Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 534 · 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.If a + b = 17 and ab = 70, what is a² + b²? (a) 149 (b) 429 (c) 289 (d) 219
2. 2.What is the median of 12, 16, 3, 15 and 5? (a) 5 (b) 3 (c) 15 (d) 12
3. 3.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 216 (d) 225
4. 4.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 41° (c) 140° (d) 220°
5. 5.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 613 (c) 480 (d) 612
6. 6.What is the smallest prime factor of 155? (a) 1 (b) 5 (c) 31 (d) 2
7. 7.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 3/11 (c) 1/9 (d) 1/11
10. 10.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4
11. 11.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 12 (b) 14 (c) 10 (d) 11
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 month? (a) 25 (b) 37 (c) 24 (d) 36
13. 13.A bag has 6 green, 6 yellow and 3 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 2/5 (c) 3/5 (d) 2/3
14. 14.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
15. 15.In a class of 15 children, 5 like tea, 11 like coffee and 2 like both. How many like only tea? (a) 3 (b) 9 (c) 4 (d) 5
16. 16.In a class of 35 children, 22 like maths, 5 like science and 2 like both. How many like at least one of the two? (a) 25 (b) 27 (c) 23 (d) 35
17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
18. 18.A drawer has lots of black, white, blue, red and yellow 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
19. 19.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 310° (c) 130° (d) 50°
20. 20.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) 90 (b) 33 (c) 10 (d) 30
21. 21.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 729 (b) 1089 (c) 739 (d) 891
22. 22.What is the mean of 4, 20, 18 and 14? (a) 15 (b) 13 (c) 16 (d) 14
23. 23.What is the distance between the points (6, 21) and (15, 9)? (a) 21 (b) 225 (c) 15 (d) 16
24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 16 (d) 15
25. 25.What is the mode of 5, 19, 6, 6, 1, 6 and 5? (a) 19 (b) 5 (c) 1 (d) 6
26. 26.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 21 (d) 7
27. 27.What are the roots of x² − 17x + 72 = 0? (a) 1 and 72 (b) 8 and 9 (c) 2 and 36 (d) 1 and 16
28. 28.What is the mean of 11, 17, 13, 4 and 5? (a) 11 (b) 12 (c) 9 (d) 10
29. 29.What is the mean of 5, 9, 5, 10, 12 and 19? (a) 9 (b) 11 (c) 12 (d) 10
30. 30.In a class of 33 children, 19 like tea, 14 like coffee and 4 like neither. How many like both? (a) 29 (b) 5 (c) 4 (d) 3
31. 31.What is the 29th term of the AP 12, 19, 26, 33, …? (a) 203 (b) 215 (c) 208 (d) 196
32. 32.A drawer has lots of black and yellow 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) 2 (c) 4 (d) 3
33. 33.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
35. 35.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 9 (c) 5 (d) 12
36. 36.What is the smallest prime factor of 65? (a) 1 (b) 13 (c) 2 (d) 5
37. 37.What is the median of 21, 40, 38, 25, 37, 6 and 16? (a) 26 (b) 25 (c) 21 (d) 37
38. 38.How many prime numbers are there between 50 and 60? (a) 4 (b) 2 (c) 3 (d) 1
39. 39.What is the midpoint of the line joining (6, 9) and (16, 1)? (a) (11, 5) (b) (5, 11) (c) (22, 10) (d) (5, 4)
40. 40.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/8 (c) 3/8 (d) 1/4

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