Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 253 · 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 a class of 26 children, 15 like cricket, 18 like football and 1 like neither. How many like both? (a) 1 (b) 8 (c) 7 (d) 25
2. 2.How many factors does 65 have? (a) 2 (b) 3 (c) 5 (d) 4
3. 3.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 12 (c) 6 (d) 18
4. 4.A drawer has lots of white and green 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) 4 (c) 5 (d) 3
5. 5.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
6. 6.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 91 (d) 196
7. 7.If a + b = 10 and ab = 16, what is (a − b)²? (a) 36 (b) 100 (c) 68 (d) 6
8. 8.In a class of 37 children, 15 like maths, 26 like science and 6 like both. How many like only maths? (a) 9 (b) 11 (c) 20 (d) 15
9. 9.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 36 (d) 64
10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 4/11 (c) 1/11 (d) 1/9
13. 13.A bag has 12 green balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 13 (c) 2 (d) 18
14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
15. 15.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 8 (c) 6 (d) 12
16. 16.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
17. 17.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 43 (b) 408 (c) 224 (d) 204
18. 18.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 38 (c) 164 (d) 184
19. 19.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 14 (c) 15 (d) 21
20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 36 (d) 25
21. 21.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 90° (b) 50° (c) 140° (d) 130°
22. 22.In a class of 39 children, 14 like dance, 27 like music and 10 like both. How many like at least one of the two? (a) 21 (b) 31 (c) 39 (d) 41
23. 23.What is the mode of 5, 10, 5, 5, 13, 3 and 13? (a) 10 (b) 5 (c) 3 (d) 13
24. 24.How many factors does 75 have? (a) 6 (b) 4 (c) 5 (d) 7
25. 25.How many factors does 89 have? (a) 1 (b) 4 (c) 3 (d) 2
26. 26.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
27. 27.What is the mode of 19, 18, 7, 3, 19, 3 and 19? (a) 7 (b) 18 (c) 19 (d) 3
28. 28.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 95° (d) 5°
29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 25 (d) 120
30. 30.A drawer has lots of green and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 4 (c) 2 (d) 3
31. 31.What is the 18th term of the AP 14, 21, 28, 35, …? (a) 140 (b) 133 (c) 126 (d) 119
32. 32.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 162 (c) 144 (d) 153
33. 33.What is the mode of 7, 17, 19, 8, 8, 19 and 8? (a) 7 (b) 19 (c) 17 (d) 8
34. 34.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 100° (d) 60°
35. 35.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 144 (d) 132
36. 36.Which is the correct factorisation of x² + 12x + 35? (a) (x + 5)(x + 7) (b) (x + 1)(x + 11) (c) (x + 1)(x + 35) (d) (x − 5)(x − 7)
37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 3 (c) 15 (d) 13
38. 38.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 12 cu cm (d) 64 cu cm
39. 39.A drawer has lots of yellow, white, black and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 8 (c) 2 (d) 5
40. 40.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 36 (c) 18 (d) 9

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad