Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 977 · 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 median of 3, 19, 2, 26 and 8? (a) 2 (b) 19 (c) 3 (d) 8
2. 2.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7
3. 3.What is the product of the roots of x² − 11x + 30 = 0? (a) 30 (b) 29 (c) 31 (d) 11
4. 4.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 36 (d) 25
5. 5.If a + b = 12 and ab = 35, what is (a − b)²? (a) 4 (b) 2 (c) 144 (d) 74
6. 6.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 409 (b) 289 (c) 539 (d) 529
7. 7.What is the 18th term of the AP 6, 15, 24, 33, …? (a) 162 (b) 153 (c) 168 (d) 159
8. 8.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 50° (b) 25° (c) 205° (d) 155°
9. 9.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 17 (d) 2
10. 10.In a class of 45 children, 19 like tea, 27 like coffee and 8 like both. How many like at least one of the two? (a) 30 (b) 38 (c) 45 (d) 46
11. 11.In a class of 20 children, 13 like mangoes, 13 like bananas and 1 like neither. How many like both? (a) 7 (b) 19 (c) 6 (d) 1
12. 12.A bag has 10 white balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 13 (c) 2 (d) 22
13. 13.What are the roots of x² − 15x + 54 = 0? (a) 1 and 54 (b) 2 and 27 (c) 6 and 9 (d) 1 and 14
14. 14.In a class of 29 children, 7 like mangoes, 15 like bananas and 9 like neither. How many like both? (a) 9 (b) 3 (c) 20 (d) 2
15. 15.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2 × 5 × 7³
16. 16.In which quadrant does the point (1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
17. 17.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 66 (c) 57 (d) 58
18. 18.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 110° (d) 130°
19. 19.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 74 (b) 492 (c) 984 (d) 528
20. 20.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
21. 21.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
22. 22.A bag has 6 white, 6 red and 3 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/5 (b) 1/3 (c) 2/3 (d) 2/5
23. 23.What is the 12th term of the AP 10, 16, 22, 28, …? (a) 72 (b) 82 (c) 76 (d) 66
24. 24.3 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 9 (c) 21 (d) 36
25. 25.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 80 (b) 13 (c) 40 (d) 48
26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
28. 28.What is the smallest prime factor of 377? (a) 1 (b) 29 (c) 13 (d) 2
29. 29.The mean of 6 numbers is 15. When the number 29 is added to them, what is the new mean? (a) 15 (b) 22 (c) 17 (d) 18
30. 30.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
31. 31.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 156 (d) 91
32. 32.In a class of 33 children, 17 like maths, 22 like science and 6 like neither. How many like both? (a) 13 (b) 27 (c) 6 (d) 12
33. 33.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
34. 34.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 110 (c) 121 (d) 55
35. 35.A bag has 3 red, 8 white and 3 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 3/11 (b) 11/14 (c) 1/3 (d) 3/14
36. 36.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 18 (d) 72
37. 37.A bag has 4 blue balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 5 (c) 2 (d) 15
38. 38.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 125° (d) 270°
39. 39.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) 51 (b) 16 (c) 48 (d) 144
40. 40.What is the smallest prime factor of 65? (a) 13 (b) 2 (c) 5 (d) 1

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