Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 466 · 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.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) 8 (b) 72 (c) 27 (d) 24
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
3. 3.What is the smallest prime factor of 161? (a) 2 (b) 23 (c) 7 (d) 1
4. 4.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 49 (d) 14
5. 5.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
6. 6.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
7. 7.What is the mean of 12, 3, 8 and 21? (a) 10 (b) 11 (c) 13 (d) 12
8. 8.What is the midpoint of the line joining (1, 4) and (11, 2)? (a) (12, 6) (b) (3, 6) (c) (6, 3) (d) (5, 1)
9. 9.How many factors does 40 have? (a) 7 (b) 6 (c) 8 (d) 9
10. 10.4 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) 28 (b) 32 (c) 56 (d) 11
11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 16 (d) 6
12. 12.In a class of 38 children, 22 like cricket, 20 like football and 6 like neither. How many like both? (a) 10 (b) 32 (c) 6 (d) 4
13. 13.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 78 (b) 9 (c) 42 (d) 39
14. 14.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 36 (c) 42 (d) 12
15. 15.In a class of 49 children, 28 like dance, 28 like music and 10 like both. How many like at least one of the two? (a) 49 (b) 36 (c) 46 (d) 56
16. 16.What is the mode of 17, 17, 12, 18, 18, 13 and 18? (a) 18 (b) 12 (c) 17 (d) 13
17. 17.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 100° (b) 80° (c) 110° (d) 150°
18. 18.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 45°
19. 19.The mean of 4 numbers is 22. When the number 42 is added to them, what is the new mean? (a) 22 (b) 26 (c) 32 (d) 27
20. 20.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
22. 22.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 3/5 (d) 1/4
23. 23.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 55° (b) 150° (c) 155° (d) 30°
24. 24.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 7482 (c) 3741 (d) 3698
25. 25.What is the sum of the roots of x² − 10x + 21 = 0? (a) 9 (b) 11 (c) 21 (d) 10
26. 26.What is the 31st term of the AP 16, 21, 26, 31, …? (a) 150 (b) 155 (c) 166 (d) 171
27. 27.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 14 (c) 15 (d) 56
28. 28.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 32 (c) 20 (d) 8
29. 29.How many factors does 111 have? (a) 3 (b) 4 (c) 5 (d) 2
30. 30.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 75° (b) 140° (c) 105° (d) 115°
31. 31.3 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 8 (b) 15 (c) 18 (d) 30
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
33. 33.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 105° (b) 120° (c) 75° (d) 135°
34. 34.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 7/8 (d) 1/8
35. 35.In a class of 15 children, 7 like dance, 10 like music and 4 like both. How many like only dance? (a) 6 (b) 3 (c) 5 (d) 7
36. 36.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
37. 37.What are the roots of x² − 8x + 15 = 0? (a) 1 and 7 (b) 2 and 6 (c) 3 and 5 (d) 1 and 15
38. 38.In a class of 45 children, 24 like cricket, 17 like football and 6 like both. How many like neither? (a) 6 (b) 4 (c) 10 (d) 16
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 20 (d) 9
40. 40.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 31 (c) 32 (d) 40

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