Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 800 · 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 midpoint of the line joining (2, 1) and (8, 3)? (a) (10, 4) (b) (3, 1) (c) (2, 5) (d) (5, 2)
2. 2.A bag has 2 red, 9 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 4/13 (b) 9/13 (c) 4/9 (d) 1/3
3. 3.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 2 (d) 1
4. 4.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 2 (d) 3
5. 5.In a class of 21 children, 17 like cricket, 11 like football and 8 like both. How many like only cricket? (a) 9 (b) 17 (c) 3 (d) 10
6. 6.In a class of 37 children, 17 like mangoes, 20 like bananas and 2 like both. How many like neither? (a) 3 (b) 2 (c) 4 (d) 0
7. 7.In a class of 25 children, 14 like cricket, 7 like football and 3 like both. How many like neither? (a) 7 (b) 10 (c) 3 (d) 4
8. 8.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 160° (d) 80°
9. 9.There are 8 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 16 (b) 32 (c) 24 (d) 10
10. 10.A bag has 5 yellow, 8 white and 7 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/10 (b) 1/4 (c) 1/3 (d) 3/4
11. 11.In which quadrant does the point (−6, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
12. 12.How many factors does 46 have? (a) 5 (b) 4 (c) 3 (d) 2
13. 13.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
15. 15.What is the sum of the roots of x² − 13x + 36 = 0? (a) 36 (b) 14 (c) 13 (d) 12
16. 16.What is the mean of 19, 6, 13, 6, 14 and 20? (a) 15 (b) 12 (c) 14 (d) 13
17. 17.In which quadrant does the point (1, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
18. 18.What is the 17th term of the AP 16, 19, 22, 25, …? (a) 64 (b) 67 (c) 51 (d) 48
19. 19.What is the midpoint of the line joining (6, 11) and (8, 5)? (a) (8, 7) (b) (1, 3) (c) (7, 8) (d) (14, 16)
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 7/36 (d) 1/6
21. 21.A bag has 7 yellow balls and 4 white 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) 8 (c) 5 (d) 11
22. 22.What is the mean of 17, 2, 19 and 10? (a) 11 (b) 16 (c) 12 (d) 13
23. 23.How many factors does 79 have? (a) 2 (b) 1 (c) 4 (d) 3
24. 24.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 12 (c) 5 (d) 6
25. 25.A drawer has lots of 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) 3 (b) 4 (c) 2 (d) 5
26. 26.In a class of 24 children, 20 like mangoes, 5 like bananas and 2 like both. How many like neither? (a) 2 (b) 3 (c) 1 (d) 0
27. 27.In a class of 41 children, 28 like tea, 20 like coffee and 9 like both. How many like neither? (a) 3 (b) 2 (c) 9 (d) 11
28. 28.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 155° (b) 105° (c) 100° (d) 75°
29. 29.What is the median of 38, 4, 11, 26 and 14? (a) 26 (b) 15 (c) 14 (d) 11
30. 30.What is the prime factorisation of 21? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3 × 7
31. 31.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 2 (d) 1
32. 32.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 125° (d) 110°
33. 33.What is the median of 35, 10, 39, 8 and 4? (a) 35 (b) 10 (c) 39 (d) 8
34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 4 (b) 3 (c) 6 (d) 5
35. 35.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
36. 36.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
37. 37.In a class of 32 children, 14 like maths, 17 like science and 6 like both. How many like at least one of the two? (a) 32 (b) 19 (c) 31 (d) 25
38. 38.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 117 (d) 39
39. 39.What are the roots of x² − 13x + 36 = 0? (a) 1 and 36 (b) 2 and 18 (c) 1 and 12 (d) 4 and 9
40. 40.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 11 (c) 48 (d) 32

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