Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 488 · 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 377? (a) 2 (b) 13 (c) 29 (d) 1
2. 2.In which quadrant does the point (8, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
3. 3.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 105° (d) 30°
4. 4.In a class of 42 children, 19 like cricket, 27 like football and 11 like both. How many like only cricket? (a) 16 (b) 8 (c) 19 (d) 15
5. 5.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 1)(x + 4) (c) (x + 2)(x + 3) (d) (x − 2)(x − 3)
6. 6.In a class of 42 children, 14 like mangoes, 21 like bananas and 10 like neither. How many like both? (a) 10 (b) 32 (c) 3 (d) 4
7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 3 (d) 5
8. 8.What is the smallest prime factor of 161? (a) 23 (b) 2 (c) 7 (d) 1
9. 9.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 105 (d) 120
10. 10.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/4 (d) 1/3
11. 11.What is the mean of 4, 9, 12 and 15? (a) 9 (b) 10 (c) 8 (d) 11
12. 12.What is the mean of 16, 7, 20, 17, 13 and 17? (a) 18 (b) 14 (c) 16 (d) 15
13. 13.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 135° (d) 100°
14. 14.The mean of 3 numbers is 15. When the number 11 is added to them, what is the new mean? (a) 13 (b) 15 (c) 16 (d) 14
15. 15.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) 14 (d) 42
16. 16.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 15 (c) 36 (d) 30
17. 17.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) 25 times (d) 5 times
18. 18.How many prime numbers are there between 30 and 40? (a) 1 (b) 4 (c) 2 (d) 3
19. 19.The mean of 7 numbers is 39. When the number 23 is added to them, what is the new mean? (a) 31 (b) 37 (c) 38 (d) 39
20. 20.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 50° (d) 25°
21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 4 (d) 6
22. 22.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 110°
23. 23.In a class of 16 children, 12 like cricket, 7 like football and 1 like neither. How many like both? (a) 1 (b) 3 (c) 15 (d) 4
24. 24.In a class of 29 children, 17 like mangoes, 19 like bananas and 5 like neither. How many like both? (a) 5 (b) 12 (c) 24 (d) 7
25. 25.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 2/3
26. 26.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 132 (b) 16 (c) 66 (d) 72
27. 27.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
28. 28.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 7 (d) 2
29. 29.What is the median of 9, 28, 24, 32 and 2? (a) 28 (b) 24 (c) 9 (d) 19
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
31. 31.A drawer has lots of red and black 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) 3 (d) 2
32. 32.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 55 (b) 558 (c) 279 (d) 306
33. 33.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
34. 34.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/4 (c) 1/8 (d) 3/4
35. 35.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
36. 36.If a + b = 19 and ab = 84, what is (a − b)²? (a) 361 (b) 193 (c) 5 (d) 25
37. 37.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 17 (b) 70 (c) 130 (d) 65
38. 38.A bag has 6 red, 3 yellow and 8 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/17 (b) 8/9 (c) 1/3 (d) 8/17
39. 39.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 45° (d) 130°
40. 40.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6

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