Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 878 · 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 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
2. 2.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 55° (c) 125° (d) 135°
3. 3.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 100 (b) 29 (c) 95 (d) 190
4. 4.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 276 (c) 552 (d) 277
5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 8 (b) 6 (c) 7 (d) 9
6. 6.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 13 (b) 15 (c) 14 (d) 21
7. 7.If a + b = 11 and ab = 24, what is (a − b)²? (a) 121 (b) 25 (c) 73 (d) 5
8. 8.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 132 (d) 24
9. 9.In a class of 34 children, 27 like mangoes, 13 like bananas and 9 like both. How many like neither? (a) 3 (b) 9 (c) 12 (d) 4
10. 10.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 2862 (c) 1431 (d) 1432
11. 11.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 90 (d) 45
12. 12.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 504 (c) 252 (d) 48
13. 13.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 308 (b) 616 (c) 48 (d) 330
14. 14.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 6) (b) (x − 2)(x − 5) (c) (x + 1)(x + 10) (d) (x + 2)(x + 5)
15. 15.What is the mode of 14, 3, 10, 10, 10, 5 and 3? (a) 10 (b) 3 (c) 5 (d) 14
16. 16.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 140° (b) 15° (c) 165° (d) 55°
17. 17.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
18. 18.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 16 (d) 64
19. 19.A bag has 9 blue balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 18 (c) 11 (d) 10
20. 20.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) 1/2 (d) 1/3
21. 21.In a class of 43 children, 23 like mangoes, 23 like bananas and 10 like both. How many like only mangoes? (a) 20 (b) 23 (c) 13 (d) 10
22. 22.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
23. 23.What is the smallest prime factor of 91? (a) 13 (b) 1 (c) 7 (d) 2
24. 24.In which quadrant does the point (1, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
25. 25.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 15 (c) 20 (d) 30
26. 26.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1584 (b) 1936 (c) 1296 (d) 1306
27. 27.In a class of 37 children, 15 like cricket, 17 like football and 2 like both. How many like at least one of the two? (a) 37 (b) 32 (c) 28 (d) 30
28. 28.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
29. 29.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 125° (d) 80°
30. 30.How many factors does 89 have? (a) 4 (b) 2 (c) 3 (d) 1
31. 31.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
32. 32.In a class of 31 children, 18 like cricket, 20 like football and 11 like both. How many like at least one of the two? (a) 27 (b) 16 (c) 38 (d) 31
33. 33.How many factors does 23 have? (a) 1 (b) 2 (c) 4 (d) 3
34. 34.In a class of 46 children, 28 like tea, 21 like coffee and 8 like both. How many like at least one of the two? (a) 33 (b) 41 (c) 49 (d) 46
35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 10 (b) 12 (c) 13 (d) 9
37. 37.What is the midpoint of the line joining (7, 3) and (17, 15)? (a) (9, 12) (b) (5, 6) (c) (24, 18) (d) (12, 9)
38. 38.The mean of 4 numbers is 22. When the number 27 is added to them, what is the new mean? (a) 25 (b) 22 (c) 24 (d) 23
39. 39.A drawer has lots of 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) 4 (b) 3 (c) 5 (d) 2
40. 40.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3854 (b) 3844 (c) 3364 (d) 3604

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