Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 572 · 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.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 72 (c) 36 (d) 42
2. 2.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 140° (d) 70°
3. 3.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 132 (d) 66
4. 4.What is the sum of the roots of x² − 14x + 45 = 0? (a) 45 (b) 13 (c) 15 (d) 14
5. 5.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 9 (c) 25 (d) 20
6. 6.In a class of 42 children, 24 like maths, 28 like science and 11 like both. How many like neither? (a) 11 (b) 1 (c) 12 (d) 2
7. 7.How many prime numbers are there between 60 and 70? (a) 4 (b) 3 (c) 2 (d) 1
8. 8.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 4 (d) 1
9. 9.What is the median of 13, 33, 4, 18 and 10? (a) 10 (b) 4 (c) 18 (d) 13
10. 10.If a + b = 20 and ab = 96, what is (a − b)²? (a) 400 (b) 16 (c) 208 (d) 4
11. 11.What is the midpoint of the line joining (9, 0) and (19, 8)? (a) (5, 4) (b) (4, 14) (c) (28, 8) (d) (14, 4)
12. 12.A bag has 6 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 7 (b) 2 (c) 9 (d) 8
13. 13.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
14. 14.A drawer has lots of blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 5 (c) 2 (d) 4
15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 8 (c) 6 (d) 7
16. 16.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
18. 18.If a + b = 8 and ab = 15, what is a² + b²? (a) 64 (b) 94 (c) 49 (d) 34
19. 19.What is the smallest prime factor of 299? (a) 23 (b) 13 (c) 2 (d) 1
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
21. 21.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 24 (c) 27 (d) 72
22. 22.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 25° (d) 130°
23. 23.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 9) (b) (x + 3)(x + 7) (c) (x − 3)(x − 7) (d) (x + 1)(x + 21)
24. 24.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
25. 25.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 160° (b) 55° (c) 75° (d) 125°
26. 26.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 42 (b) 43 (c) 52 (d) 44
27. 27.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
28. 28.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
29. 29.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 77 (b) 78 (c) 14 (d) 154
30. 30.How many factors does 41 have? (a) 2 (b) 1 (c) 3 (d) 4
31. 31.What is the 18th term of the AP 1, 5, 9, 13, …? (a) 72 (b) 69 (c) 68 (d) 73
32. 32.In which quadrant does the point (−7, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
34. 34.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3
35. 35.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 93 (c) 94 (d) 102
36. 36.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
37. 37.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 5/6 (c) 2/3 (d) 1/3
38. 38.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) 27 times (c) 9 times (d) 6 times
39. 39.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 85° (d) 15°
40. 40.What is the 34th term of the AP 1, 7, 13, 19, …? (a) 198 (b) 205 (c) 204 (d) 199

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