Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 560 · 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 80° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 45° (c) 135° (d) 125°
2. 2.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/4 (c) 1/2 (d) 1/3
3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 6 (d) 5
4. 4.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
5. 5.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
6. 6.A drawer has lots of red, white, yellow 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) 4 (b) 5 (c) 8 (d) 2
7. 7.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 135° (d) 115°
8. 8.In a class of 22 children, 16 like cricket, 7 like football and 3 like both. How many like neither? (a) 3 (b) 1 (c) 5 (d) 2
9. 9.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3042 (c) 3003 (d) 3081
10. 10.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 909 (b) 1099 (c) 1089 (d) 729
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
12. 12.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 55 (d) 66
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) 7 (c) 15 (d) 14
14. 14.Which term of the AP 4, 8, 12, 16, … is 88? (a) 21st (b) 24th (c) 23rd (d) 22nd
15. 15.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 2 (d) 4
16. 16.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
17. 17.What is the midpoint of the line joining (4, 10) and (14, 4)? (a) (7, 9) (b) (18, 14) (c) (9, 7) (d) (5, 3)
18. 18.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 279 (c) 280 (d) 258
19. 19.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 155° (b) 160° (c) 25° (d) 45°
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 15 (d) 17
22. 22.If a + b = 18 and ab = 80, what is (a − b)²? (a) 4 (b) 324 (c) 164 (d) 2
23. 23.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6396 (b) 6084 (c) 6094 (d) 6724
24. 24.In a class of 49 children, 25 like cricket, 23 like football and 9 like both. How many like at least one of the two? (a) 48 (b) 49 (c) 30 (d) 39
25. 25.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 418 (c) 417 (d) 408
26. 26.Which term of the AP 20, 28, 36, 44, … is 116? (a) 13th (b) 15th (c) 14th (d) 12th
27. 27.What is the mode of 4, 7, 4, 18, 13, 4 and 7? (a) 13 (b) 18 (c) 4 (d) 7
28. 28.In which quadrant does the point (−3, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
29. 29.In a class of 37 children, 19 like tea, 21 like coffee and 6 like both. How many like at least one of the two? (a) 28 (b) 37 (c) 34 (d) 40
30. 30.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 150° (b) 210° (c) 30° (d) 60°
31. 31.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 55° (c) 80° (d) 125°
32. 32.What is the mean of 2, 13, 13 and 16? (a) 10 (b) 13 (c) 12 (d) 11
33. 33.What is the 14th term of the AP 5, 13, 21, 29, …? (a) 104 (b) 117 (c) 109 (d) 112
34. 34.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) 30° (d) 60°
35. 35.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
36. 36.A bag has 3 white, 2 yellow and 4 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 4/9 (b) 2/3 (c) 1/2 (d) 1/3
37. 37.What is the prime factorisation of 105? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3³ × 5 × 7
38. 38.A drawer has lots of red 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) 5 (c) 4 (d) 3
39. 39.The mean of 9 numbers is 24. When the number 14 is added to them, what is the new mean? (a) 22 (b) 23 (c) 24 (d) 19
40. 40.What is the midpoint of the line joining (4, 10) and (12, 2)? (a) (16, 12) (b) (8, 6) (c) (4, 4) (d) (6, 8)

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