Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 778 · 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.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 10) (b) (x − 4)(x − 7) (c) (x + 1)(x + 28) (d) (x + 4)(x + 7)
2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
3. 3.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 55° (c) 125° (d) 110°
4. 4.What is the missing term in the AP 9, ?, 19, 24, 29? (a) 14 (b) 13 (c) 19 (d) 15
5. 5.If a + b = 8 and ab = 7, what is a² + b²? (a) 78 (b) 57 (c) 50 (d) 64
6. 6.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
7. 7.A bag has 6 red, 2 green and 6 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 4/7 (b) 1/3 (c) 3/7 (d) 9/14
8. 8.What is the mode of 3, 12, 18, 18, 5, 5 and 5? (a) 18 (b) 3 (c) 5 (d) 12
9. 9.6 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 13 (c) 48 (d) 84
10. 10.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
11. 11.The mean of 3 numbers is 28. When the number 32 is added to them, what is the new mean? (a) 28 (b) 30 (c) 31 (d) 29
12. 12.How many factors does 51 have? (a) 5 (b) 4 (c) 3 (d) 2
13. 13.How many factors does 50 have? (a) 4 (b) 5 (c) 6 (d) 7
14. 14.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
15. 15.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 20° (c) 160° (d) 70°
16. 16.A bag has 8 yellow, 8 green and 9 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 8/25 (c) 17/25 (d) 18/25
17. 17.In which quadrant does the point (5, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 110° (c) 250° (d) 70°
19. 19.A drawer has lots of 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) 2 (b) 4 (c) 5 (d) 3
20. 20.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
21. 21.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 2 (d) 7
22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
23. 23.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
25. 25.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 304 (b) 152 (c) 168 (d) 33
26. 26.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 105° (b) 95° (c) 75° (d) 160°
27. 27.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 1008 (b) 504 (c) 75 (d) 540
28. 28.A drawer has lots of red, blue, yellow, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 10 (c) 5 (d) 2
29. 29.In a class of 33 children, 27 like mangoes, 13 like bananas and 8 like both. How many like at least one of the two? (a) 24 (b) 33 (c) 40 (d) 32
30. 30.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
31. 31.In a class of 32 children, 22 like tea, 8 like coffee and 2 like both. How many like neither? (a) 2 (b) 6 (c) 5 (d) 4
32. 32.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
33. 33.In a class of 33 children, 25 like maths, 14 like science and 3 like neither. How many like both? (a) 6 (b) 9 (c) 3 (d) 30
34. 34.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 78 (d) 156
35. 35.What is the product of the roots of x² − 9x + 20 = 0? (a) 9 (b) 21 (c) 20 (d) 19
36. 36.In a class of 42 children, 22 like mangoes, 14 like bananas and 4 like both. How many like neither? (a) 10 (b) 6 (c) 4 (d) 14
37. 37.In a class of 45 children, 19 like maths, 28 like science and 8 like neither. How many like both? (a) 37 (b) 8 (c) 2 (d) 10
38. 38.Which term of the AP 10, 13, 16, 19, … is 58? (a) 19th (b) 18th (c) 17th (d) 16th
39. 39.A bag has 8 blue balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 13 (c) 10 (d) 9
40. 40.4 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) 16 (b) 20 (c) 32 (d) 8

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