Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 320 · 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 distance between the points (4, 11) and (19, 3)? (a) 23 (b) 289 (c) 17 (d) 18
2. 2.What is the mode of 12, 12, 1, 1, 12, 15 and 6? (a) 6 (b) 15 (c) 1 (d) 12
3. 3.In a class of 40 children, 21 like tea, 25 like coffee and 11 like both. How many like only tea? (a) 21 (b) 15 (c) 14 (d) 10
4. 4.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 21 (c) 36 (d) 30
5. 5.What is the median of 23, 6, 39, 33, 22, 19 and 29? (a) 29 (b) 23 (c) 22 (d) 33
6. 6.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
7. 7.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x + 7)(x + 9) (c) (x − 7)(x − 9) (d) (x + 1)(x + 15)
8. 8.In a class of 30 children, 9 like mangoes, 15 like bananas and 2 like both. How many like only mangoes? (a) 9 (b) 15 (c) 13 (d) 7
9. 9.In which quadrant does the point (7, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
11. 11.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
12. 12.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 14 (b) 13 (c) 12 (d) 17
13. 13.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2⁴ × 3²
14. 14.How many prime numbers are there between 50 and 70? (a) 3 (b) 4 (c) 6 (d) 5
15. 15.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 2 (d) 4
16. 16.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 80° (c) 100° (d) 160°
17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
18. 18.A bag has 11 blue balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 18 (d) 12
19. 19.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 342 (c) 351 (d) 352
20. 20.What is the smallest prime factor of 247? (a) 19 (b) 2 (c) 1 (d) 13
21. 21.A bag has 3 green balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 4 (b) 2 (c) 14 (d) 5
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
23. 23.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 140° (d) 135°
24. 24.A bag has 10 yellow balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 11 (c) 19 (d) 12
25. 25.What is the median of 3, 15, 14, 16, 40, 4 and 23? (a) 16 (b) 17 (c) 14 (d) 15
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
27. 27.In a class of 28 children, 19 like maths, 10 like science and 3 like neither. How many like both? (a) 1 (b) 25 (c) 3 (d) 4
28. 28.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 45° (c) 130° (d) 135°
29. 29.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
30. 30.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 184 (c) 192 (d) 174
31. 31.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 130° (d) 135°
32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/12 (c) 1/11 (d) 1/18
34. 34.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 90 (d) 17
36. 36.The mean of 4 numbers is 19. When the number 4 is added to them, what is the new mean? (a) 19 (b) 17 (c) 15 (d) 16
37. 37.A bag has 2 blue, 5 white and 9 green balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/8 (b) 15/16 (c) 1/3 (d) 7/8
38. 38.A bag has 8 yellow balls and 9 black 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) 9 (c) 17 (d) 10
39. 39.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
40. 40.What is the smallest prime factor of 115? (a) 2 (b) 5 (c) 1 (d) 23

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