Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 626 · 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.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
2. 2.What is the 11th term of the AP 16, 19, 22, 25, …? (a) 30 (b) 33 (c) 49 (d) 46
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
4. 4.A bag has 3 red, 6 green and 8 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 10/17 (b) 8/17 (c) 1/3 (d) 9/17
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
6. 6.Which is the correct factorisation of x² + 11x + 18? (a) (x + 2)(x + 9) (b) (x − 2)(x − 9) (c) (x + 1)(x + 10) (d) (x + 1)(x + 18)
7. 7.A bag has 5 white balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 11 (d) 6
8. 8.In a class of 24 children, 14 like tea, 14 like coffee and 6 like both. How many like at least one of the two? (a) 16 (b) 24 (c) 22 (d) 28
9. 9.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 78 (d) 77
10. 10.In a class of 18 children, 8 like cricket, 8 like football and 6 like neither. How many like both? (a) 5 (b) 4 (c) 12 (d) 6
11. 11.How many factors does 65 have? (a) 2 (b) 5 (c) 3 (d) 4
12. 12.What is the median of 1, 37, 3, 39, 32, 40 and 24? (a) 39 (b) 37 (c) 32 (d) 24
13. 13.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 1625 (b) 2025 (c) 2035 (d) 1225
14. 14.Using (a + b)² = a² + 2ab + b², what is 51²? (a) 2501 (b) 2401 (c) 2601 (d) 2611
15. 15.What is the prime factorisation of 21? (a) 3 × 7² (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7
16. 16.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
17. 17.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 729 (b) 1089 (c) 1099 (d) 909
18. 18.What is the 13th term of the AP 14, 18, 22, 26, …? (a) 66 (b) 52 (c) 48 (d) 62
19. 19.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 1)(x + 72) (c) (x − 8)(x − 9) (d) (x + 8)(x + 9)
20. 20.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2² × 3²
21. 21.What is the median of 10, 24, 29, 39 and 7? (a) 25 (b) 10 (c) 29 (d) 24
22. 22.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 42 (c) 84 (d) 13
23. 23.A bag has 12 black balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 15 (c) 2 (d) 13
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
25. 25.A bag has 6 green, 9 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/6 (b) 8/9 (c) 1/6 (d) 1/3
26. 26.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 65° (d) 100°
27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
29. 29.The mean of 7 numbers is 16. When the number 48 is added to them, what is the new mean? (a) 32 (b) 21 (c) 20 (d) 16
30. 30.A bag has 11 red balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 11 (c) 2 (d) 12
31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 784 (d) 812
32. 32.What is the distance between the points (2, 18) and (14, 2)? (a) 400 (b) 21 (c) 28 (d) 20
33. 33.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 198 (c) 22 (d) 66
34. 34.What is the product of the roots of x² − 11x + 30 = 0? (a) 30 (b) 11 (c) 29 (d) 31
35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
36. 36.The mean of 9 numbers is 36. When the number 66 is added to them, what is the new mean? (a) 39 (b) 36 (c) 51 (d) 40
37. 37.The mean of 5 numbers is 34. When the number 52 is added to them, what is the new mean? (a) 38 (b) 34 (c) 37 (d) 43
38. 38.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
39. 39.What is the distance between the points (9, 9) and (21, 25)? (a) 28 (b) 21 (c) 20 (d) 400
40. 40.What is the midpoint of the line joining (10, 1) and (16, 9)? (a) (3, 4) (b) (13, 5) (c) (26, 10) (d) (5, 13)

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