Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 673 · 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 75° and 55°. What is the third angle? (a) 125° (b) 50° (c) 105° (d) 130°
2. 2.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 256 sq cm (d) 512 sq cm
3. 3.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 25° (d) 30°
4. 4.In a class of 20 children, 8 like cricket, 14 like football and 5 like both. How many like neither? (a) 4 (b) 5 (c) 8 (d) 3
5. 5.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 48 (c) 37 (d) 49
6. 6.What is the mean of 9, 12, 7, 2, 5 and 13? (a) 10 (b) 9 (c) 8 (d) 7
7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
8. 8.What are the roots of x² − 17x + 72 = 0? (a) 2 and 36 (b) 8 and 9 (c) 1 and 16 (d) 1 and 72
9. 9.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 50° (d) 140°
10. 10.In a class of 26 children, 10 like maths, 16 like science and 6 like both. How many like only maths? (a) 4 (b) 5 (c) 6 (d) 10
11. 11.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 45 (c) 15 (d) 5
12. 12.How many factors does 107 have? (a) 3 (b) 2 (c) 1 (d) 4
13. 13.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 95° (b) 145° (c) 60° (d) 120°
14. 14.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7⁴
15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
16. 16.What is the smallest prime factor of 51? (a) 17 (b) 3 (c) 1 (d) 2
17. 17.In a class of 43 children, 26 like tea, 19 like coffee and 10 like both. How many like neither? (a) 9 (b) 10 (c) 18 (d) 8
18. 18.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x + 1)(x + 10) (c) (x − 5)(x − 6) (d) (x + 5)(x + 6)
19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
20. 20.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 1/4 (d) 5/6
21. 21.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
22. 22.What is the mode of 17, 5, 2, 5, 5, 13 and 2? (a) 2 (b) 5 (c) 13 (d) 17
23. 23.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 125° (d) 155°
24. 24.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7 (c) 2 × 7² (d) 2³ × 7
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 5/36 (d) 1/6
26. 26.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 1)(x + 56) (c) (x − 7)(x − 8) (d) (x + 7)(x + 8)
27. 27.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 630 (c) 595 (d) 1260
28. 28.What is the midpoint of the line joining (6, 3) and (12, 1)? (a) (9, 2) (b) (2, 9) (c) (3, 1) (d) (18, 4)
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/11 (c) 5/36 (d) 1/11
30. 30.What is the product of the roots of x² − 10x + 16 = 0? (a) 16 (b) 15 (c) 10 (d) 17
31. 31.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 1)(x + 8) (c) (x + 1)(x + 5) (d) (x + 2)(x + 4)
32. 32.What is the mean of 12, 7, 14, 16 and 6? (a) 11 (b) 12 (c) 10 (d) 13
33. 33.What is the median of 39, 28, 4, 17, 6, 32 and 7? (a) 19 (b) 7 (c) 28 (d) 17
34. 34.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 9 (c) 6 (d) 12
35. 35.How many prime numbers are there between 20 and 40? (a) 5 (b) 4 (c) 3 (d) 6
36. 36.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.What is the product of the roots of x² − 17x + 72 = 0? (a) 72 (b) 71 (c) 17 (d) 73
38. 38.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2484 (b) 2116 (c) 2126 (d) 2916
39. 39.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
40. 40.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 56 (c) 15 (d) 14

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