Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 291 · 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 midpoint of the line joining (4, 12) and (14, 10)? (a) (9, 11) (b) (11, 9) (c) (18, 22) (d) (5, 1)
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
3. 3.What is the mean of 9, 7, 2, 9 and 18? (a) 8 (b) 11 (c) 10 (d) 9
4. 4.Using (a + b)² = a² + 2ab + b², what is 85²? (a) 7225 (b) 5625 (c) 7235 (d) 6425
5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
6. 6.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 196 (d) 105
7. 7.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 462 (c) 453 (d) 380
8. 8.What is the distance between the points (4, 6) and (12, 0)? (a) 10 (b) 100 (c) 11 (d) 14
9. 9.A bag has 4 white, 8 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/7 (b) 6/7 (c) 1/3 (d) 13/14
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 4 (d) 3
11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 5 (b) 8 (c) 7 (d) 6
12. 12.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5⁴
13. 13.A bag has 9 white balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 20 (c) 10 (d) 11
14. 14.What is the smallest prime factor of 119? (a) 17 (b) 7 (c) 2 (d) 1
15. 15.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 160° (d) 120°
16. 16.What is the smallest prime factor of 187? (a) 2 (b) 1 (c) 11 (d) 17
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/11 (c) 5/36 (d) 1/6
18. 18.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 19 (b) 18 (c) 23 (d) 20
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
20. 20.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
21. 21.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4418 (c) 4465 (d) 4371
22. 22.A bag has 3 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 5 (c) 7 (d) 2
23. 23.What is the distance between the points (0, 8) and (3, 12)? (a) 5 (b) 7 (c) 25 (d) 6
24. 24.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
25. 25.The mean of 8 numbers is 25. When the number 7 is added to them, what is the new mean? (a) 23 (b) 24 (c) 25 (d) 16
26. 26.In which quadrant does the point (−3, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
27. 27.What is the median of 8, 17, 16, 2, 22, 29 and 15? (a) 16 (b) 17 (c) 15 (d) 2
28. 28.A drawer has lots of black, green, blue, yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 10 (d) 6
29. 29.In a class of 46 children, 23 like mangoes, 22 like bananas and 9 like both. How many like at least one of the two? (a) 45 (b) 36 (c) 46 (d) 27
30. 30.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2⁴ × 5 (c) 2² × 5 (d) 2³ × 5
31. 31.If a + b = 18 and ab = 77, what is (a − b)²? (a) 324 (b) 16 (c) 170 (d) 4
32. 32.In a class of 44 children, 26 like dance, 19 like music and 9 like neither. How many like both? (a) 10 (b) 1 (c) 35 (d) 9
33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 17 (d) 16
34. 34.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
35. 35.A bag has 5 yellow balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 16 (b) 6 (c) 7 (d) 2
36. 36.A bag has 7 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 9 (c) 8 (d) 2
37. 37.What is the midpoint of the line joining (7, 18) and (11, 6)? (a) (18, 24) (b) (9, 12) (c) (12, 9) (d) (2, 6)
38. 38.Which term of the AP 1, 9, 17, 25, … is 177? (a) 22nd (b) 24th (c) 23rd (d) 25th
39. 39.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
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm

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