Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 926 · 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 mean of 8, 5, 17 and 14? (a) 13 (b) 12 (c) 10 (d) 11
2. 2.What is the mean of 17, 5, 9, 2, 6 and 3? (a) 6 (b) 9 (c) 7 (d) 8
3. 3.What is the mode of 16, 17, 20, 20, 19, 20 and 19? (a) 17 (b) 19 (c) 16 (d) 20
4. 4.In a class of 22 children, 13 like cricket, 10 like football and 2 like both. How many like neither? (a) 0 (b) 2 (c) 3 (d) 1
5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
6. 6.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
7. 7.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 73 sq cm (b) 292 sq cm (c) 90 sq cm (d) 146 sq cm
8. 8.What is the mode of 11, 11, 1, 13, 13, 7 and 11? (a) 11 (b) 13 (c) 1 (d) 7
9. 9.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
10. 10.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 80 (b) 40 (c) 48 (d) 13
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
12. 12.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 1/2 (d) 2/3
13. 13.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 55 (d) 66
14. 14.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7²
15. 15.A bag has 9 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 7 (d) 10
16. 16.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 115° (c) 50° (d) 65°
17. 17.What is the midpoint of the line joining (8, 3) and (16, 5)? (a) (24, 8) (b) (4, 1) (c) (4, 12) (d) (12, 4)
18. 18.The mean of 7 numbers is 17. When the number 9 is added to them, what is the new mean? (a) 15 (b) 16 (c) 13 (d) 17
19. 19.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 220° (b) 40° (c) 110° (d) 140°
20. 20.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
21. 21.In which quadrant does the point (−2, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
22. 22.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 48 (c) 49 (d) 37
23. 23.In a class of 36 children, 16 like mangoes, 25 like bananas and 7 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 3
24. 24.A drawer has lots of black, yellow 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) 6 (c) 3 (d) 2
25. 25.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 35° (b) 155° (c) 60° (d) 145°
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 3 (d) 14
27. 27.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 9 (c) 81 (d) 30
28. 28.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 36° (c) 145° (d) 215°
29. 29.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 114 (b) 15 (c) 228 (d) 120
30. 30.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 105° (d) 40°
31. 31.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 42 (d) 49
32. 32.The mean of 5 numbers is 39. When the number 21 is added to them, what is the new mean? (a) 37 (b) 39 (c) 36 (d) 30
33. 33.A drawer has lots of red, yellow, green 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) 5 (b) 4 (c) 2 (d) 8
34. 34.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
35. 35.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 145° (d) 75°
36. 36.In a class of 36 children, 17 like cricket, 20 like football and 1 like neither. How many like both? (a) 2 (b) 3 (c) 35 (d) 1
37. 37.In a class of 28 children, 12 like cricket, 16 like football and 4 like both. How many like neither? (a) 4 (b) 5 (c) 0 (d) 8
38. 38.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 16 (d) 28
39. 39.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
40. 40.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) 15 (b) 22 (c) 21 (d) 14

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