Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 85 · 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 product of the roots of x² − 14x + 45 = 0? (a) 14 (b) 46 (c) 45 (d) 44
2. 2.In a class of 24 children, 6 like dance, 16 like music and 2 like both. How many like at least one of the two? (a) 22 (b) 24 (c) 20 (d) 18
3. 3.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) 10 (b) 90 (c) 33 (d) 30
4. 4.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 22 (d) 121
5. 5.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 100° (d) 145°
6. 6.In a class of 40 children, 19 like dance, 27 like music and 8 like both. How many like at least one of the two? (a) 40 (b) 38 (c) 30 (d) 46
7. 7.Which is the correct factorisation of x² + 12x + 32? (a) (x − 4)(x − 8) (b) (x + 4)(x + 8) (c) (x + 1)(x + 32) (d) (x + 1)(x + 11)
8. 8.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 105°
9. 9.What is the mean of 6, 8, 2, 4, 11 and 17? (a) 9 (b) 8 (c) 7 (d) 10
10. 10.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 48 (c) 135 (d) 15
11. 11.What is the mean of 4, 17, 17, 3, 2 and 11? (a) 11 (b) 10 (c) 9 (d) 8
12. 12.What is the median of 8, 33, 29, 28 and 11? (a) 29 (b) 11 (c) 27 (d) 28
13. 13.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
14. 14.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 1352 (d) 2756
15. 15.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 290° (c) 110° (d) 20°
16. 16.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
17. 17.A bag has 8 green, 7 red and 6 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/3 (b) 8/21 (c) 1/2 (d) 1/3
18. 18.A bag has 5 red balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 8 (c) 7 (d) 6
19. 19.A bag has 11 red balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 22 (b) 13 (c) 12 (d) 2
20. 20.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 14 (b) 12 (c) 11 (d) 10
21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 8 (d) 18
22. 22.There are 3 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) 21 (b) 10 (c) 24 (d) 42
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
24. 24.In which quadrant does the point (−2, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
25. 25.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) 37 (b) 36 (c) 25 (d) 24
26. 26.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) 36 (b) 37 (c) 48 (d) 49
27. 27.In a class of 26 children, 18 like dance, 11 like music and 8 like both. How many like only dance? (a) 10 (b) 18 (c) 3 (d) 15
28. 28.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
30. 30.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 11 (b) 13 (c) 12 (d) 18
31. 31.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
32. 32.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 165° (b) 130° (c) 15° (d) 65°
33. 33.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/6 (b) 5/6 (c) 1/5 (d) 1/3
34. 34.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 145° (d) 115°
35. 35.How many factors does 38 have? (a) 3 (b) 4 (c) 2 (d) 5
36. 36.What is the product of the roots of x² − 9x + 14 = 0? (a) 9 (b) 13 (c) 14 (d) 15
37. 37.What is the 37th term of the AP 16, 21, 26, 31, …? (a) 185 (b) 196 (c) 201 (d) 180
38. 38.A drawer has lots of red, blue, black, green 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) 2 (b) 6 (c) 5 (d) 10
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
40. 40.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9

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