Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 462 · 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 median of 27, 12, 19, 8 and 4? (a) 19 (b) 14 (c) 8 (d) 12
2. 2.What is the midpoint of the line joining (7, 5) and (15, 13)? (a) (9, 11) (b) (4, 4) (c) (22, 18) (d) (11, 9)
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
4. 4.What is the 13th term of the AP 6, 14, 22, 30, …? (a) 104 (b) 110 (c) 96 (d) 102
5. 5.In a class of 34 children, 14 like dance, 13 like music and 9 like neither. How many like both? (a) 9 (b) 3 (c) 25 (d) 2
6. 6.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.What is the distance between the points (4, 13) and (12, 7)? (a) 10 (b) 11 (c) 14 (d) 100
8. 8.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 126 (c) 252 (d) 33
9. 9.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 49 (d) 28
10. 10.A bag has 8 yellow, 4 red and 9 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 2/3 (b) 1/3 (c) 13/21 (d) 8/21
11. 11.How many factors does 119 have? (a) 2 (b) 3 (c) 5 (d) 4
12. 12.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 10°
13. 13.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
14. 14.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 150° (c) 55° (d) 25°
15. 15.If a + b = 21 and ab = 108, what is a² + b²? (a) 333 (b) 657 (c) 225 (d) 441
16. 16.What is the 27th term of the AP 17, 26, 35, 44, …? (a) 243 (b) 251 (c) 234 (d) 260
17. 17.What is the mean of 19, 10, 5, 18, 15 and 5? (a) 12 (b) 13 (c) 11 (d) 14
18. 18.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
19. 19.What is the midpoint of the line joining (0, 1) and (4, 13)? (a) (4, 14) (b) (7, 2) (c) (2, 6) (d) (2, 7)
20. 20.What is the midpoint of the line joining (4, 7) and (10, 5)? (a) (14, 12) (b) (7, 6) (c) (3, 1) (d) (6, 7)
21. 21.A bag has 11 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) 2 (b) 16 (c) 12 (d) 6
22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 729 (d) 53
23. 23.What is the product of the roots of x² − 17x + 72 = 0? (a) 73 (b) 72 (c) 17 (d) 71
24. 24.The mean of 4 numbers is 31. When the number 41 is added to them, what is the new mean? (a) 31 (b) 33 (c) 36 (d) 34
25. 25.5 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 10 (c) 7 (d) 20
26. 26.How many factors does 13 have? (a) 3 (b) 1 (c) 4 (d) 2
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
28. 28.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
29. 29.A bag has 3 blue, 4 green and 7 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/7 (b) 2/5 (c) 5/7 (d) 1/3
30. 30.A bag has 10 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 11 (c) 5 (d) 2
31. 31.What is the smallest prime factor of 85? (a) 1 (b) 5 (c) 2 (d) 17
32. 32.In a class of 44 children, 25 like tea, 23 like coffee and 7 like neither. How many like both? (a) 11 (b) 7 (c) 4 (d) 37
33. 33.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
34. 34.What is the midpoint of the line joining (2, 16) and (14, 4)? (a) (16, 20) (b) (6, 6) (c) (8, 10) (d) (10, 8)
35. 35.A drawer has lots of red, green, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 2 (c) 4 (d) 5
36. 36.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
37. 37.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 100° (d) 40°
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/9 (c) 3/11 (d) 1/11
39. 39.In a class of 39 children, 18 like maths, 16 like science and 4 like both. How many like neither? (a) 13 (b) 4 (c) 5 (d) 9
40. 40.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 338 (c) 400 (d) 399

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