Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 123 · 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 circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
2. 2.What is the 32nd term of the AP 5, 8, 11, 14, …? (a) 101 (b) 98 (c) 96 (d) 93
3. 3.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 135° (c) 45° (d) 160°
4. 4.What is the mean of 18, 19, 14, 4, 7 and 16? (a) 13 (b) 14 (c) 15 (d) 12
5. 5.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 100° (d) 105°
6. 6.The mean of 3 numbers is 39. When the number 51 is added to them, what is the new mean? (a) 43 (b) 45 (c) 39 (d) 42
7. 7.Which term of the AP 7, 16, 25, 34, … is 196? (a) 23rd (b) 21st (c) 24th (d) 22nd
8. 8.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 21 cu cm (d) 196 cu cm
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
10. 10.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 150° (b) 70° (c) 110° (d) 100°
11. 11.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
12. 12.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
13. 13.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 144 (d) 66
14. 14.The mean of 6 numbers is 13. When the number 20 is added to them, what is the new mean? (a) 13 (b) 14 (c) 15 (d) 16
15. 15.What is the distance between the points (4, 1) and (16, 17)? (a) 28 (b) 400 (c) 21 (d) 20
16. 16.What is the mode of 5, 5, 20, 12, 20, 20 and 1? (a) 12 (b) 1 (c) 5 (d) 20
17. 17.What is the mean of 15, 17, 15 and 9? (a) 13 (b) 15 (c) 14 (d) 16
18. 18.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 121 (d) 55
19. 19.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
20. 20.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2 × 3 × 7² (c) 2³ × 3 × 7 (d) 2² × 3 × 7
21. 21.What is the mean of 16, 8, 17, 13, 20 and 22? (a) 17 (b) 16 (c) 15 (d) 18
22. 22.A drawer has lots of red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 4 (d) 5
23. 23.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 729 cu cm (d) 486 cu cm
24. 24.In a class of 23 children, 11 like dance, 15 like music and 4 like both. How many like only dance? (a) 11 (b) 8 (c) 7 (d) 4
25. 25.Which term of the AP 6, 8, 10, 12, … is 76? (a) 36th (b) 38th (c) 35th (d) 37th
26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 19 (d) 17
27. 27.A bag has 8 white balls and 5 blue 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) 6 (c) 9 (d) 13
28. 28.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 64 (d) 16
29. 29.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 150 cu cm (c) 100 cu cm (d) 15 cu cm
30. 30.What is the midpoint of the line joining (5, 7) and (13, 9)? (a) (9, 8) (b) (18, 16) (c) (8, 9) (d) (4, 1)
31. 31.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 72 sq cm (b) 62 sq cm (c) 124 sq cm (d) 248 sq cm
32. 32.In which quadrant does the point (−2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
33. 33.What is the smallest prime factor of 169? (a) 13 (b) 3 (c) 2 (d) 1
34. 34.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 140 (b) 73 (c) 20 (d) 70
35. 35.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 36 (d) 12
36. 36.A cuboid is 10 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 40 cu cm (c) 20 cu cm (d) 88 cu cm
37. 37.A bag has 10 black balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 21 (c) 11 (d) 2
38. 38.What is the distance between the points (5, 11) and (11, 3)? (a) 11 (b) 10 (c) 100 (d) 14
39. 39.In a class of 36 children, 21 like cricket, 21 like football and 10 like both. How many like at least one of the two? (a) 32 (b) 36 (c) 42 (d) 22
40. 40.In a class of 56 children, 26 like tea, 28 like coffee and 8 like both. How many like at least one of the two? (a) 56 (b) 54 (c) 38 (d) 46

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