Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 215 · 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 fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
2. 2.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 30° (d) 20°
3. 3.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 240 (d) 25
4. 4.What is the distance between the points (1, 11) and (5, 8)? (a) 5 (b) 25 (c) 6 (d) 7
5. 5.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
6. 6.Using (a − b)² = a² − 2ab + b², what is 88²? (a) 8096 (b) 7754 (c) 8464 (d) 7744
7. 7.What is the product of the roots of x² − 9x + 18 = 0? (a) 17 (b) 18 (c) 19 (d) 9
8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
9. 9.What is the midpoint of the line joining (9, 8) and (19, 4)? (a) (5, 2) (b) (6, 14) (c) (28, 12) (d) (14, 6)
10. 10.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 882 (c) 1806 (d) 861
11. 11.What is the 32nd term of the AP 1, 4, 7, 10, …? (a) 93 (b) 96 (c) 94 (d) 97
12. 12.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6404 (b) 6734 (c) 6724 (d) 6084
13. 13.The mean of 4 numbers is 24. When the number 34 is added to them, what is the new mean? (a) 27 (b) 24 (c) 29 (d) 26
14. 14.What is the mode of 3, 4, 2, 7, 3, 4 and 3? (a) 7 (b) 2 (c) 3 (d) 4
15. 15.How many factors does 62 have? (a) 5 (b) 4 (c) 2 (d) 3
16. 16.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 42 (c) 21 (d) 10
17. 17.How many factors does 32 have? (a) 7 (b) 5 (c) 6 (d) 4
18. 18.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
19. 19.A cuboid is 8 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 448 sq cm (b) 176 sq cm (c) 352 sq cm (d) 704 sq cm
20. 20.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
21. 21.What is the sum of the roots of x² − 9x + 14 = 0? (a) 10 (b) 8 (c) 14 (d) 9
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
23. 23.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
24. 24.If a + b = 13 and ab = 42, what is (a − b)²? (a) 85 (b) 127 (c) 1 (d) 169
25. 25.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
26. 26.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
27. 27.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 66 (d) 132
28. 28.In a class of 46 children, 28 like dance, 21 like music and 8 like neither. How many like both? (a) 38 (b) 11 (c) 3 (d) 8
29. 29.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 140° (d) 115°
30. 30.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 65° (c) 140° (d) 105°
31. 31.A bag has 8 yellow balls and 11 blue 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) 19 (c) 2 (d) 9
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/11 (c) 5/36 (d) 1/11
33. 33.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2 × 5 × 7³ (c) 2⁴ × 5 × 7 (d) 2² × 5 × 7
34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 59 (d) 900
35. 35.A bag has 11 white balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 17 (d) 13
36. 36.What is the mode of 5, 4, 7, 4, 12, 7 and 7? (a) 5 (b) 7 (c) 12 (d) 4
37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 4 (d) 7
38. 38.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 120° (d) 110°
39. 39.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
40. 40.In which quadrant does the point (−7, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

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