Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 743 · 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 team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
2. 2.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 205 (c) 208 (d) 204
3. 3.What is the midpoint of the line joining (7, 3) and (15, 7)? (a) (4, 2) (b) (11, 5) (c) (5, 11) (d) (22, 10)
4. 4.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1225 (b) 1575 (c) 2025 (d) 1235
5. 5.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 16 (c) 17 (d) 72
6. 6.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 9 sq cm (d) 54 sq cm
7. 7.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2⁵ × 3
8. 8.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3003 (c) 3081 (d) 6162
9. 9.What is the midpoint of the line joining (4, 1) and (12, 5)? (a) (16, 6) (b) (4, 2) (c) (3, 8) (d) (8, 3)
10. 10.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 270° (c) 90° (d) 135°
11. 11.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
12. 12.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 45 (d) 90
13. 13.What is the 12th term of the AP 4, 11, 18, 25, …? (a) 77 (b) 84 (c) 81 (d) 88
14. 14.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 60°
15. 15.If a + b = 6 and ab = 5, what is (a − b)²? (a) 36 (b) 4 (c) 26 (d) 16
16. 16.What is the mean of 15, 7, 2 and 16? (a) 10 (b) 8 (c) 11 (d) 9
17. 17.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 630 (d) 631
18. 18.Which term of the AP 13, 20, 27, 34, … is 83? (a) 11th (b) 12th (c) 13th (d) 10th
19. 19.In a class of 35 children, 15 like maths, 29 like science and 10 like both. How many like only maths? (a) 19 (b) 6 (c) 15 (d) 5
20. 20.A bag has 3 blue balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 14 (d) 4
21. 21.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 100° (b) 155° (c) 80° (d) 125°
22. 22.What is the smallest prime factor of 55? (a) 5 (b) 2 (c) 1 (d) 11
23. 23.The mean of 3 numbers is 25. When the number 21 is added to them, what is the new mean? (a) 23 (b) 25 (c) 26 (d) 24
24. 24.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 45° (d) 55°
25. 25.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 16 (c) 51 (d) 144
26. 26.Which is the correct factorisation of x² + 13x + 36? (a) (x − 4)(x − 9) (b) (x + 1)(x + 12) (c) (x + 1)(x + 36) (d) (x + 4)(x + 9)
27. 27.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 1)(x + 12) (c) (x + 6)(x + 7) (d) (x + 1)(x + 42)
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
29. 29.A bag has 7 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 8 (c) 9 (d) 10
30. 30.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 3/4 (c) 1/2 (d) 1/3
31. 31.What is the midpoint of the line joining (2, 12) and (12, 6)? (a) (14, 18) (b) (5, 3) (c) (9, 7) (d) (7, 9)
32. 32.A bag has 3 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 4 (c) 14 (d) 5
33. 33.What is the mean of 5, 4, 15, 15 and 6? (a) 10 (b) 8 (c) 9 (d) 11
34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
35. 35.Which term of the AP 8, 17, 26, 35, … is 323? (a) 38th (b) 36th (c) 35th (d) 37th
36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 24 (d) 16
37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 1 (d) 3
38. 38.How many factors does 36 have? (a) 7 (b) 10 (c) 9 (d) 8
39. 39.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 48 (c) 39 (d) 40
40. 40.In a class of 45 children, 15 like tea, 28 like coffee and 8 like both. How many like only tea? (a) 20 (b) 15 (c) 7 (d) 17

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