Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 552 · 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 70° and 70°. What is the third angle? (a) 110° (b) 40° (c) 220° (d) 140°
2. 2.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
3. 3.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 17 (c) 18 (d) 16
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
5. 5.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 140° (b) 160° (c) 60° (d) 120°
6. 6.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 85° (c) 95° (d) 5°
7. 7.The mean of 7 numbers is 36. When the number 52 is added to them, what is the new mean? (a) 44 (b) 38 (c) 39 (d) 36
8. 8.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 95° (b) 85° (c) 135° (d) 140°
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/12 (d) 1/11
10. 10.Which term of the AP 4, 7, 10, 13, … is 112? (a) 37th (b) 38th (c) 36th (d) 39th
11. 11.If a + b = 7 and ab = 10, what is (a − b)²? (a) 49 (b) 29 (c) 9 (d) 3
12. 12.What is the distance between the points (6, 14) and (18, 5)? (a) 225 (b) 16 (c) 15 (d) 21
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
14. 14.What is the median of 8, 33, 11, 1 and 13? (a) 13 (b) 12 (c) 8 (d) 11
15. 15.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 22 (c) 21 (d) 28
16. 16.What is the mean of 8, 16, 2, 10, 5 and 13? (a) 8 (b) 11 (c) 10 (d) 9
17. 17.In a class of 19 children, 8 like dance, 5 like music and 2 like both. How many like at least one of the two? (a) 9 (b) 13 (c) 19 (d) 11
18. 18.What is the median of 35, 25, 31, 39, 18, 10 and 24? (a) 31 (b) 25 (c) 26 (d) 39
19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
20. 20.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 140° (d) 115°
21. 21.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 319 (c) 318 (d) 309
22. 22.What is the median of 10, 12, 21, 19, 28, 7 and 39? (a) 21 (b) 19 (c) 20 (d) 12
23. 23.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/5 (c) 1/3 (d) 1/6
24. 24.What is the product of the roots of x² − 17x + 72 = 0? (a) 17 (b) 71 (c) 73 (d) 72
25. 25.What is the sum of the roots of x² − 11x + 28 = 0? (a) 11 (b) 28 (c) 12 (d) 10
26. 26.A bag has 10 black balls and 11 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) 12 (c) 21 (d) 11
27. 27.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 16 (b) 22 (c) 18 (d) 17
28. 28.In a class of 33 children, 26 like tea, 14 like coffee and 8 like both. How many like at least one of the two? (a) 24 (b) 33 (c) 40 (d) 32
29. 29.In which quadrant does the point (5, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
30. 30.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 189 (c) 66 (d) 63
31. 31.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 1)(x + 15) (c) (x + 1)(x + 7) (d) (x + 3)(x + 5)
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/9 (c) 1/11 (d) 4/11
33. 33.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 1 (d) 4
34. 34.In a class of 35 children, 19 like mangoes, 25 like bananas and 10 like both. How many like at least one of the two? (a) 34 (b) 44 (c) 24 (d) 35
35. 35.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
36. 36.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4
37. 37.What is the 14th term of the AP 2, 10, 18, 26, …? (a) 104 (b) 112 (c) 106 (d) 114
38. 38.What is the 29th term of the AP 11, 16, 21, 26, …? (a) 145 (b) 140 (c) 151 (d) 156
39. 39.What is the distance between the points (9, 5) and (25, 17)? (a) 20 (b) 400 (c) 28 (d) 21
40. 40.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 7/8 (c) 1/4 (d) 3/8

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