Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 689 · 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.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
2. 2.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 125° (b) 110° (c) 235° (d) 55°
3. 3.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 24 (b) 18 (c) 20 (d) 19
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
5. 5.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 60° (d) 145°
6. 6.A drawer has lots of white, yellow, 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) 8 (b) 4 (c) 2 (d) 5
7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 9 (b) 8 (c) 7 (d) 6
8. 8.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 155° (d) 55°
9. 9.What are the roots of x² − 7x + 12 = 0? (a) 3 and 4 (b) 1 and 6 (c) 1 and 12 (d) 2 and 6
10. 10.If a + b = 12 and ab = 35, what is a² + b²? (a) 74 (b) 109 (c) 214 (d) 144
11. 11.A bag has 9 green, 6 red and 8 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 8/23 (c) 16/23 (d) 15/23
12. 12.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
13. 13.In a class of 18 children, 13 like mangoes, 6 like bananas and 2 like both. How many like at least one of the two? (a) 18 (b) 15 (c) 17 (d) 19
14. 14.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 23 (c) 72 (d) 69
15. 15.A drawer has lots of yellow, white, black, red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 5 (d) 6
16. 16.What is the prime factorisation of 63? (a) 3 × 7² (b) 3² × 7 (c) 3³ × 7 (d) 3 × 7
17. 17.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 36 (c) 81 (d) 18
18. 18.A bag has 2 yellow, 8 red and 4 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 3/7 (c) 9/14 (d) 4/7
19. 19.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
20. 20.A drawer has lots of red, yellow, white and blue 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) 5 (c) 4 (d) 8
21. 21.A drawer has lots of blue and green 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
22. 22.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2 × 3² × 5
23. 23.What is the midpoint of the line joining (2, 10) and (8, 14)? (a) (3, 2) (b) (5, 12) (c) (12, 5) (d) (10, 24)
24. 24.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
25. 25.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
26. 26.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
27. 27.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 180 (b) 18 (c) 99 (d) 90
28. 28.What is the mode of 1, 5, 19, 1, 5, 1 and 13? (a) 1 (b) 13 (c) 19 (d) 5
29. 29.In a class of 27 children, 18 like mangoes, 19 like bananas and 12 like both. How many like neither? (a) 12 (b) 2 (c) 3 (d) 14
30. 30.What is the sum of the roots of x² − 14x + 45 = 0? (a) 15 (b) 14 (c) 45 (d) 13
31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 3 (b) 4 (c) 6 (d) 5
33. 33.A bag has 11 red balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 11 (c) 2 (d) 12
34. 34.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
35. 35.What is the prime factorisation of 12? (a) 2 × 3 (b) 2 × 3² (c) 2² × 3 (d) 2³ × 3
36. 36.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.What is the sum of the roots of x² − 15x + 56 = 0? (a) 15 (b) 56 (c) 14 (d) 16
38. 38.A bag has 5 red balls and 8 black 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) 2 (c) 13 (d) 9
39. 39.What is the distance between the points (2, 5) and (8, 13)? (a) 10 (b) 14 (c) 100 (d) 11
40. 40.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 741 (d) 1482

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