Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 298 · 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.How many prime numbers are there between 20 and 50? (a) 6 (b) 9 (c) 8 (d) 7
2. 2.If a + b = 7 and ab = 12, what is a² + b²? (a) 25 (b) 37 (c) 49 (d) 73
3. 3.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 42 (d) 49
4. 4.A drawer has lots of blue, yellow, white, green and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 6 (c) 10 (d) 2
5. 5.What is the sum of all the whole numbers from 1 to 84? (a) 3570 (b) 7140 (c) 3486 (d) 3528
6. 6.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 1 and 16 (c) 2 and 36 (d) 1 and 72
7. 7.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 174 (c) 165 (d) 156
8. 8.What is the mode of 11, 1, 1, 3, 3, 16 and 1? (a) 1 (b) 3 (c) 16 (d) 11
9. 9.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 80° (c) 81° (d) 100°
10. 10.How many factors does 88 have? (a) 7 (b) 6 (c) 8 (d) 9
11. 11.In a class of 31 children, 15 like mangoes, 9 like bananas and 2 like both. How many like at least one of the two? (a) 31 (b) 24 (c) 22 (d) 20
12. 12.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 22 (c) 14 (d) 21
13. 13.What is the midpoint of the line joining (7, 8) and (11, 6)? (a) (9, 7) (b) (18, 14) (c) (7, 9) (d) (2, 1)
14. 14.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 46° (d) 90°
15. 15.How many factors does 13 have? (a) 3 (b) 2 (c) 1 (d) 4
16. 16.What is the 18th term of the AP 18, 26, 34, 42, …? (a) 162 (b) 136 (c) 144 (d) 154
17. 17.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 63 (d) 20
18. 18.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 506 (c) 231 (d) 242
19. 19.How many prime numbers are there between 40 and 60? (a) 5 (b) 6 (c) 7 (d) 4
20. 20.In a class of 38 children, 21 like cricket, 20 like football and 12 like both. How many like at least one of the two? (a) 17 (b) 38 (c) 29 (d) 41
21. 21.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/3 (c) 1/6 (d) 1/5
22. 22.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 2/3
23. 23.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/8 (d) 3/5
24. 24.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 121 (d) 110
25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
26. 26.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x − 6)(x − 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)
27. 27.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 65 cu cm (d) 64 cu cm
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 day of the week? (a) 14 (b) 15 (c) 7 (d) 8
29. 29.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
30. 30.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 25 (d) 120
31. 31.In which quadrant does the point (−3, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
32. 32.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
33. 33.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
34. 34.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.How many factors does 93 have? (a) 2 (b) 5 (c) 4 (d) 3
36. 36.A bag has 3 red balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 14 (c) 12 (d) 2
37. 37.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
38. 38.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 65° (c) 160° (d) 115°
39. 39.The mean of 3 numbers is 32. When the number 16 is added to them, what is the new mean? (a) 32 (b) 28 (c) 29 (d) 24
40. 40.A drawer has lots of green and blue 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) 5 (c) 2 (d) 3

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