Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 171 · 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.If a + b = 7 and ab = 6, what is a² + b²? (a) 49 (b) 43 (c) 37 (d) 61
2. 2.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4608 (c) 4560 (d) 9312
3. 3.What is the midpoint of the line joining (0, 14) and (6, 4)? (a) (6, 18) (b) (9, 3) (c) (3, 5) (d) (3, 9)
4. 4.In a class of 41 children, 20 like mangoes, 28 like bananas and 8 like both. How many like at least one of the two? (a) 48 (b) 41 (c) 40 (d) 32
5. 5.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 72 (c) 18 (d) 81
6. 6.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 8 (c) 31 (d) 60
7. 7.What is the 13th term of the AP 6, 8, 10, 12, …? (a) 24 (b) 30 (c) 32 (d) 26
8. 8.What are the roots of x² − 7x + 10 = 0? (a) 2 and 5 (b) 1 and 10 (c) 3 and 4 (d) 1 and 6
9. 9.A cuboid is 11 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 150 cu cm (b) 33 cu cm (c) 17 cu cm (d) 99 cu cm
10. 10.In a class of 35 children, 15 like maths, 17 like science and 2 like both. How many like neither? (a) 7 (b) 3 (c) 5 (d) 2
11. 11.What is the midpoint of the line joining (5, 16) and (9, 4)? (a) (7, 10) (b) (14, 20) (c) (10, 7) (d) (2, 6)
12. 12.A bag has 5 yellow, 8 red and 7 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 13/20 (b) 7/13 (c) 7/20 (d) 1/3
13. 13.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 66 (d) 144
14. 14.How many factors does 29 have? (a) 2 (b) 3 (c) 4 (d) 1
15. 15.What is the distance between the points (3, 19) and (19, 7)? (a) 28 (b) 400 (c) 20 (d) 21
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/36 (c) 5/11 (d) 1/6
17. 17.What is the mode of 3, 14, 3, 14, 3, 8 and 9? (a) 3 (b) 9 (c) 8 (d) 14
18. 18.What is the sum of the roots of x² − 13x + 36 = 0? (a) 13 (b) 12 (c) 14 (d) 36
19. 19.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 69 (c) 66 (d) 198
20. 20.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2850 (c) 5700 (d) 2775
21. 21.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 48 (c) 56 (d) 96
22. 22.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2³ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2⁴ × 5 × 7
23. 23.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
24. 24.How many prime numbers are there between 10 and 20? (a) 3 (b) 5 (c) 6 (d) 4
25. 25.A bag has 5 white balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 7 (c) 2 (d) 6
26. 26.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 145° (c) 325° (d) 55°
27. 27.What is the smallest prime factor of 65? (a) 5 (b) 1 (c) 2 (d) 13
28. 28.A drawer has lots of yellow and white 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) 4 (c) 5 (d) 2
29. 29.In a class of 26 children, 14 like maths, 18 like science and 11 like both. How many like only maths? (a) 3 (b) 7 (c) 8 (d) 14
30. 30.A bag has 9 green, 7 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 10/19 (c) 9/19 (d) 11/19
31. 31.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 29 (d) 22
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 15
33. 33.In a class of 29 children, 12 like maths, 18 like science and 7 like both. How many like neither? (a) 7 (b) 5 (c) 13 (d) 6
34. 34.A bag has 5 red, 9 white and 6 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 11/20 (c) 9/20 (d) 3/5
35. 35.In a class of 30 children, 14 like cricket, 15 like football and 9 like both. How many like only cricket? (a) 14 (b) 15 (c) 5 (d) 6
36. 36.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
37. 37.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 25° (d) 30°
38. 38.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 340 (b) 26 (c) 170 (d) 180
39. 39.In a class of 30 children, 19 like dance, 9 like music and 4 like both. How many like neither? (a) 4 (b) 2 (c) 10 (d) 6
40. 40.What is the mean of 14, 17, 11, 6, 5 and 25? (a) 15 (b) 13 (c) 14 (d) 12

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