Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 850 · 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. 1.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 28 (c) 56 (d) 32
2. 2.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
3. 3.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 507 (c) 508 (d) 498
4. 4.A bag has 4 blue balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 5 (c) 7 (d) 10
5. 5.What is the median of 40, 20, 11, 15, 6, 33 and 35? (a) 21 (b) 33 (c) 15 (d) 20
6. 6.Which is the correct factorisation of x² + 8x + 12? (a) (x + 2)(x + 6) (b) (x − 2)(x − 6) (c) (x + 1)(x + 12) (d) (x + 1)(x + 7)
7. 7.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 2)(x + 3) (c) (x + 1)(x + 6) (d) (x + 1)(x + 4)
8. 8.What is the mean of 6, 17, 19 and 18? (a) 15 (b) 16 (c) 12 (d) 20
9. 9.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2³ × 5 (d) 2² × 5
10. 10.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 13 (b) 15 (c) 11 (d) 12
11. 11.What is the product of the roots of x² − 11x + 28 = 0? (a) 29 (b) 27 (c) 11 (d) 28
12. 12.If a + b = 12 and ab = 32, what is (a − b)²? (a) 4 (b) 80 (c) 16 (d) 144
13. 13.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 245° (d) 130°
14. 14.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 130° (c) 50° (d) 230°
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 15 (b) 16 (c) 17 (d) 5
16. 16.How many prime numbers are there between 10 and 30? (a) 5 (b) 7 (c) 8 (d) 6
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
18. 18.A drawer has lots of green, red 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) 4 (b) 6 (c) 2 (d) 3
19. 19.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 54 sq cm (d) 36 sq cm
20. 20.What is the prime factorisation of 45? (a) 3 × 5² (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5
21. 21.In a class of 33 children, 16 like dance, 13 like music and 6 like both. How many like neither? (a) 16 (b) 4 (c) 10 (d) 6
22. 22.If a + b = 15 and ab = 44, what is a² + b²? (a) 313 (b) 137 (c) 225 (d) 181
23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 7 (b) 6 (c) 9 (d) 8
24. 24.What is the smallest prime factor of 299? (a) 2 (b) 1 (c) 13 (d) 23
25. 25.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
26. 26.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
27. 27.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 80° (c) 100° (d) 10°
28. 28.A drawer has lots of white and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 3 (d) 5
29. 29.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 49 (c) 56 (d) 98
30. 30.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 132 (d) 144
31. 31.In a class of 39 children, 18 like dance, 16 like music and 8 like neither. How many like both? (a) 3 (b) 4 (c) 31 (d) 8
32. 32.What is the smallest prime factor of 217? (a) 2 (b) 7 (c) 1 (d) 31
33. 33.A bag has 4 green balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 5 (c) 14 (d) 11
34. 34.What is the 35th term of the AP 6, 14, 22, 30, …? (a) 280 (b) 286 (c) 272 (d) 278
35. 35.What is the midpoint of the line joining (5, 8) and (13, 2)? (a) (18, 10) (b) (4, 3) (c) (5, 9) (d) (9, 5)
36. 36.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 16 (d) 24
37. 37.How many factors does 109 have? (a) 2 (b) 3 (c) 4 (d) 1
38. 38.What is the distance between the points (4, 9) and (19, 1)? (a) 289 (b) 18 (c) 23 (d) 17
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
40. 40.A bag has 4 red balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 2 (c) 5 (d) 6

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