Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 287 · 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.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 21 (d) 42
2. 2.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 125° (c) 70° (d) 250°
3. 3.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 150° (b) 270° (c) 120° (d) 90°
4. 4.How many prime numbers are there between 50 and 80? (a) 7 (b) 6 (c) 9 (d) 8
5. 5.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 5 (b) 12 (c) 9 (d) 6
6. 6.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 444 (c) 374 (d) 453
7. 7.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
8. 8.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 63 (c) 24 (d) 21
9. 9.The mean of 8 numbers is 27. When the number 36 is added to them, what is the new mean? (a) 30 (b) 28 (c) 29 (d) 27
10. 10.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 290° (c) 145° (d) 35°
11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
12. 12.If a + b = 20 and ab = 99, what is (a − b)²? (a) 202 (b) 400 (c) 2 (d) 4
13. 13.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 16 (c) 72 (d) 17
14. 14.In a class of 25 children, 15 like tea, 15 like coffee and 6 like both. How many like neither? (a) 2 (b) 7 (c) 1 (d) 6
15. 15.In which quadrant does the point (4, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
17. 17.If a + b = 10 and ab = 21, what is (a − b)²? (a) 58 (b) 100 (c) 4 (d) 16
18. 18.If a + b = 15 and ab = 56, what is a² + b²? (a) 225 (b) 113 (c) 337 (d) 169
19. 19.What is the median of 25, 36, 21, 13 and 31? (a) 25 (b) 31 (c) 21 (d) 26
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/12 (c) 1/18 (d) 1/36
21. 21.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/4 (b) 1/3 (c) 5/6 (d) 2/3
22. 22.In a class of 35 children, 26 like dance, 19 like music and 2 like neither. How many like both? (a) 2 (b) 12 (c) 10 (d) 33
23. 23.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 10° (d) 85°
24. 24.If a + b = 19 and ab = 84, what is a² + b²? (a) 361 (b) 277 (c) 193 (d) 529
25. 25.A drawer has lots of green, black, blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 4 (d) 8
26. 26.A drawer has lots of blue, red, 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) 5 (b) 4 (c) 2 (d) 8
27. 27.What is the median of 9, 2, 18, 8 and 11? (a) 11 (b) 8 (c) 18 (d) 9
28. 28.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 12 (d) 36
29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
30. 30.How many factors does 103 have? (a) 3 (b) 1 (c) 4 (d) 2
31. 31.How many factors does 18 have? (a) 7 (b) 5 (c) 4 (d) 6
32. 32.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 80 sq cm (b) 40 sq cm (c) 48 sq cm (d) 160 sq cm
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 1/11 (d) 6/11
34. 34.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/3 (b) 5/6 (c) 1/5 (d) 1/6
35. 35.A bag has 4 yellow, 7 red and 8 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 12/19 (c) 7/19 (d) 7/12
36. 36.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 24 (d) 66
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 18 (d) 19
38. 38.A cuboid is 8 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 46 sq cm (b) 92 sq cm (c) 48 sq cm (d) 184 sq cm
39. 39.A bag has 12 yellow balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 10 (c) 2 (d) 13
40. 40.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 16 (c) 32 (d) 10

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