Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 450 · 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 circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
2. 2.If a + b = 9 and ab = 18, what is (a − b)²? (a) 3 (b) 81 (c) 45 (d) 9
3. 3.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 115° (b) 65° (c) 130° (d) 245°
4. 4.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 512 sq cm (d) 384 sq cm
5. 5.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
6. 6.A bag has 6 white, 2 yellow and 2 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 3/5 (c) 2/5 (d) 2/3
7. 7.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 120° (b) 85° (c) 25° (d) 155°
8. 8.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1681 (b) 1601 (c) 1521 (d) 1691
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
10. 10.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 21 (d) 22
11. 11.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
12. 12.What is the mean of 16, 11, 2 and 19? (a) 13 (b) 16 (c) 12 (d) 11
13. 13.What is the median of 25, 22, 31, 40 and 1? (a) 26 (b) 22 (c) 25 (d) 31
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/11 (d) 1/12
15. 15.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 6 (d) 7
16. 16.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 130° (d) 95°
17. 17.What is the 23rd term of the AP 13, 19, 25, 31, …? (a) 132 (b) 145 (c) 138 (d) 151
18. 18.In a class of 25 children, 13 like dance, 9 like music and 5 like both. How many like at least one of the two? (a) 17 (b) 25 (c) 12 (d) 22
19. 19.What is the smallest prime factor of 145? (a) 2 (b) 1 (c) 29 (d) 5
20. 20.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 125° (d) 120°
21. 21.What is the distance between the points (0, 0) and (5, 12)? (a) 17 (b) 14 (c) 13 (d) 169
22. 22.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 7 (d) 12
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
24. 24.A bag has 10 green balls and 5 blue 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) 15 (c) 11 (d) 6
25. 25.A cuboid is 12 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 832 sq cm (b) 480 sq cm (c) 416 sq cm (d) 208 sq cm
26. 26.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 130° (b) 135° (c) 50° (d) 95°
27. 27.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 891 (b) 729 (c) 1089 (d) 739
28. 28.7 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
29. 29.In a class of 33 children, 24 like maths, 13 like science and 6 like both. How many like only maths? (a) 7 (b) 20 (c) 18 (d) 24
30. 30.What is the distance between the points (4, 5) and (13, 17)? (a) 21 (b) 225 (c) 15 (d) 16
31. 31.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 48 (d) 16
32. 32.If a + b = 8 and ab = 15, what is (a − b)²? (a) 34 (b) 2 (c) 4 (d) 64
33. 33.What is the 11th term of the AP 3, 9, 15, 21, …? (a) 60 (b) 63 (c) 69 (d) 66
34. 34.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 55° (c) 160° (d) 145°
35. 35.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
37. 37.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 5 (c) 16 (d) 15
38. 38.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 85° (d) 125°
39. 39.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
40. 40.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1

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