Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 658 · 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 diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
2. 2.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 70° (c) 155° (d) 135°
3. 3.In a class of 43 children, 16 like maths, 22 like science and 3 like both. How many like only maths? (a) 16 (b) 13 (c) 19 (d) 21
4. 4.A bag has 5 yellow balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 6 (c) 14 (d) 2
5. 5.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 50° (b) 10° (c) 140° (d) 170°
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
7. 7.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
9. 9.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 70° (d) 110°
10. 10.The mean of 5 numbers is 15. When the number 9 is added to them, what is the new mean? (a) 12 (b) 15 (c) 14 (d) 13
11. 11.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6396 (b) 6724 (c) 6084 (d) 6094
12. 12.How many prime numbers are there between 90 and 100? (a) 1 (b) 3 (c) 2 (d) 0
13. 13.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 5 (b) 6 (c) 9 (d) 12
14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 9 (b) 6 (c) 7 (d) 8
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
16. 16.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
18. 18.How many factors does 100 have? (a) 7 (b) 10 (c) 8 (d) 9
19. 19.What is the mean of 18, 11, 2, 13, 6 and 22? (a) 12 (b) 14 (c) 11 (d) 13
20. 20.How many prime numbers are there between 50 and 60? (a) 3 (b) 2 (c) 4 (d) 1
21. 21.A drawer has lots of 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) 5 (b) 4 (c) 3 (d) 2
22. 22.What is the 34th term of the AP 6, 14, 22, 30, …? (a) 272 (b) 278 (c) 270 (d) 264
23. 23.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 11 (b) 14 (c) 13 (d) 12
24. 24.A bag has 5 white, 4 red and 7 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 5/16 (b) 1/4 (c) 3/4 (d) 1/3
25. 25.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 23 (b) 25 (c) 32 (d) 24
26. 26.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 1034 (b) 1024 (c) 904 (d) 784
27. 27.What is the distance between the points (8, 5) and (15, 29)? (a) 31 (b) 25 (c) 26 (d) 625
28. 28.A bag has 9 white 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) 6 (b) 2 (c) 10 (d) 14
29. 29.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7³
30. 30.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/6 (c) 1/3 (d) 5/6
31. 31.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 10 (c) 32 (d) 16
32. 32.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
33. 33.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 32) (b) (x + 4)(x + 8) (c) (x + 1)(x + 11) (d) (x − 4)(x − 8)
34. 34.A drawer has lots of green 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) 5 (b) 3 (c) 2 (d) 4
35. 35.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 61° (b) 120° (c) 240° (d) 60°
36. 36.In a class of 31 children, 24 like cricket, 12 like football and 7 like both. How many like at least one of the two? (a) 31 (b) 29 (c) 22 (d) 36
37. 37.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 20 (c) 63 (d) 180
38. 38.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
39. 39.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2³ × 3
40. 40.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 84 (b) 150 (c) 75 (d) 20

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