Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 269 · 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 11 white balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 12 (b) 23 (c) 2 (d) 13
2. 2.What is the 35th term of the AP 1, 5, 9, 13, …? (a) 136 (b) 140 (c) 141 (d) 137
3. 3.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
4. 4.If a + b = 19 and ab = 84, what is a² + b²? (a) 361 (b) 193 (c) 277 (d) 529
5. 5.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 7 (d) 9
6. 6.What is the product of the roots of x² − 15x + 56 = 0? (a) 55 (b) 57 (c) 56 (d) 15
7. 7.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 130° (c) 50° (d) 40°
8. 8.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
9. 9.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7 (c) 3² × 7 (d) 3 × 7²
10. 10.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 130° (d) 45°
11. 11.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/4 (d) 1/3
12. 12.In a class of 20 children, 13 like maths, 8 like science and 2 like neither. How many like both? (a) 18 (b) 3 (c) 2 (d) 1
13. 13.What is the 23rd term of the AP 5, 12, 19, 26, …? (a) 161 (b) 166 (c) 159 (d) 154
14. 14.The mean of 8 numbers is 34. When the number 7 is added to them, what is the new mean? (a) 32 (b) 34 (c) 31 (d) 30
15. 15.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 56 (c) 64 (d) 28
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
17. 17.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 1156 (b) 686 (c) 884 (d) 676
18. 18.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) 37 (b) 49 (c) 36 (d) 48
19. 19.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
20. 20.What is the sum of the roots of x² − 8x + 12 = 0? (a) 12 (b) 8 (c) 7 (d) 9
21. 21.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 50 (b) 40 (c) 41 (d) 42
22. 22.What is the median of 10, 7, 38, 40 and 35? (a) 26 (b) 35 (c) 38 (d) 10
23. 23.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/8 (c) 1/8 (d) 3/4
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/18 (d) 1/11
25. 25.A drawer has lots of red 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) 3 (b) 4 (c) 5 (d) 2
26. 26.A bag has 7 yellow, 2 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 2/11 (c) 2/9 (d) 9/11
27. 27.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 41° (c) 140° (d) 40°
28. 28.In a class of 18 children, 9 like mangoes, 11 like bananas and 4 like both. How many like at least one of the two? (a) 16 (b) 18 (c) 12 (d) 20
29. 29.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 55 (c) 50 (d) 45
30. 30.What is the median of 30, 34, 35, 16 and 20? (a) 35 (b) 30 (c) 27 (d) 34
31. 31.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 270° (d) 90°
32. 32.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1922 (d) 1953
33. 33.In which quadrant does the point (−3, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
35. 35.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 10 (c) 33 (d) 90
36. 36.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 6416 (b) 7066 (c) 5776 (d) 7056
37. 37.What is the mean of 9, 14, 11, 12 and 19? (a) 12 (b) 15 (c) 13 (d) 14
38. 38.What is the midpoint of the line joining (2, 3) and (10, 5)? (a) (4, 6) (b) (6, 4) (c) (12, 8) (d) (4, 1)
39. 39.What is the midpoint of the line joining (5, 10) and (17, 8)? (a) (11, 9) (b) (6, 1) (c) (9, 11) (d) (22, 18)
40. 40.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°

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