Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 677 · 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 mean of 20, 4, 2 and 22? (a) 13 (b) 11 (c) 12 (d) 16
2. 2.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 13 (b) 11 (c) 17 (d) 12
3. 3.How many factors does 17 have? (a) 4 (b) 3 (c) 2 (d) 1
4. 4.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 145° (c) 160° (d) 125°
5. 5.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 5000 (c) 4950 (d) 10100
6. 6.If a + b = 15 and ab = 56, what is a² + b²? (a) 337 (b) 169 (c) 225 (d) 113
7. 7.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 21 (c) 30 (d) 36
8. 8.What is the median of 25, 5, 28, 34, 37, 35 and 1? (a) 34 (b) 29 (c) 28 (d) 25
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
10. 10.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 121 (d) 110
11. 11.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 8 (d) 27
12. 12.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
13. 13.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 41 (b) 34 (c) 36 (d) 35
14. 14.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
16. 16.In a class of 27 children, 17 like cricket, 10 like football and 7 like both. How many like neither? (a) 0 (b) 14 (c) 8 (d) 7
17. 17.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 26 (b) 27 (c) 28 (d) 36
18. 18.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
19. 19.3 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) 24 (b) 15 (c) 7 (d) 12
20. 20.The mean of 6 numbers is 25. When the number 53 is added to them, what is the new mean? (a) 29 (b) 39 (c) 30 (d) 25
21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
22. 22.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
23. 23.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 70 (b) 42 (c) 35 (d) 12
24. 24.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 31° (c) 210° (d) 150°
25. 25.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
26. 26.What is the 24th term of the AP 7, 9, 11, 13, …? (a) 46 (b) 53 (c) 55 (d) 48
27. 27.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3249 (b) 3979 (c) 3969 (d) 3609
28. 28.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
29. 29.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
30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 19 (b) 16 (c) 9 (d) 18
31. 31.What is the prime factorisation of 35? (a) 5 × 7 (b) 5 × 7² (c) 5² × 7 (d) 5³ × 7
32. 32.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
33. 33.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 135° (c) 95° (d) 85°
34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 6 (d) 3
35. 35.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 351 (c) 378 (d) 379
36. 36.In a class of 38 children, 16 like maths, 27 like science and 8 like both. How many like neither? (a) 8 (b) 11 (c) 4 (d) 3
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/36 (d) 1/11
38. 38.What is the smallest prime factor of 143? (a) 2 (b) 13 (c) 1 (d) 11
39. 39.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 424 (c) 528 (d) 529
40. 40.In a class of 26 children, 14 like mangoes, 8 like bananas and 3 like both. How many like at least one of the two? (a) 19 (b) 16 (c) 26 (d) 22

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