Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 48 · 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 80° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 35° (c) 145° (d) 100°
2. 2.The numbers 3 to 11 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) 21 (c) 24 (d) 7
3. 3.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/6 (c) 5/6 (d) 1/5
4. 4.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 5 (d) 3
5. 5.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 72 (c) 27 (d) 24
6. 6.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
7. 7.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 42 (c) 52 (d) 51
8. 8.In a class of 36 children, 20 like mangoes, 12 like bananas and 3 like both. How many like neither? (a) 4 (b) 3 (c) 7 (d) 10
9. 9.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 40° (d) 80°
10. 10.What is the distance between the points (1, 19) and (6, 7)? (a) 13 (b) 17 (c) 169 (d) 14
11. 11.In a class of 32 children, 22 like cricket, 17 like football and 2 like neither. How many like both? (a) 30 (b) 7 (c) 9 (d) 2
12. 12.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
14. 14.What is the mean of 6, 12, 10 and 20? (a) 16 (b) 12 (c) 13 (d) 11
15. 15.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
16. 16.A drawer has lots of blue and red 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) 3 (c) 5 (d) 4
17. 17.A drawer has lots of red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 5 (d) 2
18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 3 (c) 14 (d) 15
19. 19.A bag has 2 green, 5 white and 6 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/11 (b) 2/13 (c) 1/3 (d) 11/13
20. 20.In a class of 45 children, 23 like maths, 30 like science and 12 like both. How many like at least one of the two? (a) 29 (b) 45 (c) 41 (d) 53
21. 21.What is the midpoint of the line joining (2, 1) and (6, 9)? (a) (5, 4) (b) (8, 10) (c) (4, 5) (d) (2, 4)
22. 22.A bag has 3 red 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) 11 (b) 2 (c) 13 (d) 4
23. 23.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 7931 (b) 8099 (c) 8281 (d) 7921
24. 24.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 120° (b) 155° (c) 145° (d) 60°
25. 25.In a class of 30 children, 21 like mangoes, 7 like bananas and 2 like both. How many like only mangoes? (a) 5 (b) 23 (c) 21 (d) 19
26. 26.A bag has 5 yellow balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 6 (c) 11 (d) 2
27. 27.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 80° (d) 145°
28. 28.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 49 (d) 14
29. 29.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/4 (c) 7/8 (d) 1/7
30. 30.In a class of 34 children, 14 like tea, 16 like coffee and 6 like neither. How many like both? (a) 2 (b) 28 (c) 6 (d) 3
31. 31.What is the mode of 14, 7, 7, 12, 7, 9 and 12? (a) 9 (b) 7 (c) 12 (d) 14
32. 32.If a + b = 19 and ab = 90, what is (a − b)²? (a) 361 (b) 271 (c) 1 (d) 181
33. 33.A bag has 6 red, 2 green and 9 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/17 (b) 10/17 (c) 1/3 (d) 9/17
34. 34.A drawer has lots of green, white, blue, red and black 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) 10 (c) 2 (d) 5
35. 35.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
37. 37.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 1/12 (c) 1/11 (d) 2/11
39. 39.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 100° (b) 125° (c) 45° (d) 135°
40. 40.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 24) (b) (x + 3)(x + 8) (c) (x − 3)(x − 8) (d) (x + 1)(x + 10)

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