Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 196 · 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 = 4 and ab = 3, what is a² + b²? (a) 16 (b) 22 (c) 13 (d) 10
2. 2.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 61° (c) 60° (d) 240°
3. 3.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
5. 5.The mean of 7 numbers is 11. When the number 3 is added to them, what is the new mean? (a) 11 (b) 7 (c) 10 (d) 9
6. 6.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x − 6)(x − 9) (c) (x + 1)(x + 54) (d) (x + 6)(x + 9)
7. 7.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 621 (c) 622 (d) 612
8. 8.A cuboid is 11 cm long, 8 cm wide and 9 cm high. What is its volume? (a) 518 cu cm (b) 88 cu cm (c) 792 cu cm (d) 28 cu cm
9. 9.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
10. 10.What is the mean of 14, 13, 11 and 14? (a) 13 (b) 12 (c) 14 (d) 15
11. 11.In a class of 23 children, 8 like tea, 13 like coffee and 2 like both. How many like only tea? (a) 11 (b) 10 (c) 6 (d) 8
12. 12.What is the distance between the points (7, 33) and (14, 9)? (a) 625 (b) 31 (c) 25 (d) 26
13. 13.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 186 (c) 195 (d) 202
14. 14.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 5 (d) 1
15. 15.What is the mean of 9, 2, 4, 2 and 8? (a) 7 (b) 4 (c) 6 (d) 5
16. 16.What is the sum of the roots of x² − 6x + 8 = 0? (a) 8 (b) 7 (c) 6 (d) 5
17. 17.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 28 (d) 64
18. 18.A bag has 12 green balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 14 (c) 13 (d) 22
19. 19.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2126 (b) 2916 (c) 2484 (d) 2116
20. 20.How many factors does 15 have? (a) 5 (b) 2 (c) 4 (d) 3
21. 21.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) 24 (b) 36 (c) 25 (d) 37
22. 22.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 121 (d) 55
23. 23.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 65°
24. 24.What is the smallest prime factor of 69? (a) 23 (b) 2 (c) 1 (d) 3
25. 25.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 24 (c) 12 (d) 15
26. 26.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 170° (b) 110° (c) 80° (d) 10°
27. 27.What is the distance between the points (8, 1) and (15, 25)? (a) 26 (b) 31 (c) 625 (d) 25
28. 28.A drawer has lots of yellow, blue, green, black 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) 10 (b) 5 (c) 6 (d) 2
29. 29.The mean of 4 numbers is 37. When the number 22 is added to them, what is the new mean? (a) 37 (b) 34 (c) 33 (d) 35
30. 30.What is the median of 5, 39, 32, 10, 12, 8 and 35? (a) 10 (b) 32 (c) 12 (d) 13
31. 31.What is the 34th term of the AP 15, 17, 19, 21, …? (a) 81 (b) 83 (c) 68 (d) 66
32. 32.In a class of 41 children, 16 like tea, 25 like coffee and 10 like both. How many like at least one of the two? (a) 41 (b) 32 (c) 21 (d) 31
33. 33.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
34. 34.How many factors does 40 have? (a) 6 (b) 8 (c) 7 (d) 9
35. 35.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 19 (c) 171 (d) 60
36. 36.In a class of 26 children, 5 like dance, 22 like music and 1 like neither. How many like both? (a) 3 (b) 1 (c) 2 (d) 25
37. 37.A drawer has lots of green, yellow, red, black and blue 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) 5 (c) 6 (d) 10
38. 38.A cuboid is 11 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 462 sq cm (b) 185 sq cm (c) 370 sq cm (d) 740 sq cm
39. 39.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 169 (d) 156
40. 40.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 4 (d) 3

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