Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 702 · 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.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 61° (c) 60° (d) 120°
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
3. 3.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) 24 (d) 36
4. 4.How many factors does 24 have? (a) 6 (b) 9 (c) 7 (d) 8
5. 5.If a + b = 13 and ab = 22, what is (a − b)²? (a) 81 (b) 125 (c) 9 (d) 169
6. 6.What is the product of the roots of x² − 12x + 35 = 0? (a) 35 (b) 12 (c) 34 (d) 36
7. 7.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
8. 8.What is the 23rd term of the AP 2, 4, 6, 8, …? (a) 46 (b) 48 (c) 44 (d) 47
9. 9.What is the median of 8, 5, 14, 7, 30, 2 and 12? (a) 9 (b) 12 (c) 7 (d) 8
10. 10.A bag has 6 yellow, 9 white and 7 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/11 (b) 3/8 (c) 3/11 (d) 1/3
11. 11.A bag has 9 red 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) 2 (b) 13 (c) 10 (d) 5
12. 12.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
13. 13.A bag has 4 yellow, 9 white and 3 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 9/16 (c) 7/16 (d) 7/9
14. 14.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 35° (d) 145°
15. 15.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 851 (b) 961 (c) 841 (d) 899
16. 16.In a class of 32 children, 19 like cricket, 13 like football and 2 like neither. How many like both? (a) 30 (b) 1 (c) 2 (d) 3
17. 17.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/4 (c) 7/8 (d) 1/8
18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
19. 19.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
20. 20.A drawer has lots of white, black 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) 2 (b) 6 (c) 4 (d) 3
21. 21.What is the 37th term of the AP 12, 18, 24, 30, …? (a) 216 (b) 234 (c) 222 (d) 228
22. 22.A drawer has lots of blue, white 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) 3 (b) 2 (c) 6 (d) 4
23. 23.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
24. 24.If a + b = 19 and ab = 90, what is (a − b)²? (a) 271 (b) 361 (c) 181 (d) 1
25. 25.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 66 (d) 144
26. 26.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 32 (b) 20 (c) 8 (d) 16
27. 27.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 24 (b) 168 (c) 96 (d) 84
28. 28.The mean of 6 numbers is 34. When the number 41 is added to them, what is the new mean? (a) 36 (b) 35 (c) 37 (d) 34
29. 29.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 130° (d) 80°
30. 30.A drawer has lots of white, black and red 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) 6 (c) 3 (d) 4
31. 31.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
32. 32.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 155° (d) 135°
33. 33.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
34. 34.A bag has 4 green balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 2 (c) 13 (d) 5
35. 35.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
36. 36.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
37. 37.In a class of 48 children, 26 like cricket, 27 like football and 7 like both. How many like only cricket? (a) 21 (b) 20 (c) 19 (d) 26
38. 38.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 15 (d) 8
39. 39.In a class of 34 children, 17 like cricket, 25 like football and 11 like both. How many like at least one of the two? (a) 20 (b) 31 (c) 42 (d) 34
40. 40.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 5 (d) 6

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