Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 288 · 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 mode of 1, 11, 3, 3, 9, 1 and 3? (a) 3 (b) 11 (c) 9 (d) 1
2. 2.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 55° (d) 46°
3. 3.A drawer has lots of black, red, yellow, 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) 2 (b) 5 (c) 10 (d) 6
4. 4.In a class of 31 children, 15 like mangoes, 20 like bananas and 6 like neither. How many like both? (a) 6 (b) 10 (c) 4 (d) 25
5. 5.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x + 2)(x + 5) (c) (x − 2)(x − 5) (d) (x + 1)(x + 6)
6. 6.What is the mean of 19, 4, 12 and 21? (a) 15 (b) 16 (c) 14 (d) 13
7. 7.What is the smallest prime factor of 143? (a) 2 (b) 13 (c) 11 (d) 1
8. 8.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 6 (b) 5 (c) 4 (d) 7
10. 10.Using (a − b)² = a² − 2ab + b², what is 59²? (a) 3481 (b) 3721 (c) 3491 (d) 3599
11. 11.A bag has 9 green balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 10 (c) 11 (d) 15
12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 20 (d) 19
13. 13.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 361 (b) 441 (c) 401 (d) 451
14. 14.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x − 6)(x − 7) (c) (x + 6)(x + 7) (d) (x + 1)(x + 42)
15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 9 (d) 20
16. 16.In a class of 34 children, 21 like tea, 16 like coffee and 12 like both. How many like at least one of the two? (a) 13 (b) 34 (c) 37 (d) 25
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
19. 19.What is the mode of 3, 2, 18, 2, 14, 2 and 14? (a) 18 (b) 14 (c) 2 (d) 3
20. 20.A bag has 8 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 19 (b) 9 (c) 10 (d) 2
21. 21.In a class of 27 children, 12 like dance, 11 like music and 6 like both. How many like at least one of the two? (a) 23 (b) 27 (c) 11 (d) 17
22. 22.In a class of 33 children, 17 like maths, 8 like science and 2 like both. How many like neither? (a) 12 (b) 8 (c) 2 (d) 10
23. 23.How many factors does 56 have? (a) 8 (b) 7 (c) 9 (d) 6
24. 24.What is the product of the roots of x² − 11x + 30 = 0? (a) 11 (b) 29 (c) 31 (d) 30
25. 25.What is the distance between the points (8, 6) and (20, 11)? (a) 169 (b) 13 (c) 17 (d) 14
26. 26.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 49 (b) 42 (c) 13 (d) 84
27. 27.If a + b = 14 and ab = 40, what is (a − b)²? (a) 6 (b) 196 (c) 116 (d) 36
28. 28.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 270°
29. 29.Which is the correct factorisation of x² + 11x + 28? (a) (x + 4)(x + 7) (b) (x + 1)(x + 10) (c) (x + 1)(x + 28) (d) (x − 4)(x − 7)
30. 30.The mean of 3 numbers is 30. When the number 26 is added to them, what is the new mean? (a) 30 (b) 31 (c) 29 (d) 28
31. 31.A drawer has lots of black, green, white, 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) 6 (b) 5 (c) 2 (d) 10
32. 32.What is the mean of 7, 3, 2 and 4? (a) 3 (b) 5 (c) 4 (d) 6
33. 33.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 120° (c) 25° (d) 155°
34. 34.In a class of 23 children, 18 like cricket, 16 like football and 12 like both. How many like neither? (a) 13 (b) 12 (c) 1 (d) 2
35. 35.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 11 (c) 35 (d) 30
36. 36.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
37. 37.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 95° (b) 105° (c) 85° (d) 160°
38. 38.What is the midpoint of the line joining (8, 5) and (12, 3)? (a) (4, 10) (b) (20, 8) (c) (2, 1) (d) (10, 4)
39. 39.In a class of 41 children, 23 like dance, 11 like music and 3 like both. How many like only dance? (a) 30 (b) 8 (c) 23 (d) 20
40. 40.A cuboid is 9 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 230 cu cm (b) 19 cu cm (c) 45 cu cm (d) 225 cu cm

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