Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 688 · 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 12 blue balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 13 (d) 16
2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 20 (c) 19 (d) 9
3. 3.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
5. 5.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2 × 3³ (d) 2² × 3
6. 6.In a class of 32 children, 17 like cricket, 13 like football and 4 like both. How many like neither? (a) 10 (b) 2 (c) 6 (d) 4
7. 7.In a class of 28 children, 11 like tea, 15 like coffee and 7 like both. How many like at least one of the two? (a) 12 (b) 19 (c) 26 (d) 28
8. 8.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 5/8 (d) 3/5
9. 9.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 45° (d) 135°
10. 10.What is the mean of 18, 4, 19, 9, 18 and 10? (a) 12 (b) 15 (c) 13 (d) 14
11. 11.What is the mean of 2, 13, 10, 4 and 6? (a) 9 (b) 7 (c) 8 (d) 6
12. 12.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 8 (c) 30 (d) 20
13. 13.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 901 (b) 971 (c) 841 (d) 961
14. 14.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
15. 15.In which quadrant does the point (−1, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
16. 16.In a class of 43 children, 14 like maths, 28 like science and 10 like neither. How many like both? (a) 33 (b) 9 (c) 10 (d) 8
17. 17.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 30 (d) 15
18. 18.In a class of 25 children, 12 like maths, 15 like science and 3 like both. How many like only maths? (a) 12 (b) 3 (c) 9 (d) 10
19. 19.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 36° (c) 145° (d) 70°
20. 20.What is the midpoint of the line joining (0, 18) and (12, 6)? (a) (12, 24) (b) (6, 12) (c) (6, 6) (d) (12, 6)
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
22. 22.What is the 20th term of the AP 18, 20, 22, 24, …? (a) 58 (b) 40 (c) 38 (d) 56
23. 23.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
25. 25.The mean of 5 numbers is 11. When the number 35 is added to them, what is the new mean? (a) 23 (b) 16 (c) 11 (d) 15
26. 26.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
27. 27.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 110° (d) 125°
28. 28.What is the distance between the points (7, 6) and (12, 18)? (a) 14 (b) 13 (c) 169 (d) 17
29. 29.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 471 (c) 386 (d) 472
30. 30.How many factors does 28 have? (a) 4 (b) 7 (c) 5 (d) 6
31. 31.What is the sum of the roots of x² − 10x + 16 = 0? (a) 10 (b) 11 (c) 9 (d) 16
32. 32.How many factors does 43 have? (a) 3 (b) 4 (c) 2 (d) 1
33. 33.A bag has 9 yellow balls and 5 white 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) 2 (c) 14 (d) 10
34. 34.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 306 (b) 25 (c) 162 (d) 153
35. 35.How many factors does 100 have? (a) 10 (b) 9 (c) 7 (d) 8
36. 36.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
37. 37.How many factors does 40 have? (a) 7 (b) 8 (c) 9 (d) 6
38. 38.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
39. 39.A drawer has lots of red, white, blue 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) 4 (b) 5 (c) 2 (d) 8
40. 40.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6

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