Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 604 · 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 (4, 14) and (19, 6)? (a) 18 (b) 289 (c) 17 (d) 23
2. 2.In a class of 37 children, 18 like dance, 22 like music and 12 like both. How many like neither? (a) 9 (b) 10 (c) 12 (d) 21
3. 3.What is the sum of the roots of x² − 5x + 6 = 0? (a) 6 (b) 7 (c) 4 (d) 5
4. 4.In a class of 34 children, 19 like dance, 13 like music and 9 like neither. How many like both? (a) 7 (b) 8 (c) 9 (d) 25
5. 5.What is the mean of 19, 10, 8 and 19? (a) 13 (b) 16 (c) 15 (d) 14
6. 6.In a class of 40 children, 22 like maths, 27 like science and 10 like both. How many like only maths? (a) 17 (b) 22 (c) 13 (d) 12
7. 7.What is the mode of 12, 12, 11, 13, 12, 13 and 14? (a) 14 (b) 12 (c) 11 (d) 13
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
9. 9.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3249 (b) 3609 (c) 3979 (d) 3969
10. 10.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
11. 11.The mean of 3 numbers is 33. When the number 45 is added to them, what is the new mean? (a) 39 (b) 36 (c) 33 (d) 37
12. 12.A drawer has lots of red, green 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) 3 (b) 2 (c) 4 (d) 6
13. 13.In a class of 33 children, 21 like mangoes, 18 like bananas and 4 like neither. How many like both? (a) 6 (b) 4 (c) 10 (d) 29
14. 14.What is the mean of 8, 7, 2, 4 and 19? (a) 10 (b) 9 (c) 7 (d) 8
15. 15.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
16. 16.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 195° (c) 15° (d) 165°
17. 17.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 145° (d) 75°
18. 18.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
19. 19.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
20. 20.What is the smallest prime factor of 65? (a) 13 (b) 2 (c) 5 (d) 1
21. 21.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 55 (c) 110 (d) 121
22. 22.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 25 (d) 20
23. 23.A bag has 4 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 5 (c) 6 (d) 2
24. 24.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 5/6 (d) 1/4
25. 25.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 160° (c) 110° (d) 90°
26. 26.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
27. 27.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 132 (d) 24
28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
29. 29.What is the smallest prime factor of 187? (a) 2 (b) 1 (c) 17 (d) 11
30. 30.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
31. 31.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
32. 32.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 387 (c) 397 (d) 396
33. 33.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 48 (d) 24
34. 34.What is the midpoint of the line joining (2, 6) and (10, 18)? (a) (6, 12) (b) (12, 24) (c) (4, 6) (d) (12, 6)
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/12 (c) 1/36 (d) 1/11
36. 36.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
37. 37.What is the mean of 7, 2, 19 and 16? (a) 11 (b) 12 (c) 13 (d) 10
38. 38.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/5 (d) 3/8
39. 39.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 90° (d) 91°
40. 40.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 100° (b) 120° (c) 80° (d) 140°

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