Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 290 · 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.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 6375 (b) 7225 (c) 5635 (d) 5625
2. 2.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 10) (b) (x − 5)(x − 6) (c) (x + 5)(x + 6) (d) (x + 1)(x + 30)
3. 3.A bag has 6 yellow balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 4 (d) 7
4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
5. 5.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
6. 6.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 42 (c) 49 (d) 21
7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 16 (b) 17 (c) 5 (d) 15
8. 8.How many factors does 44 have? (a) 4 (b) 6 (c) 7 (d) 5
9. 9.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
10. 10.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
11. 11.What is the 30th term of the AP 6, 13, 20, 27, …? (a) 203 (b) 216 (c) 209 (d) 210
12. 12.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 66 (d) 78
13. 13.In a class of 34 children, 14 like dance, 18 like music and 7 like both. How many like neither? (a) 16 (b) 7 (c) 2 (d) 9
14. 14.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
15. 15.How many factors does 59 have? (a) 1 (b) 3 (c) 2 (d) 4
16. 16.What is the mean of 6, 7, 14, 4 and 24? (a) 11 (b) 10 (c) 13 (d) 12
17. 17.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 9 sq cm (d) 36 sq cm
18. 18.What is the distance between the points (0, 21) and (9, 9)? (a) 225 (b) 21 (c) 16 (d) 15
19. 19.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
21. 21.What is the smallest prime factor of 187? (a) 17 (b) 11 (c) 2 (d) 1
22. 22.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
23. 23.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 25 (d) 20
24. 24.What is the mode of 20, 10, 4, 20, 10, 6 and 10? (a) 6 (b) 20 (c) 4 (d) 10
25. 25.What is the smallest prime factor of 39? (a) 2 (b) 1 (c) 13 (d) 3
26. 26.How many factors does 77 have? (a) 2 (b) 5 (c) 4 (d) 3
27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
28. 28.A bag has 12 blue balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 21 (b) 14 (c) 2 (d) 13
29. 29.What is the median of 15, 4, 27, 24 and 5? (a) 24 (b) 27 (c) 5 (d) 15
30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
31. 31.What is the mean of 11, 19, 13 and 17? (a) 12 (b) 16 (c) 20 (d) 15
32. 32.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 54 cu cm (d) 27 cu cm
33. 33.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 9 (d) 27
34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 380 (d) 37
35. 35.How many factors does 26 have? (a) 4 (b) 2 (c) 5 (d) 3
36. 36.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 66 (d) 121
37. 37.What is the mode of 2, 2, 8, 2, 8, 6 and 16? (a) 16 (b) 8 (c) 2 (d) 6
38. 38.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 125° (c) 305° (d) 55°
39. 39.A bag has 4 blue balls and 5 white 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) 5 (d) 9
40. 40.In a class of 38 children, 14 like cricket, 27 like football and 6 like neither. How many like both? (a) 9 (b) 6 (c) 32 (d) 3

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