Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 306 · 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 prime factorisation of 15? (a) 3² × 5 (b) 3 × 5 (c) 3³ × 5 (d) 3 × 5²
2. 2.What is the distance between the points (8, 7) and (11, 11)? (a) 7 (b) 25 (c) 5 (d) 6
3. 3.A bag has 6 blue, 3 green and 5 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 3/11 (b) 3/14 (c) 11/14 (d) 1/3
4. 4.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5³ (d) 2⁴ × 5
5. 5.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
6. 6.What is the distance between the points (8, 7) and (16, 13)? (a) 10 (b) 14 (c) 11 (d) 100
7. 7.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 182 (d) 91
8. 8.What is the midpoint of the line joining (10, 8) and (16, 4)? (a) (26, 12) (b) (3, 2) (c) (6, 13) (d) (13, 6)
9. 9.What is the distance between the points (1, 5) and (17, 17)? (a) 400 (b) 21 (c) 28 (d) 20
10. 10.What is the 40th term of the AP 14, 22, 30, 38, …? (a) 326 (b) 312 (c) 334 (d) 320
11. 11.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
12. 12.In a class of 23 children, 14 like dance, 10 like music and 2 like neither. How many like both? (a) 1 (b) 3 (c) 21 (d) 2
13. 13.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
14. 14.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 200° (c) 20° (d) 100°
15. 15.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 196 sq cm (d) 343 sq cm
16. 16.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 32 (b) 48 (c) 11 (d) 24
17. 17.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 130° (d) 80°
18. 18.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25
19. 19.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 225 (d) 105
20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 30° (d) 15°
21. 21.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 61° (d) 30°
22. 22.In a class of 15 children, 9 like mangoes, 10 like bananas and 6 like both. How many like neither? (a) 8 (b) 6 (c) 2 (d) 3
23. 23.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 76° (c) 75° (d) 255°
24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
25. 25.A bag has 11 white balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 2 (c) 12 (d) 19
26. 26.What is the mean of 19, 17, 16 and 4? (a) 16 (b) 15 (c) 14 (d) 13
27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
28. 28.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 54 (d) 21
29. 29.The mean of 4 numbers is 29. When the number 9 is added to them, what is the new mean? (a) 25 (b) 19 (c) 26 (d) 29
30. 30.What is the median of 20, 38, 16, 21 and 12? (a) 21 (b) 16 (c) 20 (d) 19
31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 13 (d) 14
33. 33.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
34. 34.What are the roots of x² − 17x + 72 = 0? (a) 1 and 72 (b) 8 and 9 (c) 2 and 36 (d) 1 and 16
35. 35.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/3 (c) 1/5 (d) 5/6
36. 36.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
37. 37.A bag has 8 white balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 2 (c) 9 (d) 17
38. 38.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 4 (d) 1
39. 39.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 105° (b) 255° (c) 75° (d) 150°
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm

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