Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 784 · 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 area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
2. 2.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 130° (d) 100°
3. 3.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 144 (d) 132
4. 4.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
5. 5.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 66 (d) 55
6. 6.What is the mean of 2, 15, 12, 12 and 9? (a) 9 (b) 10 (c) 12 (d) 11
7. 7.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3003 (c) 3004 (d) 2926
8. 8.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 156 (b) 176 (c) 37 (d) 312
9. 9.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 3 (d) 4
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3
11. 11.A bag has 4 green balls and 11 white 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) 5 (c) 15 (d) 12
12. 12.In a class of 35 children, 21 like tea, 13 like coffee and 5 like both. How many like at least one of the two? (a) 35 (b) 34 (c) 29 (d) 24
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
14. 14.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 25 (d) 10
15. 15.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
16. 16.What is the 38th term of the AP 3, 11, 19, 27, …? (a) 307 (b) 304 (c) 296 (d) 299
17. 17.A bag has 12 yellow balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 13 (c) 2 (d) 7
18. 18.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
19. 19.What is the midpoint of the line joining (9, 0) and (15, 2)? (a) (3, 1) (b) (1, 12) (c) (12, 1) (d) (24, 2)
20. 20.In which quadrant does the point (7, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
21. 21.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 1/7 (d) 7/8
22. 22.What is the midpoint of the line joining (1, 6) and (7, 12)? (a) (8, 18) (b) (4, 9) (c) (9, 4) (d) (3, 3)
23. 23.What is the smallest prime factor of 57? (a) 19 (b) 1 (c) 2 (d) 3
24. 24.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 343 cu cm (d) 294 cu cm
25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 8 (d) 20
26. 26.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 120° (b) 95° (c) 145° (d) 35°
27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 2 (d) 4
28. 28.Which is the correct factorisation of x² + 16x + 63? (a) (x + 7)(x + 9) (b) (x + 1)(x + 15) (c) (x + 1)(x + 63) (d) (x − 7)(x − 9)
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/11 (c) 4/11 (d) 1/9
30. 30.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 7)(x + 8) (c) (x − 7)(x − 8) (d) (x + 1)(x + 56)
31. 31.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 135° (d) 115°
32. 32.A bag has 3 green balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 4 (c) 5 (d) 2
33. 33.What is the median of 34, 30, 24, 31 and 6? (a) 24 (b) 25 (c) 30 (d) 31
34. 34.In a class of 51 children, 25 like mangoes, 27 like bananas and 9 like both. How many like at least one of the two? (a) 34 (b) 51 (c) 52 (d) 43
35. 35.What is the 11th term of the AP 5, 9, 13, 17, …? (a) 49 (b) 44 (c) 45 (d) 40
36. 36.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 45 (b) 55 (c) 17 (d) 90
37. 37.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 100° (d) 140°
38. 38.What is the 30th term of the AP 12, 19, 26, 33, …? (a) 222 (b) 210 (c) 215 (d) 203
39. 39.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 35° (d) 45°
40. 40.Which is the correct factorisation of x² + 13x + 40? (a) (x − 5)(x − 8) (b) (x + 1)(x + 40) (c) (x + 1)(x + 12) (d) (x + 5)(x + 8)

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