Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 783 · 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 mode of 16, 11, 11, 7, 8, 8 and 11? (a) 8 (b) 11 (c) 7 (d) 16
2. 2.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 55° (d) 325°
3. 3.A bag has 11 white balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 12 (b) 13 (c) 21 (d) 2
4. 4.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 140° (c) 41° (d) 80°
5. 5.In a class of 35 children, 12 like dance, 26 like music and 5 like neither. How many like both? (a) 3 (b) 30 (c) 5 (d) 8
6. 6.What is the mean of 2, 11, 3, 20, 10 and 14? (a) 9 (b) 11 (c) 12 (d) 10
7. 7.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 424 (b) 232 (c) 44 (d) 212
8. 8.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1681 (b) 1521 (c) 1691 (d) 1601
9. 9.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 666 (d) 648
10. 10.What is the prime factorisation of 15? (a) 3 × 5 (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5²
11. 11.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 135° (c) 45° (d) 155°
12. 12.In a class of 41 children, 17 like cricket, 17 like football and 3 like both. How many like at least one of the two? (a) 34 (b) 41 (c) 28 (d) 31
13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
15. 15.How many factors does 35 have? (a) 2 (b) 3 (c) 4 (d) 5
16. 16.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 531 (c) 532 (d) 522
17. 17.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 125° (d) 35°
18. 18.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 10 (c) 11 (d) 16
19. 19.A bag has 6 yellow, 3 red and 2 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 6/11 (c) 5/11 (d) 7/11
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
21. 21.What is the 39th term of the AP 1, 3, 5, 7, …? (a) 76 (b) 79 (c) 78 (d) 77
22. 22.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
23. 23.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 20 (b) 21 (c) 19 (d) 28
24. 24.What is the distance between the points (8, 1) and (12, 4)? (a) 5 (b) 7 (c) 25 (d) 6
25. 25.What is the distance between the points (1, 5) and (4, 9)? (a) 7 (b) 25 (c) 5 (d) 6
26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
27. 27.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
28. 28.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
29. 29.What is the mean of 18, 2, 12, 13, 16 and 5? (a) 13 (b) 10 (c) 11 (d) 12
30. 30.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 130° (d) 25°
31. 31.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 3 (d) 2
32. 32.What is the distance between the points (0, 0) and (8, 6)? (a) 100 (b) 11 (c) 10 (d) 14
33. 33.A bag has 2 red, 9 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 2/13 (c) 11/13 (d) 2/11
34. 34.In a class of 36 children, 22 like tea, 20 like coffee and 11 like both. How many like at least one of the two? (a) 31 (b) 20 (c) 36 (d) 42
35. 35.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 36 (d) 72
36. 36.What is the median of 24, 32, 29, 7, 13, 39 and 18? (a) 24 (b) 29 (c) 7 (d) 18
37. 37.The mean of 9 numbers is 34. When the number 44 is added to them, what is the new mean? (a) 34 (b) 35 (c) 39 (d) 36
38. 38.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x − 7)(x − 9) (c) (x + 1)(x + 63) (d) (x + 7)(x + 9)
39. 39.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 1036 (c) 990 (d) 1035
40. 40.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 24 (d) 37

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