Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 885 · 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.A bag has 12 green balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 16 (c) 2 (d) 14
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
3. 3.The mean of 8 numbers is 32. When the number 23 is added to them, what is the new mean? (a) 31 (b) 33 (c) 32 (d) 30
4. 4.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 30° (b) 210° (c) 60° (d) 150°
5. 5.How many factors does 107 have? (a) 1 (b) 3 (c) 4 (d) 2
6. 6.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 48 (c) 24 (d) 32
7. 7.Which term of the AP 10, 13, 16, 19, … is 34? (a) 10th (b) 8th (c) 11th (d) 9th
8. 8.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 13 (c) 14 (d) 15
10. 10.What is the distance between the points (7, 27) and (14, 3)? (a) 31 (b) 625 (c) 26 (d) 25
11. 11.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 2 (d) 1
12. 12.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 50° (d) 320°
13. 13.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
14. 14.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
15. 15.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
16. 16.In which quadrant does the point (6, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
17. 17.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
18. 18.In which quadrant does the point (1, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
19. 19.What is the mean of 8, 6, 7 and 19? (a) 10 (b) 8 (c) 11 (d) 9
20. 20.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) 12 (b) 24 (c) 25 (d) 13
21. 21.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 21 (d) 22
22. 22.What is the distance between the points (7, 0) and (19, 5)? (a) 17 (b) 14 (c) 169 (d) 13
23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (d) 18
24. 24.A drawer has lots of 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) 4 (b) 2 (c) 3 (d) 5
25. 25.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 12) (b) (x − 3)(x − 4) (c) (x + 1)(x + 6) (d) (x + 3)(x + 4)
26. 26.In a class of 25 children, 18 like maths, 14 like science and 11 like both. How many like neither? (a) 15 (b) 11 (c) 5 (d) 4
27. 27.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 196 cu cm (d) 21 cu cm
28. 28.In a class of 31 children, 17 like cricket, 25 like football and 12 like both. How many like at least one of the two? (a) 30 (b) 31 (c) 18 (d) 42
29. 29.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 260° (c) 80° (d) 50°
30. 30.What is the midpoint of the line joining (6, 1) and (14, 3)? (a) (2, 10) (b) (10, 2) (c) (4, 1) (d) (20, 4)
31. 31.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
32. 32.In a class of 41 children, 15 like mangoes, 21 like bananas and 4 like both. How many like at least one of the two? (a) 41 (b) 28 (c) 36 (d) 32
33. 33.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 11 (c) 35 (d) 70
34. 34.What is the mode of 18, 3, 13, 18, 3, 3 and 16? (a) 18 (b) 13 (c) 16 (d) 3
35. 35.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 55° (c) 70° (d) 125°
36. 36.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 2025 (b) 1225 (c) 2035 (d) 1625
37. 37.What is the product of the roots of x² − 15x + 56 = 0? (a) 57 (b) 15 (c) 56 (d) 55
38. 38.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 105° (d) 130°
39. 39.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 18 (c) 17 (d) 72
40. 40.What is the prime factorisation of 63? (a) 3² × 7 (b) 3 × 7 (c) 3³ × 7 (d) 3 × 7²

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