? (a) 43 (b) 32 (c) 49 (d) 54
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 4 (d) 2
39. 39.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 576 (d) 456
40. 40.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 40° (c) 155° (d) 15°

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