Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 330 · 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 missing term in the AP 18, 21, 24, ?, 30? (a) 27 (b) 26 (c) 28 (d) 30
2. 2.Which is the correct factorisation of x² + 8x + 12? (a) (x + 2)(x + 6) (b) (x − 2)(x − 6) (c) (x + 1)(x + 12) (d) (x + 1)(x + 7)
3. 3.In a class of 28 children, 18 like cricket, 8 like football and 7 like neither. How many like both? (a) 21 (b) 7 (c) 5 (d) 6
4. 4.If a + b = 11 and ab = 30, what is (a − b)²? (a) 61 (b) 121 (c) 1 (d) 91
5. 5.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
6. 6.What is the median of 26, 24, 18, 8 and 1? (a) 8 (b) 18 (c) 19 (d) 24
7. 7.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 25 (c) 36 (d) 24
8. 8.What is the midpoint of the line joining (4, 3) and (10, 9)? (a) (7, 6) (b) (3, 3) (c) (14, 12) (d) (6, 7)
9. 9.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 320° (c) 50° (d) 40°
10. 10.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 1 (d) 2
12. 12.A bag has 9 red, 9 green and 9 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 10/27 (b) 2/3 (c) 1/2 (d) 1/3
13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 18 (d) 20
14. 14.What is the midpoint of the line joining (1, 16) and (13, 10)? (a) (7, 13) (b) (14, 26) (c) (6, 3) (d) (13, 7)
15. 15.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
16. 16.In a class of 40 children, 27 like maths, 22 like science and 12 like both. How many like at least one of the two? (a) 37 (b) 25 (c) 49 (d) 40
17. 17.What is the distance between the points (3, 7) and (8, 19)? (a) 17 (b) 14 (c) 13 (d) 169
18. 18.A bag has 6 red, 4 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/12 (b) 1/12 (c) 1/3 (d) 1/2
19. 19.A drawer has lots of blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 2 (d) 3
20. 20.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
21. 21.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 12 (b) 9 (c) 11 (d) 10
22. 22.What is the midpoint of the line joining (2, 14) and (6, 10)? (a) (8, 24) (b) (4, 12) (c) (2, 2) (d) (12, 4)
23. 23.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 18 (d) 45
24. 24.What are the roots of x² − 11x + 18 = 0? (a) 1 and 10 (b) 1 and 18 (c) 2 and 9 (d) 3 and 6
25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 12 (b) 13 (c) 11 (d) 4
26. 26.A bag has 2 red, 4 yellow and 3 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/9 (b) 2/9 (c) 1/3 (d) 8/9
27. 27.In a class of 38 children, 15 like tea, 18 like coffee and 2 like both. How many like only tea? (a) 15 (b) 13 (c) 20 (d) 16
28. 28.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 135° (b) 90° (c) 45° (d) 225°
29. 29.What is the sum of the roots of x² − 11x + 30 = 0? (a) 12 (b) 30 (c) 11 (d) 10
30. 30.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x − 6)(x − 7) (c) (x + 1)(x + 42) (d) (x + 6)(x + 7)
31. 31.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 418 (b) 65 (c) 770 (d) 385
32. 32.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
33. 33.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2⁴ × 5 × 7
34. 34.In which quadrant does the point (−9, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
35. 35.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
36. 36.In a class of 30 children, 19 like maths, 14 like science and 4 like both. How many like at least one of the two? (a) 33 (b) 29 (c) 25 (d) 30
37. 37.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
38. 38.If a + b = 13 and ab = 42, what is a² + b²? (a) 85 (b) 169 (c) 127 (d) 253
39. 39.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
40. 40.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 144 (d) 24

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