Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 164 · 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 smallest prime factor of 209? (a) 1 (b) 11 (c) 2 (d) 19
2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 5 (b) 7 (c) 6 (d) 4
3. 3.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/9 (c) 1/11 (d) 3/11
5. 5.In a class of 42 children, 31 like mangoes, 20 like bananas and 12 like both. How many like only mangoes? (a) 31 (b) 8 (c) 19 (d) 22
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
7. 7.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 120 (b) 65 (c) 60 (d) 22
8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 16 (d) 17
9. 9.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 756 (b) 378 (c) 408 (d) 59
10. 10.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2 × 5 × 7
11. 11.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3481 (b) 3601 (c) 3731 (d) 3721
12. 12.What is the product of the roots of x² − 16x + 63 = 0? (a) 16 (b) 62 (c) 64 (d) 63
13. 13.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
14. 14.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 13 (c) 7 (d) 11
16. 16.If a + b = 17 and ab = 72, what is (a − b)²? (a) 289 (b) 1 (c) 145 (d) 217
17. 17.What is the 27th term of the AP 7, 10, 13, 16, …? (a) 85 (b) 78 (c) 81 (d) 88
18. 18.What is the midpoint of the line joining (0, 0) and (6, 10)? (a) (5, 3) (b) (6, 10) (c) (3, 5) (d) (4, 5)
19. 19.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
20. 20.In a class of 39 children, 21 like dance, 16 like music and 5 like both. How many like neither? (a) 12 (b) 7 (c) 2 (d) 5
21. 21.In a class of 37 children, 25 like cricket, 10 like football and 6 like both. How many like at least one of the two? (a) 37 (b) 35 (c) 23 (d) 29
22. 22.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 42 (c) 21 (d) 24
23. 23.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 135° (b) 85° (c) 95° (d) 130°
24. 24.In a class of 40 children, 19 like dance, 25 like music and 10 like both. How many like neither? (a) 10 (b) 7 (c) 16 (d) 6
25. 25.What is the 23rd term of the AP 18, 26, 34, 42, …? (a) 184 (b) 176 (c) 202 (d) 194
26. 26.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
27. 27.In a class of 24 children, 5 like tea, 20 like coffee and 2 like both. How many like neither? (a) 3 (b) 1 (c) 2 (d) 0
28. 28.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
29. 29.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 21 (c) 6 (d) 54
30. 30.What is the mode of 1, 5, 18, 1, 10, 18 and 18? (a) 10 (b) 5 (c) 18 (d) 1
31. 31.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 80° (c) 100° (d) 135°
32. 32.What is the median of 23, 28, 8, 9, 27, 7 and 33? (a) 23 (b) 9 (c) 27 (d) 24
33. 33.In which quadrant does the point (3, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
34. 34.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 75° (c) 135° (d) 105°
35. 35.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
36. 36.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2⁴ × 7 (c) 2³ × 7 (d) 2 × 7⁴
37. 37.What is the mean of 9, 5, 15, 14, 6 and 17? (a) 13 (b) 12 (c) 10 (d) 11
38. 38.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 84 (c) 66 (d) 76
39. 39.There are 4 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 24 (c) 20 (d) 9
40. 40.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) 45 (c) 42 (d) 14

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