Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 394 · 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 team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 15 (d) 36
2. 2.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
5. 5.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
6. 6.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
7. 7.What is the 25th term of the AP 6, 12, 18, 24, …? (a) 144 (b) 150 (c) 151 (d) 156
8. 8.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 140° (d) 70°
9. 9.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) 40 (b) 48 (c) 13 (d) 80
10. 10.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5³
11. 11.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 210 (d) 105
12. 12.If a + b = 19 and ab = 90, what is (a − b)²? (a) 181 (b) 361 (c) 1 (d) 271
13. 13.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
14. 14.In a class of 25 children, 16 like maths, 13 like science and 8 like both. How many like at least one of the two? (a) 13 (b) 29 (c) 25 (d) 21
15. 15.In which quadrant does the point (−9, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
16. 16.A bag has 6 black balls and 5 yellow 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) 6 (c) 2 (d) 7
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
18. 18.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/8 (c) 1/4 (d) 1/7
19. 19.What is the midpoint of the line joining (10, 7) and (20, 13)? (a) (5, 3) (b) (15, 10) (c) (30, 20) (d) (10, 15)
20. 20.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 55° (d) 70°
21. 21.What is the midpoint of the line joining (3, 18) and (7, 8)? (a) (2, 5) (b) (5, 13) (c) (13, 5) (d) (10, 26)
22. 22.What is the midpoint of the line joining (1, 17) and (3, 7)? (a) (1, 5) (b) (2, 12) (c) (4, 24) (d) (12, 2)
23. 23.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 8 (c) 7 (d) 15
24. 24.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 16 (d) 56
25. 25.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
26. 26.A bag has 8 red, 8 white and 6 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 7/11 (c) 4/7 (d) 4/11
27. 27.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/8 (d) 1/4
28. 28.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 21 (c) 22 (d) 14
29. 29.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 70 (b) 20 (c) 60 (d) 120
30. 30.A bag has 7 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 15 (c) 2 (d) 9
31. 31.How many prime numbers are there between 70 and 80? (a) 4 (b) 2 (c) 5 (d) 3
32. 32.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 182 (c) 196 (d) 105
33. 33.What is the mode of 13, 13, 4, 2, 11, 2 and 13? (a) 2 (b) 4 (c) 11 (d) 13
34. 34.What is the distance between the points (3, 9) and (11, 24)? (a) 17 (b) 23 (c) 289 (d) 18
35. 35.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
36. 36.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 9 (c) 25 (d) 20
37. 37.What is the smallest prime factor of 145? (a) 1 (b) 5 (c) 29 (d) 2
38. 38.What is the 26th term of the AP 11, 15, 19, 23, …? (a) 104 (b) 100 (c) 111 (d) 115
39. 39.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
40. 40.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 6416 (b) 7056 (c) 5776 (d) 7066

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