Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 925 · 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.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) 144 (b) 16 (c) 51 (d) 48
2. 2.What is the mean of 11, 7, 4, 5, 13 and 20? (a) 11 (b) 10 (c) 9 (d) 12
3. 3.A bag has 4 black balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 5 (d) 10
4. 4.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
5. 5.A bag has 11 blue balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 12 (c) 2 (d) 19
6. 6.What are the roots of x² − 15x + 54 = 0? (a) 1 and 54 (b) 1 and 14 (c) 6 and 9 (d) 2 and 27
7. 7.What is the distance between the points (1, 8) and (13, 24)? (a) 28 (b) 21 (c) 400 (d) 20
8. 8.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 110° (b) 95° (c) 85° (d) 155°
9. 9.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 729 (b) 909 (c) 1089 (d) 1099
10. 10.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 56 (c) 64 (d) 28
11. 11.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
12. 12.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
13. 13.What is the mean of 20, 2, 4, 4 and 15? (a) 11 (b) 8 (c) 10 (d) 9
14. 14.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
15. 15.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2³ × 5 (d) 2² × 5
16. 16.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 40° (c) 30° (d) 140°
17. 17.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 40°
18. 18.How many prime numbers are there between 60 and 80? (a) 6 (b) 5 (c) 4 (d) 7
19. 19.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 6)(x + 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)
20. 20.What is the mean of 18, 15, 9, 5 and 13? (a) 13 (b) 15 (c) 12 (d) 10
21. 21.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7⁴
22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
23. 23.What is the 35th term of the AP 10, 19, 28, 37, …? (a) 325 (b) 316 (c) 306 (d) 315
24. 24.What is the mean of 19, 2, 11, 19, 11 and 10? (a) 11 (b) 13 (c) 14 (d) 12
25. 25.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
26. 26.A drawer has lots of white and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 4 (d) 3
27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 17 (b) 6 (c) 16 (d) 15
28. 28.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 50° (d) 160°
29. 29.What is the mean of 18, 16, 2, 14, 18 and 10? (a) 14 (b) 13 (c) 15 (d) 12
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 1/6 (d) 7/36
31. 31.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
32. 32.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 9 (c) 40 (d) 20
33. 33.Which term of the AP 4, 8, 12, 16, … is 108? (a) 26th (b) 28th (c) 27th (d) 29th
34. 34.A bag has 10 blue balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 15 (c) 2 (d) 12
35. 35.In a class of 37 children, 26 like cricket, 20 like football and 2 like neither. How many like both? (a) 9 (b) 2 (c) 35 (d) 11
36. 36.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 354 (c) 364 (d) 314
37. 37.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 72 (c) 16 (d) 17
38. 38.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
39. 39.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 9 (c) 25 (d) 20
40. 40.A bag has 7 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 13 (d) 7

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