Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 549 · 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 straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 10° (c) 80° (d) 100°
2. 2.A drawer has lots of blue and white 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) 5 (c) 3 (d) 2
3. 3.A bag has 5 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 2 (c) 9 (d) 7
4. 4.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 36 (c) 108 (d) 12
5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 1 (d) 3
6. 6.In which quadrant does the point (2, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
7. 7.In a class of 41 children, 26 like maths, 17 like science and 11 like both. How many like at least one of the two? (a) 43 (b) 21 (c) 32 (d) 41
8. 8.In a class of 36 children, 13 like dance, 22 like music and 9 like neither. How many like both? (a) 9 (b) 7 (c) 27 (d) 8
9. 9.A cuboid is 9 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 159 sq cm (b) 378 sq cm (c) 318 sq cm (d) 636 sq cm
10. 10.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) 50° (c) 140° (d) 40°
11. 11.What is the mean of 17, 9, 16, 2, 19 and 9? (a) 14 (b) 12 (c) 11 (d) 13
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 4 (d) 2
13. 13.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 125° (b) 55° (c) 160° (d) 145°
14. 14.In a class of 36 children, 10 like tea, 26 like coffee and 6 like both. How many like neither? (a) 6 (b) 0 (c) 12 (d) 7
15. 15.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 60° (d) 330°
16. 16.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4656 (c) 9312 (d) 4608
17. 17.What is the median of 33, 19, 31, 13, 39, 38 and 9? (a) 33 (b) 13 (c) 26 (d) 31
18. 18.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
19. 19.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 4 (d) 6
20. 20.8 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) 64 (b) 32 (c) 40 (d) 12
21. 21.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
22. 22.What is the mean of 7, 8, 19 and 2? (a) 10 (b) 12 (c) 8 (d) 9
23. 23.A bag has 5 white balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 10 (c) 7 (d) 2
24. 24.In which quadrant does the point (−9, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
25. 25.What is the 10th term of the AP 1, 4, 7, 10, …? (a) 28 (b) 30 (c) 27 (d) 31
26. 26.In which quadrant does the point (5, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
27. 27.If a + b = 16 and ab = 60, what is (a − b)²? (a) 16 (b) 136 (c) 256 (d) 4
28. 28.In a class of 39 children, 21 like mangoes, 25 like bananas and 10 like both. How many like only mangoes? (a) 21 (b) 15 (c) 11 (d) 14
29. 29.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 24 (c) 28 (d) 48
30. 30.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 135° (c) 45° (d) 136°
31. 31.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2³ × 5 (c) 2⁴ × 5 (d) 2 × 5⁴
32. 32.What is the midpoint of the line joining (7, 1) and (13, 11)? (a) (6, 10) (b) (3, 5) (c) (10, 6) (d) (20, 12)
33. 33.A bag has 8 yellow balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 9 (d) 18
34. 34.If a + b = 18 and ab = 80, what is a² + b²? (a) 484 (b) 324 (c) 164 (d) 244
35. 35.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 42 (d) 14
36. 36.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 115° (c) 70° (d) 110°
37. 37.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 472 (c) 601 (d) 591
38. 38.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
39. 39.What is the smallest prime factor of 91? (a) 7 (b) 2 (c) 13 (d) 1
40. 40.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6

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