Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 452 · 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.A bag has 7 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 9 (c) 13 (d) 2
2. 2.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
3. 3.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2 × 3 × 5³ (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
4. 4.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
5. 5.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 48 (c) 24 (d) 11
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
7. 7.How many factors does 13 have? (a) 1 (b) 3 (c) 2 (d) 4
8. 8.How many factors does 84 have? (a) 11 (b) 13 (c) 10 (d) 12
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/6 (c) 5/36 (d) 1/11
10. 10.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 135° (b) 120° (c) 105° (d) 60°
11. 11.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 70° (d) 50°
12. 12.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
13. 13.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
14. 14.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
15. 15.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 72 (d) 36
16. 16.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 150° (b) 50° (c) 20° (d) 160°
17. 17.What is the midpoint of the line joining (2, 9) and (8, 5)? (a) (5, 7) (b) (10, 14) (c) (3, 2) (d) (7, 5)
18. 18.In which quadrant does the point (7, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
19. 19.In a class of 33 children, 10 like cricket, 20 like football and 5 like both. How many like neither? (a) 5 (b) 8 (c) 3 (d) 13
20. 20.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 55° (d) 46°
21. 21.A bag has 10 black 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) 11 (c) 2 (d) 15
22. 22.How many factors does 49 have? (a) 1 (b) 2 (c) 4 (d) 3
23. 23.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 635 (b) 425 (c) 625 (d) 225
24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 5 (d) 4
25. 25.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 14 (c) 42 (d) 49
26. 26.What is the 13th term of the AP 19, 25, 31, 37, …? (a) 78 (b) 97 (c) 72 (d) 91
27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
28. 28.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 486 (d) 402
29. 29.A drawer has lots of yellow and red 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) 5 (c) 4 (d) 2
30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
31. 31.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 321 (c) 312 (d) 286
32. 32.What is the mean of 7, 5, 12, 11, 4 and 15? (a) 11 (b) 10 (c) 9 (d) 8
33. 33.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) 22 (d) 21
34. 34.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
35. 35.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 14 (c) 45 (d) 42
36. 36.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
37. 37.How many factors does 21 have? (a) 3 (b) 5 (c) 4 (d) 2
38. 38.The mean of 8 numbers is 30. When the number 48 is added to them, what is the new mean? (a) 30 (b) 33 (c) 32 (d) 39
39. 39.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 370 (c) 369 (d) 318
40. 40.How many factors does 31 have? (a) 2 (b) 1 (c) 3 (d) 4

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