Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 197 · 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.Using (a − b)² = a² − 2ab + b², what is 58²? (a) 3596 (b) 3374 (c) 3364 (d) 3844
2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 19 (d) 17
3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 66 (d) 55
4. 4.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
5. 5.What is the mode of 16, 8, 5, 16, 16, 5 and 7? (a) 5 (b) 16 (c) 7 (d) 8
6. 6.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 55 (c) 22 (d) 121
7. 7.What is the product of the roots of x² − 6x + 8 = 0? (a) 6 (b) 9 (c) 7 (d) 8
8. 8.Using (a + b)² = a² + 2ab + b², what is 103²? (a) 10009 (b) 9409 (c) 10609 (d) 10619
9. 9.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 30 (d) 15
10. 10.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/7 (c) 1/4 (d) 7/8
11. 11.What is the distance between the points (1, 2) and (5, 5)? (a) 25 (b) 5 (c) 6 (d) 7
12. 12.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 98 (c) 49 (d) 14
13. 13.If a + b = 19 and ab = 90, what is a² + b²? (a) 361 (b) 541 (c) 181 (d) 271
14. 14.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 400 cu cm (d) 30 cu cm
15. 15.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
16. 16.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) 36 (b) 37 (c) 49 (d) 48
17. 17.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
18. 18.How many prime numbers are there between 40 and 60? (a) 5 (b) 4 (c) 6 (d) 7
19. 19.What is the distance between the points (9, 1) and (24, 9)? (a) 289 (b) 23 (c) 17 (d) 18
20. 20.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/4 (c) 3/4 (d) 1/8
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 5/36 (c) 1/9 (d) 1/11
22. 22.What is the smallest prime factor of 203? (a) 29 (b) 7 (c) 1 (d) 2
23. 23.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 132 (d) 66
24. 24.In a class of 25 children, 20 like dance, 8 like music and 5 like both. How many like at least one of the two? (a) 18 (b) 28 (c) 25 (d) 23
25. 25.In which quadrant does the point (8, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.What is the mode of 15, 15, 7, 7, 18, 13 and 15? (a) 7 (b) 13 (c) 18 (d) 15
27. 27.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 48 (d) 144
28. 28.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 160° (d) 65°
29. 29.What is the 29th term of the AP 16, 23, 30, 37, …? (a) 196 (b) 219 (c) 212 (d) 203
30. 30.What is the mean of 6, 7, 13, 11 and 13? (a) 9 (b) 11 (c) 10 (d) 12
31. 31.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 686 (b) 676 (c) 884 (d) 1156
32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
33. 33.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
34. 34.A bag has 8 white balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 11 (c) 9 (d) 4
35. 35.What is the mean of 4, 14, 4, 10 and 8? (a) 7 (b) 10 (c) 8 (d) 9
36. 36.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 200° (c) 160° (d) 20°
37. 37.Which term of the AP 10, 13, 16, 19, … is 46? (a) 12th (b) 14th (c) 15th (d) 13th
38. 38.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
39. 39.A bag has 6 blue, 6 white and 2 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 6/7 (b) 1/7 (c) 1/6 (d) 1/3
40. 40.If a + b = 12 and ab = 35, what is a² + b²? (a) 214 (b) 109 (c) 144 (d) 74

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