Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 936 · 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.In a class of 38 children, 12 like dance, 22 like music and 7 like neither. How many like both? (a) 7 (b) 31 (c) 3 (d) 4
2. 2.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 56 (d) 64
3. 3.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 60° (d) 330°
4. 4.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
6. 6.The mean of 5 numbers is 27. When the number 51 is added to them, what is the new mean? (a) 31 (b) 27 (c) 39 (d) 32
7. 7.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 55° (c) 110° (d) 125°
8. 8.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 80 sq cm (b) 112 sq cm (c) 224 sq cm (d) 56 sq cm
9. 9.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 250 (b) 270 (c) 500 (d) 43
10. 10.What is the median of 38, 3, 20, 1 and 4? (a) 20 (b) 5 (c) 3 (d) 4
11. 11.What is the smallest prime factor of 115? (a) 23 (b) 5 (c) 1 (d) 2
12. 12.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 64 (d) 16
13. 13.In which quadrant does the point (−5, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11
15. 15.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
16. 16.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
17. 17.The mean of 5 numbers is 37. When the number 61 is added to them, what is the new mean? (a) 42 (b) 41 (c) 37 (d) 49
18. 18.In a class of 24 children, 9 like tea, 14 like coffee and 4 like both. How many like neither? (a) 4 (b) 9 (c) 5 (d) 1
19. 19.What is the 12th term of the AP 18, 22, 26, 30, …? (a) 48 (b) 62 (c) 44 (d) 66
20. 20.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2³ × 3² × 7
21. 21.What is the median of 1, 9, 7, 21, 16, 32 and 30? (a) 21 (b) 16 (c) 9 (d) 17
22. 22.A bag has 11 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 15 (b) 13 (c) 12 (d) 2
23. 23.In which quadrant does the point (3, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
24. 24.A cuboid is 8 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 112 cu cm (b) 172 cu cm (c) 17 cu cm (d) 16 cu cm
25. 25.How many factors does 22 have? (a) 2 (b) 5 (c) 3 (d) 4
26. 26.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
27. 27.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 3 (d) 4
28. 28.A bag has 9 green, 2 white and 4 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 11/15 (b) 1/3 (c) 4/5 (d) 4/15
29. 29.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/4 (c) 7/8 (d) 1/7
30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
31. 31.In which quadrant does the point (6, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.Which is the correct factorisation of x² + 5x + 6? (a) (x + 2)(x + 3) (b) (x − 2)(x − 3) (c) (x + 1)(x + 6) (d) (x + 1)(x + 4)
33. 33.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 13 (d) 12
34. 34.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
35. 35.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 154 (c) 172 (d) 163
36. 36.What is the sum of the roots of x² − 8x + 15 = 0? (a) 15 (b) 8 (c) 7 (d) 9
37. 37.In which quadrant does the point (3, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
38. 38.What is the midpoint of the line joining (7, 7) and (11, 11)? (a) (2, 2) (b) (18, 18) (c) (9, 9) (d) (10, 9)
39. 39.What is the midpoint of the line joining (4, 9) and (8, 5)? (a) (2, 2) (b) (12, 14) (c) (7, 6) (d) (6, 7)
40. 40.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 154 (d) 136

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