Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 454 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
2. 2.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 48 (d) 24
3. 3.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
4. 4.What is the median of 4, 36, 37, 16 and 6? (a) 37 (b) 16 (c) 6 (d) 36
5. 5.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
6. 6.A bag has 5 green balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 6 (c) 14 (d) 2
7. 7.A bag has 6 green, 9 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 11/17 (b) 6/17 (c) 1/3 (d) 12/17
8. 8.Which is the correct factorisation of x² + 11x + 24? (a) (x + 3)(x + 8) (b) (x + 1)(x + 10) (c) (x − 3)(x − 8) (d) (x + 1)(x + 24)
9. 9.What is the smallest prime factor of 253? (a) 1 (b) 23 (c) 11 (d) 2
10. 10.In a class of 12 children, 5 like cricket, 7 like football and 2 like both. How many like neither? (a) 0 (b) 3 (c) 4 (d) 2
11. 11.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 6 (d) 7
12. 12.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 115° (c) 66° (d) 130°
13. 13.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
16. 16.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
17. 17.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 21 (b) 9 (c) 14 (d) 28
18. 18.A bag has 11 blue balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 15 (b) 12 (c) 13 (d) 2
19. 19.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 225 (b) 375 (c) 625 (d) 235
20. 20.What is the distance between the points (7, 9) and (15, 24)? (a) 289 (b) 23 (c) 18 (d) 17
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 17 (d) 19
22. 22.In a class of 35 children, 18 like maths, 12 like science and 5 like both. How many like neither? (a) 15 (b) 5 (c) 10 (d) 11
23. 23.In a class of 29 children, 17 like tea, 16 like coffee and 12 like both. How many like only tea? (a) 5 (b) 17 (c) 13 (d) 4
24. 24.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 8 (c) 7 (d) 14
25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
26. 26.What is the mean of 20, 5, 12 and 7? (a) 13 (b) 10 (c) 11 (d) 12
27. 27.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 62 sq cm (b) 124 sq cm (c) 248 sq cm (d) 72 sq cm
28. 28.If a + b = 17 and ab = 70, what is (a − b)²? (a) 289 (b) 3 (c) 149 (d) 9
29. 29.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 45) (b) (x + 1)(x + 13) (c) (x − 5)(x − 9) (d) (x + 5)(x + 9)
30. 30.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 130° (b) 140° (c) 90° (d) 270°
31. 31.What is the distance between the points (0, 10) and (15, 2)? (a) 289 (b) 23 (c) 17 (d) 18
32. 32.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x + 1)(x + 8) (c) (x − 2)(x − 4) (d) (x + 1)(x + 5)
33. 33.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
34. 34.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 25 (c) 13 (d) 12
35. 35.A bag has 7 white balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 2 (c) 18 (d) 9
36. 36.In a class of 40 children, 18 like cricket, 25 like football and 5 like both. How many like at least one of the two? (a) 33 (b) 43 (c) 40 (d) 38
37. 37.A bag has 3 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 5 (c) 7 (d) 2
38. 38.A bag has 11 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 16 (c) 13 (d) 2
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 20 (d) 120

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