Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 429 · 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 area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 4 (d) 15
3. 3.How many factors does 98 have? (a) 6 (b) 5 (c) 4 (d) 7
4. 4.What is the sum of the roots of x² − 5x + 6 = 0? (a) 4 (b) 5 (c) 7 (d) 6
5. 5.The mean of 8 numbers is 15. When the number 24 is added to them, what is the new mean? (a) 16 (b) 15 (c) 17 (d) 18
6. 6.What is the 19th term of the AP 17, 25, 33, 41, …? (a) 169 (b) 161 (c) 152 (d) 144
7. 7.The mean of 4 numbers is 16. When the number 11 is added to them, what is the new mean? (a) 14 (b) 16 (c) 17 (d) 15
8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
9. 9.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
10. 10.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 140° (d) 100°
11. 11.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
12. 12.A bag has 5 blue balls and 11 green 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) 2 (c) 16 (d) 6
13. 13.In a class of 26 children, 11 like cricket, 14 like football and 4 like both. How many like at least one of the two? (a) 26 (b) 25 (c) 17 (d) 21
14. 14.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 70°
15. 15.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 1)(x + 14) (c) (x − 7)(x − 8) (d) (x + 7)(x + 8)
16. 16.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) 14 (b) 8 (c) 7 (d) 15
17. 17.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
18. 18.What is the product of the roots of x² − 10x + 21 = 0? (a) 22 (b) 20 (c) 21 (d) 10
19. 19.A bag has 6 green, 6 red and 9 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 4/7 (b) 3/4 (c) 1/3 (d) 3/7
20. 20.A bag has 10 green balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 17 (c) 12 (d) 11
21. 21.What is the mean of 19, 10, 6, 19, 18 and 18? (a) 16 (b) 18 (c) 15 (d) 14
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
23. 23.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
24. 24.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 532 (c) 522 (d) 426
25. 25.What is the mean of 3, 11, 20 and 6? (a) 8 (b) 9 (c) 10 (d) 11
26. 26.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
27. 27.What is the midpoint of the line joining (2, 6) and (12, 0)? (a) (7, 3) (b) (3, 7) (c) (5, 3) (d) (14, 6)
28. 28.What is the smallest prime factor of 403? (a) 31 (b) 1 (c) 2 (d) 13
29. 29.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 1625 (b) 2035 (c) 2025 (d) 1225
30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
31. 31.If a + b = 10 and ab = 9, what is a² + b²? (a) 91 (b) 100 (c) 82 (d) 118
32. 32.What is the mode of 3, 3, 8, 17, 3, 11 and 11? (a) 11 (b) 8 (c) 3 (d) 17
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 5/36 (c) 4/11 (d) 1/11
34. 34.What is the 29th term of the AP 3, 9, 15, 21, …? (a) 177 (b) 168 (c) 171 (d) 174
35. 35.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/4 (d) 1/8
36. 36.Which term of the AP 1, 6, 11, 16, … is 176? (a) 38th (b) 35th (c) 36th (d) 37th
37. 37.How many prime numbers are there between 90 and 110? (a) 6 (b) 7 (c) 4 (d) 5
38. 38.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 66 (d) 110
39. 39.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 3 (d) 1
40. 40.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 240 (c) 25 (d) 120

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