Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 740 · 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 18th term of the AP 18, 25, 32, 39, …? (a) 126 (b) 137 (c) 119 (d) 144
2. 2.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
3. 3.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
4. 4.What is the prime factorisation of 42? (a) 2 × 3 × 7 (b) 2 × 3 × 7² (c) 2³ × 3 × 7 (d) 2² × 3 × 7
5. 5.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 20 (b) 12 (c) 13 (d) 14
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 3/11 (d) 1/11
7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
8. 8.How many prime numbers are there between 20 and 40? (a) 6 (b) 4 (c) 3 (d) 5
9. 9.A cuboid is 12 cm long, 8 cm wide and 6 cm high. What is its total surface area? (a) 576 sq cm (b) 216 sq cm (c) 864 sq cm (d) 432 sq cm
10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
11. 11.What is the distance between the points (3, 8) and (9, 16)? (a) 10 (b) 11 (c) 100 (d) 14
12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 9 (c) 10 (d) 8
13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 21 (d) 15
14. 14.A bag has 4 green balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 8 (c) 6 (d) 5
15. 15.In a class of 38 children, 24 like mangoes, 10 like bananas and 10 like neither. How many like both? (a) 28 (b) 6 (c) 7 (d) 10
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
17. 17.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
18. 18.What is the midpoint of the line joining (0, 13) and (10, 9)? (a) (5, 2) (b) (11, 5) (c) (10, 22) (d) (5, 11)
19. 19.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 105 (c) 25 (d) 114
20. 20.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 45° (c) 225° (d) 135°
21. 21.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 342 (c) 162 (d) 153
22. 22.In a class of 35 children, 9 like cricket, 23 like football and 6 like neither. How many like both? (a) 3 (b) 4 (c) 6 (d) 29
23. 23.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
24. 24.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5
25. 25.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 35 (c) 28 (d) 56
26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
27. 27.A bag has 4 white balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 9 (d) 5
28. 28.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 142 (c) 134 (d) 133
29. 29.The mean of 7 numbers is 23. When the number 7 is added to them, what is the new mean? (a) 22 (b) 15 (c) 23 (d) 21
30. 30.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 90 (d) 55
31. 31.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
32. 32.In a class of 41 children, 19 like maths, 23 like science and 6 like both. How many like neither? (a) 11 (b) 4 (c) 6 (d) 5
33. 33.The mean of 6 numbers is 38. When the number 66 is added to them, what is the new mean? (a) 42 (b) 38 (c) 52 (d) 43
34. 34.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 54 (c) 45 (d) 36
35. 35.In a class of 30 children, 19 like tea, 9 like coffee and 2 like both. How many like only tea? (a) 17 (b) 21 (c) 7 (d) 19
36. 36.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1596 (c) 1653 (d) 1654
37. 37.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
38. 38.What is the median of 21, 35, 17, 4, 16, 22 and 28? (a) 21 (b) 22 (c) 4 (d) 17
39. 39.What is the smallest prime factor of 187? (a) 11 (b) 2 (c) 17 (d) 1
40. 40.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm

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