Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 179 · 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 are the roots of x² − 10x + 16 = 0? (a) 3 and 7 (b) 2 and 8 (c) 1 and 9 (d) 1 and 16
2. 2.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 576 (c) 567 (d) 456
3. 3.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 27 (b) 28 (c) 26 (d) 31
4. 4.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 340 (c) 339 (d) 330
5. 5.What is the 39th term of the AP 10, 14, 18, 22, …? (a) 152 (b) 156 (c) 162 (d) 166
6. 6.A drawer has lots of blue, black, red 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) 5 (b) 8 (c) 2 (d) 4
7. 7.How many factors does 74 have? (a) 2 (b) 5 (c) 4 (d) 3
8. 8.What is the distance between the points (8, 9) and (20, 14)? (a) 169 (b) 14 (c) 13 (d) 17
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
10. 10.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
11. 11.What is the median of 9, 19, 5, 3, 11, 16 and 35? (a) 11 (b) 14 (c) 16 (d) 3
12. 12.What is the distance between the points (8, 1) and (24, 13)? (a) 28 (b) 21 (c) 400 (d) 20
13. 13.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 14 (c) 15 (d) 7
14. 14.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
15. 15.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
16. 16.A bag has 3 green balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 8 (c) 4 (d) 2
17. 17.What is the distance between the points (1, 5) and (8, 29)? (a) 26 (b) 31 (c) 625 (d) 25
18. 18.Which term of the AP 9, 17, 25, 33, … is 97? (a) 13th (b) 11th (c) 14th (d) 12th
19. 19.If a + b = 4 and ab = 3, what is (a − b)²? (a) 2 (b) 10 (c) 4 (d) 16
20. 20.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
21. 21.What is the midpoint of the line joining (2, 4) and (12, 0)? (a) (14, 4) (b) (2, 7) (c) (5, 2) (d) (7, 2)
22. 22.How many factors does 36 have? (a) 8 (b) 10 (c) 9 (d) 7
23. 23.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 21 (b) 10 (c) 28 (d) 42
24. 24.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 34 (b) 29 (c) 27 (d) 28
25. 25.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
26. 26.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 6 (b) 7 (c) 8 (d) 9
27. 27.In a class of 34 children, 22 like cricket, 20 like football and 9 like both. How many like at least one of the two? (a) 33 (b) 42 (c) 34 (d) 24
28. 28.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 579 (c) 588 (d) 589
29. 29.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 7/8 (d) 1/4
30. 30.A bag has 3 green, 3 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 6/13 (b) 7/13 (c) 1/3 (d) 8/13
31. 31.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
32. 32.In a class of 50 children, 27 like dance, 25 like music and 12 like both. How many like at least one of the two? (a) 52 (b) 50 (c) 40 (d) 28
33. 33.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
34. 34.In which quadrant does the point (9, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
35. 35.What is the mean of 17, 7, 12 and 8? (a) 13 (b) 11 (c) 12 (d) 10
36. 36.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 240 (d) 25
37. 37.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 90° (c) 120° (d) 270°
38. 38.What is the median of 8, 38, 16, 33 and 5? (a) 20 (b) 8 (c) 33 (d) 16
39. 39.What is the mode of 18, 19, 14, 14, 14, 16 and 18? (a) 19 (b) 16 (c) 18 (d) 14
40. 40.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 105° (d) 130°

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