Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 845 · 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 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 369 (c) 318 (d) 360
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/11 (d) 1/9
3. 3.What is the median of 4, 14, 24, 9 and 1? (a) 24 (b) 14 (c) 9 (d) 4
4. 4.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 75 (b) 20 (c) 150 (d) 84
5. 5.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 125° (d) 85°
6. 6.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
7. 7.What is the smallest prime factor of 57? (a) 3 (b) 19 (c) 2 (d) 1
8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
9. 9.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 25° (c) 115° (d) 295°
10. 10.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
11. 11.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/3 (c) 5/6 (d) 1/6
12. 12.What is the midpoint of the line joining (6, 0) and (18, 8)? (a) (12, 4) (b) (24, 8) (c) (6, 4) (d) (4, 12)
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
14. 14.What is the distance between the points (8, 19) and (13, 7)? (a) 17 (b) 169 (c) 14 (d) 13
15. 15.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 3 (d) 2
16. 16.What is the mode of 12, 12, 20, 12, 20, 8 and 3? (a) 20 (b) 3 (c) 8 (d) 12
17. 17.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8291 (b) 7921 (c) 8101 (d) 8281
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
19. 19.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 15° (b) 40° (c) 155° (d) 165°
20. 20.What is the smallest prime factor of 133? (a) 2 (b) 19 (c) 7 (d) 1
21. 21.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 105° (c) 75° (d) 210°
22. 22.In a class of 42 children, 25 like tea, 16 like coffee and 6 like neither. How many like both? (a) 6 (b) 36 (c) 5 (d) 4
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) 3/4 (d) 1/8
24. 24.What is the 21st term of the AP 16, 24, 32, 40, …? (a) 184 (b) 160 (c) 168 (d) 176
25. 25.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 2 (d) 7
26. 26.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 60° (d) 160°
27. 27.How many factors does 80 have? (a) 11 (b) 9 (c) 10 (d) 8
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
29. 29.In a class of 31 children, 16 like cricket, 18 like football and 4 like neither. How many like both? (a) 27 (b) 4 (c) 7 (d) 3
30. 30.What is the median of 11, 14, 7, 33, 35, 25 and 1? (a) 25 (b) 33 (c) 18 (d) 14
31. 31.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 27 (c) 8 (d) 24
32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 17 (b) 16 (c) 15 (d) 5
33. 33.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 95° (b) 160° (c) 85° (d) 115°
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
35. 35.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
36. 36.What is the mode of 20, 8, 19, 19, 19, 10 and 10? (a) 10 (b) 20 (c) 8 (d) 19
37. 37.The mean of 4 numbers is 13. When the number 18 is added to them, what is the new mean? (a) 13 (b) 14 (c) 16 (d) 15
38. 38.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
39. 39.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 80° (d) 20°
40. 40.What is the median of 27, 17, 19, 34 and 28? (a) 19 (b) 27 (c) 25 (d) 28

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