Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 911 · 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 sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 153 (d) 33
2. 2.In which quadrant does the point (−7, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.A drawer has lots of black, green, red 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) 8 (b) 4 (c) 2 (d) 5
4. 4.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 165° (c) 30° (d) 16°
5. 5.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 75° (c) 105° (d) 15°
6. 6.A cuboid is 6 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 108 sq cm (b) 144 sq cm (c) 288 sq cm (d) 72 sq cm
7. 7.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 46 (c) 28 (d) 37
8. 8.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
9. 9.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 65°
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) 48 (b) 45 (c) 15 (d) 135
11. 11.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/6 (c) 1/5 (d) 5/6
12. 12.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 12 (d) 13
13. 13.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 4 (d) 2
14. 14.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x − 7)(x − 9) (c) (x + 1)(x + 15) (d) (x + 7)(x + 9)
15. 15.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 2 (d) 3
16. 16.What is the mean of 7, 3, 6, 9 and 10? (a) 6 (b) 9 (c) 8 (d) 7
17. 17.A bag has 4 yellow, 6 green and 7 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 11/17 (b) 10/17 (c) 7/17 (d) 1/3
18. 18.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 24 (c) 16 (d) 48
19. 19.A bag has 2 yellow, 6 blue and 9 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 8/17 (b) 1/3 (c) 9/17 (d) 10/17
20. 20.A bag has 4 white balls and 7 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) 5 (c) 8 (d) 2
21. 21.The mean of 4 numbers is 21. When the number 16 is added to them, what is the new mean? (a) 22 (b) 19 (c) 20 (d) 21
22. 22.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 25 (d) 120
23. 23.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
24. 24.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 5 (d) 1
25. 25.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 80° (b) 260° (c) 100° (d) 160°
26. 26.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 6 (d) 5
27. 27.A bag has 9 yellow balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 2 (c) 10 (d) 11
28. 28.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 196 (d) 182
29. 29.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 30 (b) 28 (c) 27 (d) 26
30. 30.What is the product of the roots of x² − 16x + 63 = 0? (a) 16 (b) 64 (c) 62 (d) 63
31. 31.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
32. 32.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 130° (b) 160° (c) 110° (d) 70°
33. 33.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 26 (b) 25 (c) 24 (d) 32
34. 34.Which is the correct factorisation of x² + 14x + 48? (a) (x − 6)(x − 8) (b) (x + 1)(x + 13) (c) (x + 1)(x + 48) (d) (x + 6)(x + 8)
35. 35.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72
36. 36.A bag has 2 blue, 7 white and 8 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 2/17 (c) 16/17 (d) 15/17
37. 37.In a class of 46 children, 22 like dance, 23 like music and 4 like both. How many like at least one of the two? (a) 41 (b) 45 (c) 46 (d) 37
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 15 (d) 16
39. 39.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) 37 (b) 36 (c) 48 (d) 49
40. 40.How many factors does 24 have? (a) 8 (b) 7 (c) 9 (d) 6

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