Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 966 · 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 (1, 4) and (16, 12)? (a) 17 (b) 289 (c) 18 (d) 23
2. 2.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 15 (c) 8 (d) 14
3. 3.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 30° (b) 110° (c) 150° (d) 100°
4. 4.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 100 (d) 90
5. 5.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
6. 6.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 17 (b) 15 (c) 22 (d) 16
7. 7.A bag has 8 white balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 17 (d) 10
8. 8.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
9. 9.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
10. 10.What is the midpoint of the line joining (0, 22) and (10, 10)? (a) (10, 32) (b) (5, 6) (c) (5, 16) (d) (16, 5)
11. 11.What is the mean of 13, 16, 4, 14 and 18? (a) 14 (b) 13 (c) 12 (d) 15
12. 12.What is the midpoint of the line joining (3, 0) and (15, 2)? (a) (6, 1) (b) (1, 9) (c) (9, 1) (d) (18, 2)
13. 13.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 105° (c) 76° (d) 255°
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
15. 15.A bag has 3 white, 6 blue and 8 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/17 (b) 8/17 (c) 1/3 (d) 8/9
16. 16.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
18. 18.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
19. 19.Which is the correct factorisation of x² + 9x + 20? (a) (x + 4)(x + 5) (b) (x + 1)(x + 20) (c) (x + 1)(x + 8) (d) (x − 4)(x − 5)
20. 20.In a class of 41 children, 25 like cricket, 13 like football and 6 like both. How many like neither? (a) 6 (b) 3 (c) 9 (d) 15
21. 21.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
22. 22.In a class of 33 children, 18 like mangoes, 23 like bananas and 12 like both. How many like at least one of the two? (a) 41 (b) 17 (c) 33 (d) 29
23. 23.What is the distance between the points (6, 7) and (9, 11)? (a) 25 (b) 7 (c) 5 (d) 6
24. 24.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 6 (c) 12 (d) 9
25. 25.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5³
26. 26.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 22 (d) 121
27. 27.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 110° (b) 290° (c) 70° (d) 145°
28. 28.If a + b = 10 and ab = 24, what is (a − b)²? (a) 100 (b) 52 (c) 4 (d) 2
29. 29.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1609 (b) 1369 (c) 1849 (d) 1859
30. 30.A bag has 7 yellow, 7 white and 8 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 7/22 (b) 1/3 (c) 15/22 (d) 7/15
31. 31.The mean of 8 numbers is 20. When the number 2 is added to them, what is the new mean? (a) 19 (b) 18 (c) 11 (d) 20
32. 32.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 130° (b) 115° (c) 65° (d) 245°
33. 33.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30
34. 34.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 120° (d) 70°
35. 35.There are 3 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) 30 (b) 18 (c) 8 (d) 15
36. 36.In a class of 18 children, 8 like mangoes, 11 like bananas and 1 like neither. How many like both? (a) 1 (b) 3 (c) 17 (d) 2
37. 37.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 6 (d) 5
38. 38.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36
39. 39.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 270 (d) 258
40. 40.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times

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