Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 35 · 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.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
2. 2.In a class of 36 children, 11 like cricket, 18 like football and 3 like both. How many like at least one of the two? (a) 36 (b) 29 (c) 23 (d) 26
3. 3.A bag has 9 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 12 (c) 2 (d) 20
4. 4.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
7. 7.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 130° (d) 35°
8. 8.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 36° (c) 35° (d) 215°
9. 9.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 50° (d) 25°
10. 10.How many factors does 53 have? (a) 4 (b) 1 (c) 3 (d) 2
11. 11.What is the median of 27, 29, 35, 18, 36, 31 and 25? (a) 31 (b) 18 (c) 27 (d) 29
12. 12.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 7 (c) 15 (d) 12
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
14. 14.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 53 (d) 62
15. 15.In a class of 57 children, 28 like mangoes, 31 like bananas and 12 like both. How many like at least one of the two? (a) 59 (b) 57 (c) 47 (d) 35
16. 16.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
17. 17.A bag has 5 white balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 7 (c) 11 (d) 2
18. 18.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 11 (b) 9 (c) 8 (d) 10
19. 19.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/8 (d) 3/4
20. 20.What is the midpoint of the line joining (1, 15) and (9, 7)? (a) (10, 22) (b) (5, 11) (c) (11, 5) (d) (4, 4)
21. 21.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
22. 22.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 130° (d) 50°
23. 23.Which term of the AP 4, 11, 18, 25, … is 242? (a) 37th (b) 35th (c) 34th (d) 36th
24. 24.What is the midpoint of the line joining (10, 12) and (18, 6)? (a) (9, 14) (b) (4, 3) (c) (28, 18) (d) (14, 9)
25. 25.In a class of 51 children, 28 like mangoes, 24 like bananas and 8 like neither. How many like both? (a) 9 (b) 8 (c) 1 (d) 43
26. 26.What is the mean of 19, 5, 6 and 6? (a) 10 (b) 12 (c) 9 (d) 8
27. 27.In a class of 37 children, 16 like cricket, 25 like football and 7 like both. How many like at least one of the two? (a) 27 (b) 34 (c) 41 (d) 37
28. 28.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 8281 (b) 7931 (c) 8099 (d) 7921
29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 6 (b) 18 (c) 17 (d) 16
30. 30.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 33 sq cm (b) 132 sq cm (c) 36 sq cm (d) 66 sq cm
31. 31.In a class of 25 children, 14 like cricket, 10 like football and 3 like both. How many like only cricket? (a) 11 (b) 7 (c) 14 (d) 15
32. 32.What is the smallest prime factor of 145? (a) 29 (b) 2 (c) 5 (d) 1
33. 33.What is the 38th term of the AP 14, 18, 22, 26, …? (a) 152 (b) 166 (c) 162 (d) 148
34. 34.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 38 (b) 39 (c) 37 (d) 46
35. 35.What is the mode of 20, 2, 20, 2, 20, 13 and 17? (a) 20 (b) 17 (c) 13 (d) 2
36. 36.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 13 (c) 24 (d) 25
37. 37.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x + 1)(x + 42) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
38. 38.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 21 (d) 42
39. 39.A bag has 5 white, 4 red and 5 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 9/14 (b) 5/14 (c) 1/3 (d) 5/7
40. 40.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x + 1)(x + 63) (c) (x + 7)(x + 9) (d) (x − 7)(x − 9)

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