Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 322 · 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 sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 30 (d) 15
2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
3. 3.What is the median of 16, 15, 18, 1 and 9? (a) 9 (b) 18 (c) 16 (d) 15
4. 4.A bag has 10 blue balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 21 (c) 2 (d) 12
5. 5.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
6. 6.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 160° (d) 50°
7. 7.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
8. 8.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
9. 9.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 3 (d) 1
10. 10.In a class of 43 children, 25 like maths, 26 like science and 3 like neither. How many like both? (a) 3 (b) 40 (c) 11 (d) 8
11. 11.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 30 (c) 21 (d) 36
12. 12.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 160° (c) 120° (d) 100°
13. 13.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 179 (b) 180 (c) 170 (d) 188
14. 14.The mean of 5 numbers is 19. When the number 13 is added to them, what is the new mean? (a) 16 (b) 19 (c) 18 (d) 17
15. 15.What is the 18th term of the AP 6, 8, 10, 12, …? (a) 42 (b) 36 (c) 40 (d) 34
16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 13 (d) 14
17. 17.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
18. 18.In a class of 39 children, 12 like cricket, 23 like football and 6 like both. How many like only cricket? (a) 6 (b) 17 (c) 12 (d) 16
19. 19.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
20. 20.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
21. 21.A bag has 4 blue, 7 green and 5 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 11/16 (c) 3/4 (d) 5/16
22. 22.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 55° (c) 110° (d) 20°
23. 23.How many factors does 63 have? (a) 7 (b) 4 (c) 5 (d) 6
24. 24.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3487 (c) 3403 (d) 3486
25. 25.In a class of 41 children, 14 like cricket, 26 like football and 9 like both. How many like neither? (a) 9 (b) 19 (c) 1 (d) 10
26. 26.The mean of 9 numbers is 37. When the number 7 is added to them, what is the new mean? (a) 37 (b) 35 (c) 22 (d) 34
27. 27.A bag has 8 black balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 9 (c) 2 (d) 10
28. 28.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 63 (c) 21 (d) 24
29. 29.If a + b = 17 and ab = 70, what is (a − b)²? (a) 149 (b) 289 (c) 9 (d) 3
30. 30.What is the smallest prime factor of 39? (a) 1 (b) 2 (c) 3 (d) 13
31. 31.In a class of 47 children, 22 like cricket, 28 like football and 10 like both. How many like at least one of the two? (a) 30 (b) 47 (c) 50 (d) 40
32. 32.In a class of 29 children, 16 like cricket, 14 like football and 5 like neither. How many like both? (a) 1 (b) 24 (c) 6 (d) 5
33. 33.What is the product of the roots of x² − 11x + 30 = 0? (a) 30 (b) 29 (c) 31 (d) 11
34. 34.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
35. 35.What is the median of 17, 11, 36, 7 and 14? (a) 11 (b) 14 (c) 36 (d) 17
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
37. 37.In a class of 41 children, 16 like cricket, 29 like football and 9 like both. How many like only cricket? (a) 12 (b) 16 (c) 7 (d) 20
38. 38.A drawer has lots of blue, red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 6 (d) 4
39. 39.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 56) (c) (x + 7)(x + 8) (d) (x + 1)(x + 14)
40. 40.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 115° (b) 135° (c) 110° (d) 70°

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