Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 601 · 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.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 144 (d) 48
2. 2.What is the 31st term of the AP 12, 18, 24, 30, …? (a) 198 (b) 192 (c) 180 (d) 186
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
4. 4.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 240° (d) 60°
5. 5.The mean of 6 numbers is 24. When the number 17 is added to them, what is the new mean? (a) 24 (b) 22 (c) 23 (d) 25
6. 6.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
7. 7.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 10 (c) 15 (d) 20
8. 8.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 1089 (b) 739 (c) 891 (d) 729
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
10. 10.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 627 (c) 496 (d) 636
11. 11.In a class of 22 children, 14 like tea, 8 like coffee and 5 like both. How many like only tea? (a) 5 (b) 14 (c) 3 (d) 9
12. 12.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 225° (c) 45° (d) 135°
13. 13.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 158 (c) 166 (d) 148
14. 14.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 704 (b) 385 (c) 62 (d) 352
15. 15.What is the prime factorisation of 35? (a) 5 × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5² × 7
16. 16.In a class of 41 children, 22 like dance, 19 like music and 3 like both. How many like only dance? (a) 19 (b) 3 (c) 16 (d) 22
17. 17.In which quadrant does the point (−9, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
18. 18.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 61 (b) 804 (c) 432 (d) 402
19. 19.What is the median of 40, 23, 36, 30 and 33? (a) 36 (b) 33 (c) 34 (d) 30
20. 20.What is the midpoint of the line joining (8, 9) and (10, 19)? (a) (1, 5) (b) (14, 9) (c) (18, 28) (d) (9, 14)
21. 21.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 30°
22. 22.What is the distance between the points (8, 0) and (12, 3)? (a) 25 (b) 7 (c) 5 (d) 6
23. 23.What is the smallest prime factor of 33? (a) 1 (b) 3 (c) 11 (d) 2
24. 24.If a + b = 8 and ab = 12, what is a² + b²? (a) 64 (b) 52 (c) 88 (d) 40
25. 25.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
26. 26.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2⁴ × 5 (d) 2 × 5³
27. 27.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) 24 (b) 7 (c) 21 (d) 63
28. 28.A bag has 11 black balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 19 (b) 13 (c) 12 (d) 2
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
30. 30.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 140° (c) 280° (d) 100°
31. 31.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 51 (d) 54
32. 32.What is the product of the roots of x² − 7x + 12 = 0? (a) 7 (b) 12 (c) 11 (d) 13
33. 33.If a + b = 11 and ab = 18, what is a² + b²? (a) 85 (b) 157 (c) 103 (d) 121
34. 34.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
35. 35.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
36. 36.In which quadrant does the point (9, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
37. 37.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
38. 38.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 12 (d) 48
39. 39.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 8)(x + 9)
40. 40.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10

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