Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 629 · 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.In which quadrant does the point (2, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
2. 2.What is the prime factorisation of 180? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2³ × 3² × 5
3. 3.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
4. 4.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) 7 (b) 14 (c) 8 (d) 15
5. 5.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 280° (c) 40° (d) 100°
6. 6.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
7. 7.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
8. 8.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 72 (d) 81
9. 9.What is the sum of the roots of x² − 10x + 24 = 0? (a) 10 (b) 24 (c) 9 (d) 11
10. 10.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 36 (d) 18
11. 11.What is the midpoint of the line joining (9, 5) and (11, 1)? (a) (20, 6) (b) (10, 3) (c) (1, 2) (d) (3, 10)
12. 12.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 100° (d) 145°
13. 13.A drawer has lots of blue, yellow, black, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 10 (d) 6
14. 14.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 405 (c) 348 (d) 415
15. 15.How many prime numbers are there between 20 and 40? (a) 3 (b) 4 (c) 6 (d) 5
16. 16.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 216 cu cm (d) 217 cu cm
17. 17.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
18. 18.What is the distance between the points (9, 13) and (21, 4)? (a) 16 (b) 15 (c) 21 (d) 225
19. 19.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 70° (d) 20°
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/18 (c) 2/11 (d) 1/11
21. 21.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
22. 22.A drawer has lots of red, black 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) 6 (b) 4 (c) 3 (d) 2
23. 23.What is the product of the roots of x² − 11x + 28 = 0? (a) 28 (b) 27 (c) 11 (d) 29
24. 24.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
25. 25.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
26. 26.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 35) (b) (x + 5)(x + 7) (c) (x − 5)(x − 7) (d) (x + 1)(x + 11)
27. 27.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
29. 29.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 240 (d) 20
30. 30.What is the mode of 12, 16, 19, 1, 16, 19 and 19? (a) 12 (b) 1 (c) 19 (d) 16
31. 31.How many factors does 119 have? (a) 5 (b) 2 (c) 3 (d) 4
32. 32.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 49 (c) 37 (d) 36
33. 33.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
34. 34.A cuboid is 9 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 234 cu cm (b) 20 cu cm (c) 18 cu cm (d) 162 cu cm
35. 35.A bag has 3 yellow balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 5 (c) 14 (d) 4
36. 36.There are 7 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) 42 (b) 10 (c) 28 (d) 21
37. 37.What is the distance between the points (3, 6) and (15, 22)? (a) 21 (b) 28 (c) 20 (d) 400
38. 38.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 42 (c) 49 (d) 21
39. 39.In a class of 45 children, 26 like dance, 22 like music and 6 like both. How many like at least one of the two? (a) 45 (b) 36 (c) 42 (d) 48
40. 40.In a class of 30 children, 10 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 22 (b) 30 (c) 27 (d) 26

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