Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 963 · 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 bag has 5 white, 6 green and 4 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/2 (b) 1/3 (c) 2/3 (d) 2/5
2. 2.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
4. 4.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
5. 5.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
6. 6.What is the median of 21, 38, 7, 15, 12, 13 and 30? (a) 16 (b) 21 (c) 13 (d) 15
7. 7.A bag has 6 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 13 (c) 8 (d) 7
8. 8.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2145 (c) 2178 (d) 4422
9. 9.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 80° (d) 100°
10. 10.In which quadrant does the point (2, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
11. 11.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 8)(x + 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
12. 12.What is the product of the roots of x² − 5x + 6 = 0? (a) 7 (b) 6 (c) 8 (d) 5
13. 13.What is the 32nd term of the AP 9, 18, 27, 36, …? (a) 288 (b) 297 (c) 289 (d) 279
14. 14.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 81 (d) 72
15. 15.In a class of 43 children, 17 like cricket, 23 like football and 6 like both. How many like at least one of the two? (a) 40 (b) 28 (c) 34 (d) 43
16. 16.What is the midpoint of the line joining (8, 7) and (12, 19)? (a) (2, 6) (b) (13, 10) (c) (20, 26) (d) (10, 13)
17. 17.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
18. 18.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
19. 19.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 210° (d) 31°
20. 20.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 36 sq cm (d) 27 sq cm
21. 21.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 70° (c) 130° (d) 110°
22. 22.Which term of the AP 15, 18, 21, 24, … is 39? (a) 9th (b) 13th (c) 8th (d) 10th
23. 23.In a class of 47 children, 29 like dance, 24 like music and 9 like both. How many like only dance? (a) 29 (b) 15 (c) 23 (d) 20
24. 24.What is the mean of 8, 4, 2 and 18? (a) 7 (b) 10 (c) 8 (d) 9
25. 25.If a + b = 5 and ab = 4, what is (a − b)²? (a) 25 (b) 3 (c) 17 (d) 9
26. 26.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
27. 27.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
28. 28.How many factors does 84 have? (a) 11 (b) 12 (c) 13 (d) 10
29. 29.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 99 (c) 33 (d) 11
30. 30.What is the mode of 20, 6, 3, 3, 6, 7 and 3? (a) 3 (b) 20 (c) 7 (d) 6
31. 31.If a + b = 9 and ab = 20, what is (a − b)²? (a) 81 (b) 41 (c) 61 (d) 1
32. 32.What is the midpoint of the line joining (8, 11) and (14, 1)? (a) (6, 11) (b) (11, 6) (c) (22, 12) (d) (3, 5)
33. 33.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 55 (d) 90
34. 34.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 1)(x + 10) (c) (x + 5)(x + 6) (d) (x + 1)(x + 30)
35. 35.A bag has 10 black balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 2 (c) 12 (d) 14
36. 36.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 55 (d) 100
37. 37.Which term of the AP 1, 4, 7, 10, … is 55? (a) 20th (b) 18th (c) 19th (d) 21st
38. 38.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 120 (d) 20
39. 39.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
40. 40.What is the midpoint of the line joining (2, 3) and (4, 1)? (a) (6, 4) (b) (1, 1) (c) (2, 3) (d) (3, 2)

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