Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 579 · 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 straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 170° (c) 10° (d) 11°
2. 2.How many factors does 12 have? (a) 5 (b) 4 (c) 6 (d) 7
3. 3.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 7921 (b) 8281 (c) 8101 (d) 8291
4. 4.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
5. 5.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 90 (d) 20
6. 6.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 95° (b) 60° (c) 145° (d) 120°
7. 7.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
8. 8.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) 66 (c) 189 (d) 63
9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 15 (d) 13
10. 10.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 425 (b) 225 (c) 625 (d) 635
11. 11.How many prime numbers are there between 40 and 50? (a) 5 (b) 4 (c) 2 (d) 3
12. 12.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 30 (d) 27
13. 13.The mean of 8 numbers is 28. When the number 19 is added to them, what is the new mean? (a) 28 (b) 29 (c) 26 (d) 27
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
15. 15.How many factors does 90 have? (a) 11 (b) 12 (c) 13 (d) 10
16. 16.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3200 (d) 3240
17. 17.How many prime numbers are there between 40 and 60? (a) 6 (b) 4 (c) 5 (d) 7
18. 18.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
19. 19.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 148 (c) 157 (d) 166
20. 20.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 40° (d) 30°
21. 21.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 619 (c) 618 (d) 609
22. 22.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 366 (b) 396 (c) 58 (d) 732
23. 23.A drawer has lots of yellow, white, red and blue 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) 2 (d) 8
24. 24.What is the missing term in the AP 17, 24, 31, ?, 45? (a) 39 (b) 45 (c) 37 (d) 38
25. 25.What is the median of 10, 13, 37, 23 and 16? (a) 23 (b) 16 (c) 13 (d) 37
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
27. 27.In a class of 26 children, 13 like dance, 9 like music and 9 like neither. How many like both? (a) 6 (b) 5 (c) 17 (d) 9
28. 28.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 80° (b) 120° (c) 20° (d) 160°
29. 29.A bag has 4 white, 2 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/9 (b) 1/9 (c) 2/3 (d) 1/3
30. 30.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 265° (d) 86°
31. 31.What is the midpoint of the line joining (6, 4) and (12, 10)? (a) (18, 14) (b) (7, 9) (c) (9, 7) (d) (3, 3)
32. 32.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1250 (c) 1225 (d) 2550
33. 33.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 145° (c) 215° (d) 35°
34. 34.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
35. 35.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
36. 36.In a class of 45 children, 23 like mangoes, 20 like bananas and 8 like both. How many like at least one of the two? (a) 45 (b) 35 (c) 27 (d) 43
37. 37.What is the median of 14, 4, 24, 32 and 27? (a) 27 (b) 25 (c) 14 (d) 24
38. 38.In a class of 27 children, 18 like maths, 11 like science and 6 like both. How many like neither? (a) 10 (b) 6 (c) 5 (d) 4
39. 39.In which quadrant does the point (1, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.What is the 11th term of the AP 8, 12, 16, 20, …? (a) 48 (b) 44 (c) 52 (d) 40

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