Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 482 · 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 (3, 22) and (15, 6)? (a) 21 (b) 400 (c) 28 (d) 20
2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
3. 3.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 70 (c) 52 (d) 62
4. 4.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 438 (c) 549 (d) 550
5. 5.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3081 (c) 6320 (d) 3161
6. 6.What is the median of 1, 33, 20, 3, 32, 10 and 14? (a) 10 (b) 3 (c) 20 (d) 14
7. 7.What is the mean of 8, 14, 17, 16, 4 and 19? (a) 12 (b) 13 (c) 14 (d) 15
8. 8.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x + 1)(x + 8) (c) (x − 4)(x − 5) (d) (x + 4)(x + 5)
9. 9.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 252 (c) 270 (d) 261
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 1/11 (c) 5/36 (d) 4/11
11. 11.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 120 (d) 20
12. 12.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
13. 13.If a + b = 13 and ab = 40, what is (a − b)²? (a) 3 (b) 9 (c) 89 (d) 169
14. 14.Which term of the AP 9, 16, 23, 30, … is 247? (a) 36th (b) 34th (c) 37th (d) 35th
15. 15.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
16. 16.In a class of 36 children, 13 like mangoes, 16 like bananas and 3 like both. How many like only mangoes? (a) 3 (b) 10 (c) 13 (d) 20
17. 17.A bag has 12 blue balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 13 (c) 15 (d) 14
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
19. 19.The mean of 7 numbers is 17. When the number 25 is added to them, what is the new mean? (a) 21 (b) 17 (c) 18 (d) 19
20. 20.What is the mode of 20, 20, 15, 18, 14, 14 and 14? (a) 18 (b) 20 (c) 15 (d) 14
21. 21.What is the product of the roots of x² − 9x + 20 = 0? (a) 20 (b) 9 (c) 19 (d) 21
22. 22.What is the distance between the points (7, 12) and (10, 8)? (a) 7 (b) 5 (c) 25 (d) 6
23. 23.A bag has 7 black balls and 3 yellow 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) 4 (c) 8 (d) 10
24. 24.What is the smallest prime factor of 33? (a) 11 (b) 2 (c) 1 (d) 3
25. 25.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 192 (b) 26 (c) 180 (d) 360
26. 26.How many factors does 78 have? (a) 9 (b) 6 (c) 8 (d) 7
27. 27.In a class of 45 children, 17 like mangoes, 32 like bananas and 8 like neither. How many like both? (a) 8 (b) 4 (c) 12 (d) 37
28. 28.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 150° (b) 55° (c) 85° (d) 125°
29. 29.In a class of 30 children, 20 like mangoes, 14 like bananas and 11 like both. How many like at least one of the two? (a) 12 (b) 34 (c) 23 (d) 30
30. 30.A bag has 5 blue, 9 red and 8 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 17/22 (c) 5/22 (d) 5/17
31. 31.A bag has 4 green, 2 red and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 3/4 (b) 1/3 (c) 7/8 (d) 1/4
32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
33. 33.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 217 sq cm (d) 144 sq cm
34. 34.A drawer has lots of black, blue, yellow, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 6 (d) 2
35. 35.How many factors does 14 have? (a) 3 (b) 5 (c) 4 (d) 2
36. 36.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 729 (d) 756
37. 37.How many prime numbers are there between 90 and 100? (a) 1 (b) 0 (c) 2 (d) 3
38. 38.In a class of 21 children, 9 like mangoes, 14 like bananas and 5 like both. How many like neither? (a) 5 (b) 8 (c) 4 (d) 3
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 5 (d) 15
40. 40.In which quadrant does the point (−6, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

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