Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 382 · 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) 12 (b) 48 (c) 16 (d) 24
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
3. 3.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
4. 4.A bag has 4 white balls and 5 blue 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) 9 (c) 5 (d) 6
5. 5.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 21 (b) 23 (c) 27 (d) 22
6. 6.In a class of 33 children, 19 like cricket, 16 like football and 4 like both. How many like only cricket? (a) 17 (b) 12 (c) 15 (d) 19
7. 7.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
8. 8.What is the mean of 13, 7, 16, 18, 3 and 9? (a) 10 (b) 12 (c) 13 (d) 11
9. 9.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
11. 11.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 15 (c) 8 (d) 7
12. 12.In a class of 32 children, 16 like tea, 15 like coffee and 6 like both. How many like only tea? (a) 16 (b) 9 (c) 17 (d) 10
13. 13.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
14. 14.How many factors does 19 have? (a) 1 (b) 4 (c) 2 (d) 3
15. 15.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 115° (b) 120° (c) 55° (d) 125°
16. 16.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
17. 17.A drawer has lots of white, yellow, blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 8 (c) 5 (d) 4
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
19. 19.In a class of 40 children, 27 like cricket, 13 like football and 8 like both. How many like at least one of the two? (a) 24 (b) 32 (c) 40 (d) 33
20. 20.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
21. 21.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 18 (c) 21 (d) 54
22. 22.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 12) (b) (x + 1)(x + 40) (c) (x + 5)(x + 8) (d) (x − 5)(x − 8)
23. 23.In a class of 45 children, 26 like mangoes, 23 like bananas and 7 like both. How many like at least one of the two? (a) 49 (b) 42 (c) 35 (d) 45
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
25. 25.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 60° (d) 30°
26. 26.In a class of 44 children, 25 like mangoes, 24 like bananas and 11 like both. How many like at least one of the two? (a) 27 (b) 38 (c) 44 (d) 49
27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 7 (b) 17 (c) 18 (d) 19
28. 28.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
29. 29.What is the mean of 2, 5, 20, 3, 8 and 16? (a) 11 (b) 8 (c) 9 (d) 10
30. 30.A bag has 9 yellow, 2 blue and 5 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 5/11 (b) 1/3 (c) 11/16 (d) 5/16
31. 31.What is the midpoint of the line joining (5, 10) and (15, 0)? (a) (10, 5) (b) (20, 10) (c) (5, 10) (d) (5, 5)
32. 32.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 3/8 (c) 1/4 (d) 7/8
33. 33.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 42 (b) 43 (c) 84 (d) 9
34. 34.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 11 (d) 2
35. 35.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
36. 36.In which quadrant does the point (8, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
37. 37.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
38. 38.What is the mean of 9, 13, 13, 3, 2 and 2? (a) 7 (b) 8 (c) 9 (d) 6
39. 39.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 45° (d) 46°

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