Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 539 · 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.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 140° (b) 120° (c) 80° (d) 100°
2. 2.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 135 (c) 48 (d) 15
3. 3.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 45 (d) 90
4. 4.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 296 (c) 327 (d) 337
5. 5.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
6. 6.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 33 (d) 36
7. 7.A bag has 12 blue balls and 13 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 25 (c) 14 (d) 2
8. 8.What is the smallest prime factor of 121? (a) 3 (b) 11 (c) 2 (d) 1
9. 9.The mean of 3 numbers is 25. When the number 21 is added to them, what is the new mean? (a) 23 (b) 26 (c) 25 (d) 24
10. 10.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 3 (d) 2
11. 11.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 505 (c) 504 (d) 408
12. 12.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 21 (d) 49
13. 13.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 130° (b) 160° (c) 70° (d) 50°
14. 14.A drawer has lots of red, black, yellow 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) 2 (c) 5 (d) 8
15. 15.Which term of the AP 5, 14, 23, 32, … is 347? (a) 39th (b) 41st (c) 38th (d) 40th
16. 16.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 10 (d) 15
17. 17.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
18. 18.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 240 (d) 25
19. 19.What is the median of 8, 26, 27, 19, 15, 9 and 3? (a) 15 (b) 16 (c) 19 (d) 9
20. 20.How many factors does 46 have? (a) 3 (b) 2 (c) 4 (d) 5
21. 21.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
22. 22.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 144 (d) 132
23. 23.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2⁴ × 3² × 7
24. 24.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
25. 25.What is the median of 2, 30, 20, 37, 32, 1 and 28? (a) 37 (b) 28 (c) 20 (d) 30
26. 26.A bag has 7 blue balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 17 (b) 2 (c) 9 (d) 8
27. 27.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 50° (b) 230° (c) 115° (d) 130°
28. 28.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 90 (c) 30 (d) 10
29. 29.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 65° (c) 135° (d) 115°
30. 30.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 66° (c) 65° (d) 115°
31. 31.In a class of 40 children, 24 like maths, 19 like science and 8 like both. How many like at least one of the two? (a) 35 (b) 40 (c) 43 (d) 27
32. 32.A bag has 7 red, 2 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
33. 33.There are 4 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 8 (c) 12 (d) 16
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/9 (c) 1/12 (d) 3/11
35. 35.A bag has 10 white balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 9 (d) 18
36. 36.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) 125 times (c) 10 times (d) 5 times
37. 37.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 75° (b) 115° (c) 10° (d) 170°
38. 38.In a class of 23 children, 16 like dance, 13 like music and 3 like neither. How many like both? (a) 20 (b) 6 (c) 3 (d) 9
39. 39.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
40. 40.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 325 (b) 350 (c) 55 (d) 650

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