Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 458 · 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 3, 10, 15, 20, 16 and 14? (a) 13 (b) 14 (c) 15 (d) 12
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/36 (c) 5/11 (d) 1/6
4. 4.A bag has 8 green, 5 red and 9 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 7/11 (b) 13/22 (c) 1/3 (d) 9/22
5. 5.In a class of 33 children, 19 like maths, 8 like science and 9 like neither. How many like both? (a) 4 (b) 3 (c) 24 (d) 9
6. 6.What is the mean of 14, 12, 19 and 15? (a) 20 (b) 12 (c) 15 (d) 16
7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
8. 8.A bag has 3 white balls and 5 red 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) 8 (c) 4 (d) 6
9. 9.In a class of 47 children, 26 like maths, 27 like science and 11 like both. How many like neither? (a) 6 (b) 5 (c) 16 (d) 11
10. 10.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) 15 (b) 14 (c) 7 (d) 8
11. 11.In a class of 37 children, 22 like mangoes, 17 like bananas and 2 like neither. How many like both? (a) 2 (b) 5 (c) 35 (d) 4
12. 12.What is the mode of 10, 14, 3, 10, 3, 13 and 3? (a) 3 (b) 13 (c) 14 (d) 10
13. 13.A bag has 2 yellow, 7 white and 3 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 5/12 (b) 1/3 (c) 7/12 (d) 5/7
14. 14.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 64 (b) 112 (c) 15 (d) 56
15. 15.The mean of 4 numbers is 16. When the number 36 is added to them, what is the new mean? (a) 26 (b) 16 (c) 20 (d) 21
16. 16.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 80° (d) 140°
17. 17.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 1 (d) 2
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/18 (c) 1/12 (d) 1/11
19. 19.A bag has 10 red balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 5 (d) 14
20. 20.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
21. 21.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 8 (c) 27 (d) 24
22. 22.A bag has 3 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 12 (c) 2 (d) 10
23. 23.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
24. 24.In which quadrant does the point (−9, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
25. 25.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
26. 26.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
27. 27.In a class of 45 children, 24 like cricket, 22 like football and 5 like neither. How many like both? (a) 5 (b) 1 (c) 6 (d) 40
28. 28.What is the median of 15, 26, 6, 19, 22, 34 and 28? (a) 26 (b) 23 (c) 22 (d) 19
29. 29.The mean of 6 numbers is 29. When the number 8 is added to them, what is the new mean? (a) 26 (b) 25 (c) 29 (d) 27
30. 30.What is the midpoint of the line joining (5, 1) and (17, 3)? (a) (11, 2) (b) (6, 1) (c) (2, 11) (d) (22, 4)
31. 31.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
33. 33.A bag has 7 red balls and 4 black 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) 5 (c) 11 (d) 8
34. 34.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 140° (c) 135° (d) 45°
35. 35.In a class of 25 children, 18 like cricket, 14 like football and 10 like both. How many like only cricket? (a) 18 (b) 4 (c) 8 (d) 11
36. 36.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 245° (b) 130° (c) 115° (d) 65°
37. 37.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) 37 (d) 49
38. 38.If a + b = 16 and ab = 63, what is a² + b²? (a) 382 (b) 256 (c) 193 (d) 130
39. 39.In a class of 21 children, 9 like tea, 9 like coffee and 3 like both. How many like neither? (a) 3 (b) 6 (c) 7 (d) 9
40. 40.A drawer has lots of yellow, white, red, 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) 5 (b) 10 (c) 6 (d) 2

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