Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 111 · 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 book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 579 (c) 589 (d) 588
2. 2.What is the mean of 14, 12, 19, 16 and 4? (a) 12 (b) 14 (c) 15 (d) 13
3. 3.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 49 (d) 42
4. 4.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
5. 5.If a + b = 18 and ab = 80, what is a² + b²? (a) 164 (b) 324 (c) 244 (d) 484
6. 6.In a class of 22 children, 6 like tea, 13 like coffee and 6 like neither. How many like both? (a) 16 (b) 4 (c) 6 (d) 3
7. 7.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 81 (c) 30 (d) 27
8. 8.How many factors does 20 have? (a) 6 (b) 4 (c) 5 (d) 7
9. 9.In a class of 30 children, 10 like dance, 17 like music and 4 like both. How many like neither? (a) 7 (b) 11 (c) 4 (d) 3
10. 10.If a + b = 3 and ab = 2, what is a² + b²? (a) 5 (b) 9 (c) 13 (d) 7
11. 11.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 12 (d) 15
12. 12.A bag has 12 black balls and 4 green 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) 16 (c) 5 (d) 13
13. 13.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 11 (d) 25
14. 14.How many prime numbers are there between 20 and 40? (a) 5 (b) 3 (c) 4 (d) 6
15. 15.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
16. 16.What is the midpoint of the line joining (1, 5) and (7, 13)? (a) (3, 4) (b) (9, 4) (c) (4, 9) (d) (8, 18)
17. 17.What is the 25th term of the AP 9, 15, 21, 27, …? (a) 144 (b) 159 (c) 153 (d) 150
18. 18.What is the mean of 16, 20, 4, 16 and 9? (a) 13 (b) 12 (c) 14 (d) 15
19. 19.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
20. 20.What is the missing term in the AP 18, 22, ?, 30, 34? (a) 27 (b) 30 (c) 25 (d) 26
21. 21.What is the mode of 1, 9, 11, 11, 18, 18 and 18? (a) 1 (b) 11 (c) 18 (d) 9
22. 22.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 110° (c) 85° (d) 95°
23. 23.In a class of 43 children, 25 like mangoes, 22 like bananas and 3 like neither. How many like both? (a) 3 (b) 4 (c) 7 (d) 40
24. 24.Using (a − b)² = a² − 2ab + b², what is 56²? (a) 3146 (b) 4096 (c) 3136 (d) 3584
25. 25.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 72 (c) 81 (d) 45
26. 26.What is the sum of the roots of x² − 13x + 42 = 0? (a) 14 (b) 42 (c) 12 (d) 13
27. 27.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/5 (c) 5/6 (d) 1/6
28. 28.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 145° (c) 35° (d) 55°
29. 29.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
30. 30.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
31. 31.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
32. 32.What is the midpoint of the line joining (7, 3) and (13, 5)? (a) (10, 4) (b) (3, 1) (c) (20, 8) (d) (4, 10)
33. 33.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 155° (b) 150° (c) 55° (d) 125°
34. 34.What is the mean of 14, 2, 3, 20, 16 and 11? (a) 10 (b) 13 (c) 12 (d) 11
35. 35.In a class of 52 children, 29 like maths, 30 like science and 10 like both. How many like neither? (a) 3 (b) 13 (c) 10 (d) 4
36. 36.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
37. 37.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 1)(x + 5) (c) (x + 1)(x + 8) (d) (x + 2)(x + 4)
38. 38.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 132 (d) 78
39. 39.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 56 (c) 15 (d) 14
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm

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