Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 486 · 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 31st term of the AP 5, 11, 17, 23, …? (a) 185 (b) 186 (c) 180 (d) 191
2. 2.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
3. 3.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 198 (c) 66 (d) 22
4. 4.How many factors does 113 have? (a) 1 (b) 4 (c) 2 (d) 3
5. 5.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
6. 6.A bag has 11 blue balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 12 (c) 2 (d) 19
7. 7.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
8. 8.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 90° (c) 140° (d) 270°
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
10. 10.What is the 35th term of the AP 18, 22, 26, 30, …? (a) 136 (b) 154 (c) 140 (d) 158
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
12. 12.What is the distance between the points (3, 14) and (15, 9)? (a) 14 (b) 17 (c) 169 (d) 13
13. 13.In a class of 24 children, 17 like tea, 14 like coffee and 9 like both. How many like at least one of the two? (a) 13 (b) 31 (c) 24 (d) 22
14. 14.What is the product of the roots of x² − 12x + 27 = 0? (a) 28 (b) 27 (c) 26 (d) 12
15. 15.A bag has 6 blue, 8 yellow and 3 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/17 (b) 9/17 (c) 8/9 (d) 1/3
16. 16.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 3 (d) 6
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
18. 18.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) 12 (b) 24 (c) 13 (d) 25
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
20. 20.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 35° (b) 75° (c) 140° (d) 145°
21. 21.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 10 (c) 30 (d) 48
22. 22.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 14 (c) 40 (d) 80
23. 23.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
24. 24.What is the midpoint of the line joining (7, 11) and (13, 1)? (a) (6, 10) (b) (3, 5) (c) (20, 12) (d) (10, 6)
25. 25.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 1)(x + 42) (c) (x + 1)(x + 12) (d) (x + 6)(x + 7)
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 day of the week? (a) 21 (b) 29 (c) 28 (d) 22
27. 27.In a class of 41 children, 21 like maths, 15 like science and 3 like both. How many like at least one of the two? (a) 30 (b) 33 (c) 36 (d) 41
28. 28.What is the distance between the points (6, 4) and (22, 16)? (a) 20 (b) 28 (c) 400 (d) 21
29. 29.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
30. 30.In a class of 24 children, 10 like cricket, 12 like football and 5 like both. How many like at least one of the two? (a) 22 (b) 24 (c) 17 (d) 12
31. 31.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 55 (c) 100 (d) 90
32. 32.What is the smallest prime factor of 161? (a) 1 (b) 23 (c) 2 (d) 7
33. 33.The numbers 5 to 13 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) 9 (c) 27 (d) 81
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 13 (d) 14
35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 5 (b) 8 (c) 7 (d) 6
36. 36.A bag has 4 yellow balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 2 (c) 5 (d) 6
37. 37.What is the prime factorisation of 18? (a) 2 × 3² (b) 2 × 3³ (c) 2² × 3² (d) 2² × 3
38. 38.What is the distance between the points (3, 7) and (7, 10)? (a) 7 (b) 5 (c) 6 (d) 25
39. 39.A bag has 3 yellow balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 4 (c) 2 (d) 8
40. 40.What is the mode of 15, 14, 18, 15, 17, 18 and 18? (a) 15 (b) 14 (c) 18 (d) 17

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