Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 265 · 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.Which is the correct factorisation of x² + 15x + 54? (a) (x + 6)(x + 9) (b) (x + 1)(x + 54) (c) (x + 1)(x + 14) (d) (x − 6)(x − 9)
2. 2.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 45 (c) 42 (d) 126
3. 3.In a class of 18 children, 10 like tea, 11 like coffee and 4 like both. How many like neither? (a) 2 (b) 4 (c) 5 (d) 1
4. 4.How many prime numbers are there between 90 and 110? (a) 6 (b) 5 (c) 4 (d) 7
5. 5.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
6. 6.The mean of 7 numbers is 17. When the number 49 is added to them, what is the new mean? (a) 17 (b) 22 (c) 21 (d) 33
7. 7.In a class of 48 children, 30 like maths, 22 like science and 12 like both. How many like at least one of the two? (a) 40 (b) 52 (c) 48 (d) 28
8. 8.What is the product of the roots of x² − 14x + 48 = 0? (a) 14 (b) 49 (c) 47 (d) 48
9. 9.Using (a − b)² = a² − 2ab + b², what is 58²? (a) 3596 (b) 3374 (c) 3844 (d) 3364
10. 10.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 48 (c) 47 (d) 38
11. 11.There are 6 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 24 (c) 10 (d) 48
12. 12.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 210° (c) 150° (d) 31°
13. 13.What is the median of 10, 37, 12, 23, 7, 40 and 8? (a) 23 (b) 10 (c) 13 (d) 12
14. 14.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 85° (d) 86°
15. 15.In a class of 32 children, 18 like maths, 19 like science and 9 like both. How many like neither? (a) 5 (b) 13 (c) 4 (d) 9
16. 16.How many factors does 41 have? (a) 2 (b) 3 (c) 4 (d) 1
17. 17.In a class of 20 children, 11 like tea, 11 like coffee and 3 like both. How many like only tea? (a) 8 (b) 9 (c) 3 (d) 11
18. 18.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 45 (b) 550 (c) 297 (d) 275
19. 19.A bag has 5 white balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 6 (c) 2 (d) 9
20. 20.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 17 (c) 18 (d) 16
21. 21.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 270° (b) 125° (c) 145° (d) 90°
22. 22.A bag has 4 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 6 (c) 2 (d) 12
23. 23.In a class of 38 children, 23 like cricket, 13 like football and 4 like both. How many like only cricket? (a) 19 (b) 9 (c) 25 (d) 23
24. 24.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 55 (b) 335 (c) 330 (d) 660
25. 25.A bag has 8 white balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 9 (c) 20 (d) 10
26. 26.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 9 (c) 25 (d) 30
27. 27.A bag has 9 white, 7 green and 4 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 17/20 (b) 1/3 (c) 4/5 (d) 1/5
28. 28.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2⁴ × 3²
29. 29.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
30. 30.A bag has 4 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 4 (c) 7 (d) 2
31. 31.What is the smallest prime factor of 121? (a) 1 (b) 3 (c) 2 (d) 11
32. 32.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5³
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
34. 34.In which quadrant does the point (4, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
35. 35.In a class of 32 children, 19 like cricket, 7 like football and 9 like neither. How many like both? (a) 4 (b) 9 (c) 3 (d) 23
36. 36.A bag has 7 blue, 3 yellow and 8 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 4/9 (b) 11/18 (c) 1/3 (d) 5/9
37. 37.A bag has 5 blue, 3 green and 2 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 3/10 (b) 3/7 (c) 7/10 (d) 1/3
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 8 (d) 19
39. 39.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1953 (c) 1922 (d) 1891
40. 40.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 28 (c) 10 (d) 24

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