Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 323 · 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.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 1/4 (d) 3/5
2. 2.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
3. 3.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 4 (d) 1
4. 4.How many prime numbers are there between 10 and 30? (a) 5 (b) 6 (c) 7 (d) 8
5. 5.A drawer has lots of blue, red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 2 (d) 6
6. 6.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 8659 (b) 7569 (c) 8649 (d) 8109
7. 7.A drawer has lots of black, white, green, blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
8. 8.What is the distance between the points (3, 9) and (12, 21)? (a) 225 (b) 15 (c) 16 (d) 21
9. 9.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 56 (c) 96 (d) 14
10. 10.In a class of 38 children, 24 like cricket, 18 like football and 3 like neither. How many like both? (a) 7 (b) 3 (c) 35 (d) 4
11. 11.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 22 (c) 29 (d) 21
12. 12.A bag has 8 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 9 (b) 10 (c) 2 (d) 18
13. 13.What is the mean of 5, 12, 20 and 23? (a) 20 (b) 15 (c) 16 (d) 12
14. 14.In which quadrant does the point (−9, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
15. 15.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 155° (d) 65°
16. 16.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 12 (c) 18 (d) 6
17. 17.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 115° (d) 35°
18. 18.What is the mode of 2, 17, 3, 17, 3, 1 and 3? (a) 2 (b) 3 (c) 17 (d) 1
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) 21 (b) 22 (c) 14 (d) 15
20. 20.In a class of 29 children, 6 like maths, 18 like science and 3 like both. How many like at least one of the two? (a) 29 (b) 24 (c) 18 (d) 21
21. 21.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 46° (c) 135° (d) 45°
22. 22.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 39 (b) 41 (c) 49 (d) 40
23. 23.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
24. 24.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
26. 26.A drawer has lots of red, blue and white 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) 6 (c) 3 (d) 4
27. 27.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 1166 (b) 676 (c) 916 (d) 1156
28. 28.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 3/11 (c) 1/9 (d) 1/12
30. 30.A drawer has lots of yellow, white, red, green 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) 6 (b) 10 (c) 5 (d) 2
31. 31.3 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 21 (c) 24 (d) 42
32. 32.If a + b = 7 and ab = 12, what is (a − b)²? (a) 25 (b) 49 (c) 1 (d) 37
33. 33.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 110° (d) 145°
34. 34.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
35. 35.In a class of 44 children, 18 like mangoes, 27 like bananas and 6 like neither. How many like both? (a) 7 (b) 38 (c) 6 (d) 1
36. 36.What is the mean of 18, 5, 9, 8 and 5? (a) 11 (b) 9 (c) 10 (d) 8
37. 37.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) 46° (d) 45°
38. 38.What is the smallest prime factor of 341? (a) 2 (b) 11 (c) 1 (d) 31
39. 39.What is the distance between the points (6, 22) and (14, 7)? (a) 289 (b) 23 (c) 17 (d) 18
40. 40.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 6 times (d) 2 times

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