Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 879 · 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.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
2. 2.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 35 (c) 60 (d) 11
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 20 (b) 21 (c) 19 (d) 9
4. 4.A drawer has lots of red, yellow 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) 2 (c) 4 (d) 3
5. 5.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 409 (c) 344 (d) 399
6. 6.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4
7. 7.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 65° (c) 160° (d) 20°
8. 8.What is the median of 27, 19, 35, 18, 9, 39 and 23? (a) 18 (b) 19 (c) 23 (d) 27
9. 9.In a class of 38 children, 14 like maths, 24 like science and 10 like neither. How many like both? (a) 11 (b) 10 (c) 28 (d) 9
10. 10.The mean of 4 numbers is 29. When the number 44 is added to them, what is the new mean? (a) 33 (b) 32 (c) 31 (d) 29
11. 11.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
12. 12.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x − 8)(x − 9) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
13. 13.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 36 (c) 37 (d) 48
14. 14.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 110° (c) 55° (d) 20°
15. 15.Which term of the AP 5, 10, 15, 20, … is 40? (a) 9th (b) 8th (c) 7th (d) 10th
16. 16.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
17. 17.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
18. 18.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
19. 19.In a class of 47 children, 19 like tea, 21 like coffee and 2 like both. How many like only tea? (a) 2 (b) 19 (c) 26 (d) 17
20. 20.A drawer has lots of white 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) 2 (c) 4 (d) 5
21. 21.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
22. 22.What is the median of 36, 31, 6, 7, 21, 28 and 25? (a) 25 (b) 28 (c) 22 (d) 7
23. 23.In a class of 22 children, 8 like maths, 11 like science and 2 like both. How many like only maths? (a) 8 (b) 6 (c) 11 (d) 9
24. 24.Which term of the AP 4, 6, 8, 10, … is 24? (a) 10th (b) 12th (c) 11th (d) 13th
25. 25.What is the 13th term of the AP 14, 21, 28, 35, …? (a) 84 (b) 91 (c) 105 (d) 98
26. 26.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 10 (c) 25 (d) 15
27. 27.A bag has 9 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 10 (c) 4 (d) 2
28. 28.In a class of 27 children, 18 like maths, 16 like science and 10 like both. How many like at least one of the two? (a) 27 (b) 24 (c) 34 (d) 14
29. 29.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 8 (d) 19
31. 31.A drawer has lots of blue, red, white 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) 5 (b) 4 (c) 8 (d) 2
32. 32.In a class of 42 children, 22 like mangoes, 26 like bananas and 11 like both. How many like at least one of the two? (a) 42 (b) 37 (c) 48 (d) 26
33. 33.The mean of 4 numbers is 40. When the number 55 is added to them, what is the new mean? (a) 43 (b) 40 (c) 44 (d) 42
34. 34.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
35. 35.A bag has 9 yellow balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 11 (c) 2 (d) 10
36. 36.What is the 22nd term of the AP 10, 15, 20, 25, …? (a) 110 (b) 105 (c) 120 (d) 115
37. 37.How many factors does 24 have? (a) 6 (b) 8 (c) 7 (d) 9
38. 38.A bag has 6 yellow balls and 3 red 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) 9 (c) 2 (d) 7
39. 39.What is the midpoint of the line joining (2, 6) and (14, 16)? (a) (6, 5) (b) (16, 22) (c) (11, 8) (d) (8, 11)
40. 40.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 3035 (b) 2025 (c) 2525 (d) 3025

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