Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 751 · 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.A bag has 2 white, 4 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 4/5 (c) 1/4 (d) 1/5
2. 2.In which quadrant does the point (−4, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
3. 3.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) 25 (b) 13 (c) 24 (d) 12
4. 4.In a class of 40 children, 15 like maths, 24 like science and 4 like both. How many like neither? (a) 4 (b) 5 (c) 1 (d) 9
5. 5.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 42 (c) 78 (d) 39
6. 6.What is the distance between the points (8, 0) and (11, 4)? (a) 6 (b) 25 (c) 5 (d) 7
7. 7.How many factors does 98 have? (a) 5 (b) 6 (c) 4 (d) 7
8. 8.A bag has 10 white balls and 11 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) 12 (c) 21 (d) 11
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
10. 10.What is the distance between the points (8, 4) and (14, 12)? (a) 14 (b) 10 (c) 100 (d) 11
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
12. 12.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 50° (d) 25°
13. 13.What is the midpoint of the line joining (8, 5) and (20, 11)? (a) (6, 3) (b) (28, 16) (c) (14, 8) (d) (8, 14)
14. 14.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
16. 16.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 44 (b) 52 (c) 42 (d) 43
17. 17.In which quadrant does the point (−5, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
18. 18.What is the 34th term of the AP 14, 23, 32, 41, …? (a) 306 (b) 297 (c) 320 (d) 311
19. 19.In a class of 40 children, 28 like tea, 16 like coffee and 6 like neither. How many like both? (a) 4 (b) 6 (c) 34 (d) 10
20. 20.A bag has 7 yellow balls and 8 red 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) 9 (c) 2 (d) 8
21. 21.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
22. 22.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2⁴ × 3 (c) 2² × 3 (d) 2³ × 3
23. 23.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
24. 24.What is the midpoint of the line joining (0, 8) and (2, 10)? (a) (1, 1) (b) (1, 9) (c) (9, 1) (d) (2, 18)
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
26. 26.The mean of 4 numbers is 31. When the number 26 is added to them, what is the new mean? (a) 30 (b) 31 (c) 32 (d) 29
27. 27.There are 6 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) 42 (b) 12 (c) 36 (d) 72
28. 28.What is the mean of 14, 7, 16, 15 and 8? (a) 10 (b) 13 (c) 15 (d) 12
29. 29.What is the median of 7, 8, 23, 11, 10, 13 and 35? (a) 12 (b) 13 (c) 11 (d) 10
30. 30.3 T-shirts and 2 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) 5 (c) 6 (d) 12
31. 31.What are the roots of x² − 10x + 16 = 0? (a) 3 and 7 (b) 1 and 16 (c) 1 and 9 (d) 2 and 8
32. 32.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
33. 33.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 121 (d) 55
34. 34.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 80° (d) 100°
35. 35.A bag has 4 blue, 5 white and 7 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/16 (b) 5/8 (c) 1/3 (d) 9/16
36. 36.Which is the correct factorisation of x² + 15x + 54? (a) (x + 6)(x + 9) (b) (x + 1)(x + 14) (c) (x − 6)(x − 9) (d) (x + 1)(x + 54)
37. 37.What is the midpoint of the line joining (4, 13) and (16, 5)? (a) (9, 10) (b) (6, 4) (c) (20, 18) (d) (10, 9)
38. 38.In a class of 21 children, 9 like dance, 14 like music and 5 like both. How many like only dance? (a) 9 (b) 7 (c) 4 (d) 5
39. 39.How many factors does 111 have? (a) 2 (b) 3 (c) 5 (d) 4
40. 40.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7

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