Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 968 · 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.What is the 20th term of the AP 8, 11, 14, 17, …? (a) 65 (b) 60 (c) 57 (d) 68
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
3. 3.Which is the correct factorisation of x² + 10x + 16? (a) (x − 2)(x − 8) (b) (x + 1)(x + 16) (c) (x + 1)(x + 9) (d) (x + 2)(x + 8)
4. 4.In a class of 29 children, 23 like tea, 16 like coffee and 2 like neither. How many like both? (a) 12 (b) 27 (c) 10 (d) 2
5. 5.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 51 (b) 264 (c) 240 (d) 480
6. 6.In a class of 48 children, 25 like mangoes, 19 like bananas and 6 like both. How many like at least one of the two? (a) 48 (b) 38 (c) 32 (d) 44
7. 7.What is the median of 26, 21, 29, 24 and 3? (a) 24 (b) 29 (c) 26 (d) 21
8. 8.What is the midpoint of the line joining (8, 4) and (12, 16)? (a) (2, 6) (b) (10, 10) (c) (11, 10) (d) (20, 20)
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
10. 10.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
11. 11.What is the mode of 13, 10, 20, 13, 20, 3 and 20? (a) 10 (b) 3 (c) 13 (d) 20
12. 12.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 75° (c) 15° (d) 285°
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
14. 14.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 529 (c) 519 (d) 424
15. 15.In which quadrant does the point (−7, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
16. 16.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 11 (d) 25
17. 17.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
18. 18.What is the product of the roots of x² − 13x + 40 = 0? (a) 40 (b) 39 (c) 41 (d) 13
19. 19.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
20. 20.A drawer has lots of red, blue 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) 3 (b) 2 (c) 6 (d) 4
21. 21.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 7)(x + 8) (c) (x − 7)(x − 8) (d) (x + 1)(x + 56)
22. 22.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2738 (c) 2775 (d) 5550
23. 23.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
26. 26.What are the roots of x² − 6x + 8 = 0? (a) 1 and 5 (b) 2 and 5 (c) 1 and 8 (d) 2 and 4
27. 27.A bag has 5 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 8 (c) 2 (d) 6
28. 28.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
29. 29.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 345 (c) 302 (d) 336
30. 30.What is the mean of 7, 12, 4, 16, 7 and 14? (a) 10 (b) 11 (c) 9 (d) 12
31. 31.A drawer has lots of white, red, yellow, black and blue 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) 6 (c) 10 (d) 2
32. 32.In a class of 34 children, 11 like dance, 19 like music and 5 like both. How many like neither? (a) 4 (b) 14 (c) 5 (d) 9
33. 33.What is the midpoint of the line joining (3, 10) and (5, 20)? (a) (15, 4) (b) (4, 15) (c) (1, 5) (d) (8, 30)
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
35. 35.In which quadrant does the point (9, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
36. 36.Which is the correct factorisation of x² + 11x + 18? (a) (x + 2)(x + 9) (b) (x − 2)(x − 9) (c) (x + 1)(x + 18) (d) (x + 1)(x + 10)
37. 37.A drawer has lots of green, yellow, black and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 8 (d) 4
38. 38.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
39. 39.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2 × 3² (d) 2² × 3
40. 40.In a class of 30 children, 6 like tea, 20 like coffee and 2 like both. How many like at least one of the two? (a) 22 (b) 26 (c) 24 (d) 30

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