Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 413 · 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 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
2. 2.A bag has 4 red, 3 white and 7 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 3/14 (c) 3/11 (d) 11/14
3. 3.What is the smallest prime factor of 93? (a) 31 (b) 3 (c) 2 (d) 1
4. 4.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 95° (d) 140°
5. 5.In a class of 29 children, 12 like cricket, 14 like football and 9 like neither. How many like both? (a) 7 (b) 9 (c) 6 (d) 20
6. 6.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 40 (d) 70
7. 7.In a class of 45 children, 19 like dance, 21 like music and 8 like neither. How many like both? (a) 3 (b) 4 (c) 37 (d) 8
8. 8.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 15° (c) 30° (d) 165°
9. 9.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
10. 10.What is the mode of 5, 5, 10, 9, 14, 9 and 9? (a) 10 (b) 9 (c) 5 (d) 14
11. 11.A bag has 10 blue balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 12 (c) 18 (d) 11
12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 72 (d) 36
14. 14.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 66 (b) 132 (c) 67 (d) 11
15. 15.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 135° (d) 75°
16. 16.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
18. 18.In which quadrant does the point (1, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
19. 19.A bag has 4 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 5 (c) 14 (d) 6
20. 20.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 6416 (b) 7066 (c) 5776 (d) 7056
21. 21.In which quadrant does the point (−5, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
22. 22.A bag has 6 yellow, 9 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/9 (b) 1/18 (c) 1/2 (d) 1/3
23. 23.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 300° (c) 30° (d) 60°
24. 24.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 486 cu cm (d) 324 cu cm
25. 25.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
26. 26.If a + b = 15 and ab = 56, what is (a − b)²? (a) 225 (b) 1 (c) 113 (d) 169
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 7/36 (d) 1/6
28. 28.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 8 (d) 6
29. 29.What are the roots of x² − 13x + 36 = 0? (a) 1 and 36 (b) 1 and 12 (c) 2 and 18 (d) 4 and 9
30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 5 (c) 9 (d) 10
31. 31.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) 30 (c) 9 (d) 27
32. 32.A bag has 5 red balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 4 (c) 6 (d) 2
33. 33.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 55 (c) 110 (d) 22
34. 34.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6399 (b) 6251 (c) 6561 (d) 6241
35. 35.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 65° (d) 130°
36. 36.What is the mean of 11, 6, 7, 8 and 18? (a) 9 (b) 12 (c) 10 (d) 11
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/36 (d) 5/11
38. 38.A bag has 9 red balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 19 (b) 11 (c) 2 (d) 10
39. 39.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 144 sq cm (d) 216 sq cm
40. 40.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5 × 7² (c) 5 × 7 (d) 5² × 7

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