Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 95 · 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 an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
2. 2.What is the 38th term of the AP 15, 22, 29, 36, …? (a) 259 (b) 281 (c) 266 (d) 274
3. 3.A bag has 8 blue, 8 yellow and 8 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/3 (b) 1/3 (c) 3/8 (d) 1/2
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
5. 5.If a + b = 15 and ab = 56, what is (a − b)²? (a) 169 (b) 113 (c) 1 (d) 225
6. 6.What is the mean of 5, 10, 8, 8 and 14? (a) 10 (b) 11 (c) 9 (d) 8
7. 7.What is the midpoint of the line joining (8, 2) and (10, 14)? (a) (1, 6) (b) (8, 9) (c) (9, 8) (d) (18, 16)
8. 8.What is the 30th term of the AP 9, 15, 21, 27, …? (a) 183 (b) 180 (c) 174 (d) 189
9. 9.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 36 (c) 37 (d) 49
10. 10.Which is the correct factorisation of x² + 14x + 45? (a) (x − 5)(x − 9) (b) (x + 1)(x + 13) (c) (x + 1)(x + 45) (d) (x + 5)(x + 9)
11. 11.A drawer has lots of yellow, green 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) 3 (b) 6 (c) 2 (d) 4
12. 12.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 20 (d) 45
13. 13.What is the midpoint of the line joining (5, 7) and (15, 11)? (a) (5, 2) (b) (10, 9) (c) (20, 18) (d) (9, 10)
14. 14.What is the sum of the roots of x² − 12x + 27 = 0? (a) 11 (b) 27 (c) 13 (d) 12
15. 15.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
16. 16.In a class of 40 children, 18 like dance, 20 like music and 9 like neither. How many like both? (a) 31 (b) 8 (c) 9 (d) 7
17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
18. 18.In a class of 33 children, 14 like tea, 21 like coffee and 6 like both. How many like neither? (a) 6 (b) 10 (c) 5 (d) 4
19. 19.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 130° (d) 40°
20. 20.In a class of 34 children, 17 like cricket, 9 like football and 2 like both. How many like only cricket? (a) 17 (b) 7 (c) 25 (d) 15
21. 21.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
22. 22.What is the median of 18, 10, 5, 36, 20, 13 and 38? (a) 18 (b) 13 (c) 20 (d) 36
23. 23.A bag has 4 green, 7 blue and 4 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 8/15 (b) 7/15 (c) 3/5 (d) 1/3
24. 24.In which quadrant does the point (1, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
25. 25.What is the 21st term of the AP 18, 20, 22, 24, …? (a) 42 (b) 60 (c) 40 (d) 58
26. 26.A bag has 5 green, 3 red and 7 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 2/3 (c) 1/2 (d) 2/5
27. 27.A drawer has lots of 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) 2 (b) 5 (c) 4 (d) 3
28. 28.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 49 (c) 650 (d) 325
29. 29.In a class of 43 children, 17 like cricket, 23 like football and 7 like both. How many like only cricket? (a) 20 (b) 16 (c) 17 (d) 10
30. 30.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
31. 31.A drawer has lots of black, yellow, blue, white 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) 2 (b) 6 (c) 10 (d) 5
32. 32.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 95° (d) 85°
33. 33.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 50 (b) 25 (c) 30 (d) 10
34. 34.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 2850 (c) 2888 (d) 5852
35. 35.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) 13 (b) 24 (c) 25 (d) 12
36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
37. 37.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
38. 38.A cuboid is 12 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 168 sq cm (b) 244 sq cm (c) 488 sq cm (d) 122 sq cm
39. 39.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5³
40. 40.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7

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