Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 361 · 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.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
2. 2.What is the mode of 19, 11, 15, 15, 19, 15 and 13? (a) 11 (b) 15 (c) 19 (d) 13
3. 3.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
4. 4.What is the median of 24, 23, 27, 36 and 28? (a) 28 (b) 27 (c) 24 (d) 26
5. 5.A drawer has lots of blue, black, white, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 6 (d) 2
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
7. 7.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
8. 8.In a class of 28 children, 14 like dance, 17 like music and 7 like both. How many like at least one of the two? (a) 31 (b) 24 (c) 28 (d) 17
9. 9.In a class of 28 children, 9 like mangoes, 14 like bananas and 8 like neither. How many like both? (a) 4 (b) 8 (c) 20 (d) 3
10. 10.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 110 (b) 111 (c) 220 (d) 15
11. 11.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
12. 12.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
14. 14.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 27 (c) 72 (d) 24
15. 15.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
16. 16.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
17. 17.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 140° (b) 40° (c) 115° (d) 105°
18. 18.7 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) 42 (b) 13 (c) 49 (d) 84
19. 19.What is the median of 40, 7, 20, 23 and 11? (a) 11 (b) 20 (c) 23 (d) 21
20. 20.A bag has 9 white balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 10 (c) 11 (d) 2
21. 21.What is the 29th term of the AP 11, 13, 15, 17, …? (a) 67 (b) 58 (c) 56 (d) 69
22. 22.Which term of the AP 17, 19, 21, 23, … is 95? (a) 42nd (b) 40th (c) 41st (d) 39th
23. 23.What is the median of 10, 15, 27, 11, 28, 19 and 14? (a) 19 (b) 11 (c) 15 (d) 14
24. 24.In a class of 28 children, 6 like cricket, 16 like football and 2 like both. How many like at least one of the two? (a) 20 (b) 18 (c) 22 (d) 28
25. 25.In a class of 43 children, 19 like tea, 29 like coffee and 9 like both. How many like only tea? (a) 14 (b) 19 (c) 20 (d) 10
26. 26.What is the smallest prime factor of 21? (a) 1 (b) 7 (c) 2 (d) 3
27. 27.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
28. 28.In a class of 39 children, 30 like mangoes, 18 like bananas and 11 like both. How many like at least one of the two? (a) 26 (b) 48 (c) 37 (d) 39
29. 29.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
30. 30.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 15 (c) 14 (d) 22
31. 31.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 17 (b) 15 (c) 20 (d) 16
32. 32.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
33. 33.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
34. 34.Which is the correct factorisation of x² + 14x + 48? (a) (x + 6)(x + 8) (b) (x − 6)(x − 8) (c) (x + 1)(x + 48) (d) (x + 1)(x + 13)
35. 35.In a class of 34 children, 16 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 32 (b) 36 (c) 28 (d) 34
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/36 (c) 1/11 (d) 5/11
37. 37.A bag has 10 red balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 15 (c) 12 (d) 11
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 18 (b) 9 (c) 19 (d) 20
39. 39.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
40. 40.How many factors does 82 have? (a) 2 (b) 3 (c) 4 (d) 5

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