Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 221 · 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 canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 15 (c) 30 (d) 20
2. 2.In a class of 40 children, 16 like tea, 23 like coffee and 4 like both. How many like at least one of the two? (a) 35 (b) 31 (c) 39 (d) 40
3. 3.A bag has 3 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 4 (c) 8 (d) 6
4. 4.What is the 28th term of the AP 14, 21, 28, 35, …? (a) 203 (b) 189 (c) 210 (d) 196
5. 5.In a class of 32 children, 14 like dance, 12 like music and 4 like both. How many like neither? (a) 4 (b) 6 (c) 10 (d) 14
6. 6.What is the 29th term of the AP 16, 22, 28, 34, …? (a) 190 (b) 184 (c) 168 (d) 174
7. 7.How many factors does 99 have? (a) 7 (b) 6 (c) 4 (d) 5
8. 8.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 80° (c) 81° (d) 260°
9. 9.In which quadrant does the point (−3, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
11. 11.A bag has 5 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 6 (c) 2 (d) 9
12. 12.A bag has 3 yellow balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 4 (c) 2 (d) 10
13. 13.What is the mean of 10, 11, 3 and 4? (a) 8 (b) 9 (c) 7 (d) 6
14. 14.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
15. 15.In a class of 34 children, 22 like dance, 19 like music and 12 like both. How many like at least one of the two? (a) 17 (b) 29 (c) 41 (d) 34
16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 16 (b) 14 (c) 15 (d) 4
17. 17.What is the median of 25, 5, 13, 24 and 32? (a) 24 (b) 25 (c) 13 (d) 23
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
19. 19.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 132 (c) 114 (d) 124
20. 20.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
21. 21.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 110° (d) 85°
22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
23. 23.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 864 sq cm
24. 24.The mean of 3 numbers is 37. When the number 25 is added to them, what is the new mean? (a) 34 (b) 37 (c) 31 (d) 35
25. 25.If a + b = 18 and ab = 72, what is (a − b)²? (a) 6 (b) 36 (c) 180 (d) 324
26. 26.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
27. 27.The mean of 7 numbers is 37. When the number 53 is added to them, what is the new mean? (a) 45 (b) 40 (c) 39 (d) 37
28. 28.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5³ (c) 2³ × 3 × 5 (d) 2² × 3 × 5
29. 29.The mean of 3 numbers is 19. When the number 11 is added to them, what is the new mean? (a) 18 (b) 17 (c) 15 (d) 19
30. 30.A drawer has lots of blue, white, black, green 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) 5 (b) 6 (c) 10 (d) 2
31. 31.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
32. 32.A bag has 5 yellow balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 2 (c) 7 (d) 11
33. 33.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 24 (d) 132
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/9 (c) 1/11 (d) 4/11
35. 35.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 42 (d) 13
36. 36.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
37. 37.In a class of 49 children, 24 like cricket, 24 like football and 7 like neither. How many like both? (a) 42 (b) 6 (c) 7 (d) 5
38. 38.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 10 (b) 11 (c) 12 (d) 15
39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 1 (d) 4
40. 40.In a class of 33 children, 18 like dance, 17 like music and 5 like both. How many like at least one of the two? (a) 33 (b) 35 (c) 25 (d) 30

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