Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 11 · 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 angles of a triangle are 45° and 110°. What is the third angle? (a) 25° (b) 135° (c) 70° (d) 155°
2. 2.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
3. 3.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
4. 4.What is the smallest prime factor of 169? (a) 1 (b) 2 (c) 3 (d) 13
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
6. 6.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 7 (b) 6 (c) 9 (d) 8
8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 8 (b) 6 (c) 5 (d) 7
9. 9.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 160° (b) 95° (c) 105° (d) 20°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 35° (c) 145° (d) 290°
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/9 (c) 1/11 (d) 3/11
12. 12.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 110° (d) 70°
13. 13.What is the smallest prime factor of 77? (a) 11 (b) 2 (c) 7 (d) 1
14. 14.If a + b = 9 and ab = 14, what is (a − b)²? (a) 81 (b) 53 (c) 5 (d) 25
15. 15.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
16. 16.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 704 (c) 703 (d) 666
17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
18. 18.If a + b = 20 and ab = 99, what is a² + b²? (a) 202 (b) 598 (c) 400 (d) 301
19. 19.How many factors does 36 have? (a) 7 (b) 9 (c) 10 (d) 8
20. 20.In a class of 29 children, 15 like cricket, 22 like football and 10 like both. How many like neither? (a) 12 (b) 10 (c) 3 (d) 2
21. 21.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2³ × 3 (d) 2⁴ × 3
22. 22.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
23. 23.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 155° (d) 145°
24. 24.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 56 (c) 28 (d) 36
25. 25.7 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) 14 (b) 56 (c) 49 (d) 98
26. 26.What is the 11th term of the AP 1, 7, 13, 19, …? (a) 67 (b) 60 (c) 66 (d) 61
27. 27.How many prime numbers are there between 60 and 90? (a) 6 (b) 8 (c) 7 (d) 9
28. 28.In a class of 44 children, 19 like dance, 25 like music and 5 like both. How many like at least one of the two? (a) 44 (b) 34 (c) 40 (d) 39
29. 29.What is the midpoint of the line joining (2, 10) and (8, 22)? (a) (3, 6) (b) (10, 32) (c) (5, 16) (d) (16, 5)
30. 30.A drawer has lots of blue, black 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) 2 (b) 4 (c) 3 (d) 6
31. 31.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 595 (c) 561 (d) 1190
32. 32.What is the median of 17, 23, 26, 34, 18, 16 and 11? (a) 23 (b) 34 (c) 18 (d) 17
33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 4 (c) 3 (d) 5
34. 34.A bag has 3 blue balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 4 (b) 5 (c) 15 (d) 2
35. 35.In which quadrant does the point (3, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
36. 36.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 120° (b) 35° (c) 145° (d) 95°
37. 37.A bag has 3 red, 5 green and 2 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 3/5 (b) 1/3 (c) 1/2 (d) 1/10
38. 38.What is the mean of 4, 20, 13, 12, 17 and 12? (a) 14 (b) 12 (c) 13 (d) 15
39. 39.What is the smallest prime factor of 319? (a) 11 (b) 1 (c) 29 (d) 2
40. 40.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 115° (d) 135°

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