Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 600 · 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.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 140° (b) 120° (c) 100° (d) 60°
2. 2.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 280 (c) 303 (d) 313
3. 3.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 155° (b) 110° (c) 70° (d) 135°
4. 4.A bag has 7 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 2 (c) 9 (d) 12
5. 5.How many factors does 70 have? (a) 6 (b) 8 (c) 7 (d) 9
6. 6.Which is the correct factorisation of x² + 7x + 12? (a) (x + 3)(x + 4) (b) (x + 1)(x + 6) (c) (x − 3)(x − 4) (d) (x + 1)(x + 12)
7. 7.A bag has 6 green balls and 3 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) 9 (c) 4 (d) 7
8. 8.What is the mean of 19, 8, 10 and 7? (a) 13 (b) 11 (c) 12 (d) 10
9. 9.In a class of 24 children, 6 like cricket, 17 like football and 3 like neither. How many like both? (a) 3 (b) 21 (c) 1 (d) 2
10. 10.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
11. 11.A bag has 9 blue, 8 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 11/19 (c) 8/19 (d) 8/11
12. 12.3 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) 12 (b) 9 (c) 6 (d) 18
13. 13.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
14. 14.A bag has 12 black balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 22 (b) 2 (c) 13 (d) 11
15. 15.The mean of 3 numbers is 26. When the number 14 is added to them, what is the new mean? (a) 20 (b) 26 (c) 24 (d) 23
16. 16.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 55 (c) 90 (d) 100
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 6/11 (c) 1/6 (d) 1/11
18. 18.How many factors does 58 have? (a) 2 (b) 4 (c) 3 (d) 5
19. 19.How many factors does 56 have? (a) 7 (b) 6 (c) 8 (d) 9
20. 20.What is the sum of the roots of x² − 11x + 30 = 0? (a) 11 (b) 10 (c) 12 (d) 30
21. 21.What is the smallest prime factor of 77? (a) 7 (b) 2 (c) 11 (d) 1
22. 22.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11025 (b) 11035 (c) 10025 (d) 9025
23. 23.A bag has 8 white balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 6 (c) 2 (d) 9
24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
25. 25.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) 37 (d) 25
26. 26.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
27. 27.In a class of 51 children, 26 like tea, 30 like coffee and 6 like neither. How many like both? (a) 6 (b) 5 (c) 45 (d) 11
28. 28.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
29. 29.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 32 (c) 16 (d) 8
30. 30.A bag has 9 red, 3 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 10/19 (b) 9/19 (c) 1/3 (d) 9/10
31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
32. 32.A bag has 10 red balls and 8 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) 18 (c) 11 (d) 9
33. 33.What is the 38th term of the AP 9, 13, 17, 21, …? (a) 152 (b) 157 (c) 161 (d) 148
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
35. 35.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 28 (b) 32 (c) 30 (d) 29
36. 36.What is the mean of 3, 2, 4, 10, 9 and 8? (a) 6 (b) 5 (c) 7 (d) 8
37. 37.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 48 (c) 16 (d) 144
38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
39. 39.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 352 (c) 200 (d) 176
40. 40.What is the median of 26, 13, 11, 29 and 35? (a) 29 (b) 13 (c) 11 (d) 26

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