Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 401 · 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.If a + b = 13 and ab = 12, what is a² + b²? (a) 169 (b) 193 (c) 145 (d) 157
2. 2.What is the midpoint of the line joining (10, 17) and (22, 7)? (a) (32, 24) (b) (6, 5) (c) (16, 12) (d) (12, 16)
3. 3.What is the sum of the roots of x² − 13x + 40 = 0? (a) 13 (b) 40 (c) 12 (d) 14
4. 4.A bag has 5 yellow balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 16 (c) 2 (d) 6
5. 5.A bag has 9 green balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 13 (c) 10 (d) 2
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
7. 7.What is the midpoint of the line joining (4, 7) and (10, 15)? (a) (3, 4) (b) (7, 11) (c) (11, 7) (d) (14, 22)
8. 8.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 5 (c) 7 (d) 6
9. 9.What is the distance between the points (0, 8) and (12, 24)? (a) 21 (b) 400 (c) 28 (d) 20
10. 10.The mean of 3 numbers is 18. When the number 14 is added to them, what is the new mean? (a) 18 (b) 17 (c) 16 (d) 19
11. 11.A bag has 11 blue balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 21 (d) 13
12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 2 (d) 4
13. 13.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 17 (b) 14 (c) 13 (d) 12
14. 14.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
15. 15.If a + b = 9 and ab = 18, what is a² + b²? (a) 63 (b) 81 (c) 117 (d) 45
16. 16.How many factors does 73 have? (a) 1 (b) 4 (c) 2 (d) 3
17. 17.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 138 (c) 33 (d) 246
18. 18.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/5 (c) 1/6 (d) 1/3
19. 19.What is the mode of 6, 3, 9, 9, 9, 3 and 12? (a) 9 (b) 6 (c) 3 (d) 12
20. 20.In a class of 41 children, 25 like maths, 11 like science and 5 like both. How many like at least one of the two? (a) 36 (b) 41 (c) 26 (d) 31
21. 21.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
22. 22.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2016 (c) 4160 (d) 2048
23. 23.A bag has 4 green, 5 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 4/7 (c) 4/11 (d) 7/11
24. 24.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 341 (b) 638 (c) 319 (d) 49
25. 25.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 169 (d) 156
26. 26.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
27. 27.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 361 (b) 371 (c) 441 (d) 399
28. 28.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
29. 29.In a class of 51 children, 29 like tea, 25 like coffee and 11 like both. How many like neither? (a) 19 (b) 11 (c) 8 (d) 9
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/12 (c) 1/11 (d) 1/9
31. 31.How many factors does 18 have? (a) 4 (b) 7 (c) 5 (d) 6
32. 32.What is the smallest prime factor of 115? (a) 23 (b) 5 (c) 2 (d) 1
33. 33.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) 66 (b) 22 (c) 69 (d) 198
34. 34.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/8 (d) 3/4
35. 35.How many factors does 104 have? (a) 9 (b) 8 (c) 7 (d) 6
36. 36.A bag has 4 blue, 2 yellow and 3 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 4/5 (b) 1/3 (c) 5/9 (d) 4/9
37. 37.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 1 (d) 23
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 7 (d) 19
39. 39.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
40. 40.What is the 40th term of the AP 12, 16, 20, 24, …? (a) 172 (b) 168 (c) 160 (d) 156

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