Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 906 · 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.A bag has 8 green balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 17 (b) 9 (c) 2 (d) 10
2. 2.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 166 (c) 156 (d) 174
3. 3.The mean of 9 numbers is 32. When the number 22 is added to them, what is the new mean? (a) 30 (b) 32 (c) 27 (d) 31
4. 4.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3² (c) 2² × 3 (d) 2 × 3²
5. 5.What is the median of 39, 20, 12, 21 and 28? (a) 24 (b) 12 (c) 28 (d) 21
6. 6.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
7. 7.What is the sum of the roots of x² − 9x + 14 = 0? (a) 10 (b) 9 (c) 14 (d) 8
8. 8.What is the mode of 1, 16, 1, 1, 16, 2 and 14? (a) 2 (b) 14 (c) 1 (d) 16
9. 9.What is the mode of 20, 20, 15, 16, 15, 20 and 3? (a) 15 (b) 3 (c) 16 (d) 20
10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
11. 11.What is the mode of 7, 15, 9, 8, 9, 9 and 15? (a) 15 (b) 7 (c) 8 (d) 9
12. 12.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
13. 13.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 55° (b) 235° (c) 110° (d) 125°
14. 14.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3979 (b) 3969 (c) 3609 (d) 3249
15. 15.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 4) (b) (x + 2)(x + 3) (c) (x + 1)(x + 6) (d) (x − 2)(x − 3)
16. 16.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 8 (d) 72
17. 17.What is the product of the roots of x² − 10x + 16 = 0? (a) 10 (b) 15 (c) 16 (d) 17
18. 18.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2116 (b) 2926 (c) 2516 (d) 2916
19. 19.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
20. 20.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 140° (d) 70°
21. 21.What is the distance between the points (0, 7) and (12, 16)? (a) 16 (b) 21 (c) 225 (d) 15
22. 22.A drawer has lots of red, blue 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) 2 (b) 4 (c) 6 (d) 3
23. 23.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
24. 24.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 75° (d) 105°
25. 25.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 2 (d) 5
26. 26.How many factors does 81 have? (a) 3 (b) 6 (c) 4 (d) 5
27. 27.3 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 15 (c) 18 (d) 8
28. 28.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 72 (c) 36 (d) 42
29. 29.In a class of 38 children, 17 like tea, 21 like coffee and 3 like both. How many like at least one of the two? (a) 36 (b) 38 (c) 32 (d) 35
30. 30.A bag has 5 yellow balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 6 (c) 12 (d) 2
31. 31.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 312 (c) 361 (d) 351
32. 32.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 21 (c) 24 (d) 63
33. 33.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 4235 (b) 3025 (c) 4225 (d) 3625
34. 34.Which term of the AP 19, 27, 35, 43, … is 211? (a) 24th (b) 25th (c) 27th (d) 26th
35. 35.In a class of 23 children, 11 like dance, 10 like music and 7 like both. How many like at least one of the two? (a) 23 (b) 7 (c) 14 (d) 21
36. 36.How many factors does 27 have? (a) 3 (b) 2 (c) 5 (d) 4
37. 37.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
39. 39.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
40. 40.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6

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