Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 58 · 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 55° each. What is the third angle? (a) 70° (b) 35° (c) 55° (d) 125°
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
3. 3.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) 21 (c) 28 (d) 22
4. 4.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) 36 (b) 37 (c) 25 (d) 24
5. 5.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 2 (d) 1
6. 6.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 140° (b) 120° (c) 40° (d) 100°
7. 7.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 46 (c) 54 (d) 45
8. 8.What is the smallest prime factor of 119? (a) 17 (b) 1 (c) 7 (d) 2
9. 9.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 85° (d) 86°
10. 10.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x + 5)(x + 6) (c) (x − 5)(x − 6) (d) (x + 1)(x + 10)
11. 11.A bag has 4 red, 6 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 6/13 (c) 6/7 (d) 7/13
12. 12.What is the 33rd term of the AP 20, 27, 34, 41, …? (a) 224 (b) 231 (c) 251 (d) 244
13. 13.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 9 (c) 36 (d) 24
14. 14.In a class of 45 children, 26 like mangoes, 24 like bananas and 5 like neither. How many like both? (a) 10 (b) 5 (c) 11 (d) 40
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
16. 16.What is the mean of 17, 3, 8 and 16? (a) 13 (b) 12 (c) 11 (d) 10
17. 17.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 325° (c) 55° (d) 35°
18. 18.What is the median of 28, 11, 34, 8 and 3? (a) 28 (b) 8 (c) 34 (d) 11
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
20. 20.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 6) (b) (x + 2)(x + 5) (c) (x + 1)(x + 10) (d) (x − 2)(x − 5)
21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
22. 22.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
23. 23.What is the midpoint of the line joining (7, 3) and (9, 5)? (a) (4, 8) (b) (16, 8) (c) (1, 1) (d) (8, 4)
24. 24.Using (a − b)² = a² − 2ab + b², what is 95²? (a) 9975 (b) 9035 (c) 11025 (d) 9025
25. 25.What is the mean of 15, 16, 3 and 14? (a) 11 (b) 12 (c) 13 (d) 16
26. 26.In which quadrant does the point (−9, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
27. 27.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
28. 28.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) 13 (d) 25
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
30. 30.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 120° (d) 60°
31. 31.How many prime numbers are there between 10 and 30? (a) 6 (b) 5 (c) 7 (d) 8
32. 32.If a + b = 17 and ab = 60, what is (a − b)²? (a) 289 (b) 7 (c) 169 (d) 49
33. 33.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 115° (c) 110° (d) 135°
34. 34.How many factors does 103 have? (a) 4 (b) 3 (c) 1 (d) 2
35. 35.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 2/3 (c) 5/6 (d) 1/3
36. 36.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
37. 37.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 56 (c) 38 (d) 48
38. 38.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 1 (d) 4
39. 39.What is the mean of 3, 10, 16 and 23? (a) 14 (b) 12 (c) 15 (d) 13
40. 40.What is the mode of 20, 20, 11, 11, 11, 12 and 19? (a) 12 (b) 20 (c) 19 (d) 11

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