Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 556 · 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.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 105° (c) 75° (d) 145°
2. 2.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 105° (c) 75° (d) 285°
3. 3.Which is the correct factorisation of x² + 15x + 54? (a) (x + 6)(x + 9) (b) (x + 1)(x + 14) (c) (x + 1)(x + 54) (d) (x − 6)(x − 9)
4. 4.What is the mode of 4, 20, 20, 3, 3, 5 and 3? (a) 3 (b) 20 (c) 5 (d) 4
5. 5.What is the mode of 17, 9, 19, 1, 9, 1 and 1? (a) 9 (b) 19 (c) 17 (d) 1
6. 6.A bag has 8 green, 3 yellow and 3 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 4/7 (b) 3/7 (c) 3/4 (d) 1/3
7. 7.A bag has 6 white, 4 green and 2 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 7/12 (b) 1/2 (c) 1/3 (d) 1/12
8. 8.In a class of 32 children, 16 like dance, 24 like music and 11 like both. How many like neither? (a) 11 (b) 14 (c) 3 (d) 4
9. 9.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
10. 10.What is the smallest prime factor of 85? (a) 17 (b) 1 (c) 5 (d) 2
11. 11.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 10201 (b) 9999 (c) 9811 (d) 9801
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 7/36 (c) 1/6 (d) 6/11
13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
14. 14.What is the product of the roots of x² − 11x + 18 = 0? (a) 17 (b) 18 (c) 11 (d) 19
15. 15.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 7/8 (d) 1/7
16. 16.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 33 (c) 90 (d) 10
17. 17.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 55 (d) 66
18. 18.A bag has 10 blue balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 2 (c) 13 (d) 12
19. 19.In a class of 42 children, 24 like tea, 18 like coffee and 5 like both. How many like neither? (a) 10 (b) 6 (c) 0 (d) 5
20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
21. 21.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 36 (c) 30 (d) 60
22. 22.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 64 (c) 28 (d) 36
23. 23.What is the mode of 18, 13, 13, 5, 16, 5 and 13? (a) 16 (b) 18 (c) 13 (d) 5
24. 24.A bag has 5 green, 3 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 9/11 (b) 3/11 (c) 8/11 (d) 1/3
25. 25.If a + b = 21 and ab = 108, what is a² + b²? (a) 441 (b) 333 (c) 225 (d) 657
26. 26.What is the mode of 4, 4, 17, 7, 12, 7 and 7? (a) 12 (b) 7 (c) 17 (d) 4
27. 27.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 36 (d) 21
28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
29. 29.What is the smallest prime factor of 49? (a) 7 (b) 2 (c) 3 (d) 1
30. 30.What is the mode of 10, 14, 20, 10, 1, 20 and 20? (a) 10 (b) 20 (c) 14 (d) 1
31. 31.What is the midpoint of the line joining (0, 15) and (6, 7)? (a) (3, 4) (b) (11, 3) (c) (6, 22) (d) (3, 11)
32. 32.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 112 (b) 56 (c) 64 (d) 15
33. 33.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
34. 34.Which term of the AP 19, 21, 23, 25, … is 87? (a) 34th (b) 36th (c) 37th (d) 35th
35. 35.What is the midpoint of the line joining (4, 9) and (10, 3)? (a) (14, 12) (b) (7, 6) (c) (3, 3) (d) (6, 7)
36. 36.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 36 (d) 12
37. 37.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 20 (c) 60 (d) 180
38. 38.In which quadrant does the point (−9, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
39. 39.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 50° (d) 25°
40. 40.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 4 (d) 2

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