Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 421 · 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.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
2. 2.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 589 (c) 579 (d) 464
3. 3.If a + b = 11 and ab = 30, what is a² + b²? (a) 91 (b) 121 (c) 61 (d) 181
4. 4.Which is the correct factorisation of x² + 6x + 8? (a) (x + 1)(x + 5) (b) (x + 1)(x + 8) (c) (x − 2)(x − 4) (d) (x + 2)(x + 4)
5. 5.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
6. 6.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 21 (d) 42
7. 7.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
8. 8.There are 4 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) 56 (b) 28 (c) 32 (d) 11
9. 9.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
10. 10.A bag has 7 green, 8 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/9 (b) 5/9 (c) 1/3 (d) 4/5
11. 11.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 784 (b) 1034 (c) 1024 (d) 904
12. 12.What is the midpoint of the line joining (5, 6) and (7, 14)? (a) (10, 6) (b) (1, 4) (c) (12, 20) (d) (6, 10)
13. 13.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 2/3 (d) 1/4
14. 14.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
15. 15.Which is the correct factorisation of x² + 13x + 40? (a) (x − 5)(x − 8) (b) (x + 1)(x + 40) (c) (x + 5)(x + 8) (d) (x + 1)(x + 12)
16. 16.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
17. 17.A bag has 6 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 15 (d) 10
18. 18.A bag has 2 blue, 8 green and 9 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 2/19 (b) 1/3 (c) 2/17 (d) 17/19
19. 19.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 85° (b) 140° (c) 135° (d) 95°
20. 20.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2² × 3² × 7
21. 21.How many factors does 108 have? (a) 10 (b) 13 (c) 11 (d) 12
22. 22.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 252 (b) 42 (c) 234 (d) 468
23. 23.A bag has 10 black balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 22 (c) 2 (d) 12
24. 24.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) 27 (c) 9 (d) 81
25. 25.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 136 (b) 68 (c) 72 (d) 12
26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
27. 27.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
28. 28.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 16 (c) 5 (d) 15
30. 30.How many prime numbers are there between 70 and 80? (a) 3 (b) 2 (c) 5 (d) 4
31. 31.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
32. 32.In a class of 28 children, 16 like dance, 14 like music and 8 like both. How many like at least one of the two? (a) 28 (b) 22 (c) 30 (d) 14
33. 33.In a class of 34 children, 11 like mangoes, 24 like bananas and 6 like both. How many like neither? (a) 5 (b) 11 (c) 6 (d) 4
34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
35. 35.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/7 (c) 1/8 (d) 7/8
36. 36.What is the median of 29, 17, 27, 40, 8, 28 and 15? (a) 17 (b) 28 (c) 40 (d) 27
37. 37.In a class of 46 children, 23 like tea, 20 like coffee and 5 like both. How many like only tea? (a) 15 (b) 26 (c) 23 (d) 18
38. 38.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 30 cu cm
39. 39.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11

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