Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 892 · 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 fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
2. 2.If a + b = 6 and ab = 5, what is (a − b)²? (a) 36 (b) 26 (c) 4 (d) 16
3. 3.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 160° (b) 55° (c) 125° (d) 75°
4. 4.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 18 (d) 54
5. 5.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
6. 6.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
7. 7.8 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 64 (c) 15 (d) 112
8. 8.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/3 (c) 1/4 (d) 1/2
9. 9.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 70° (b) 250° (c) 110° (d) 140°
10. 10.What is the missing term in the AP 7, 13, 19, ?, 31? (a) 25 (b) 24 (c) 26 (d) 31
11. 11.What is the 39th term of the AP 16, 20, 24, 28, …? (a) 168 (b) 172 (c) 156 (d) 152
12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
13. 13.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 280° (c) 100° (d) 10°
14. 14.In a class of 53 children, 26 like maths, 25 like science and 6 like both. How many like neither? (a) 2 (b) 14 (c) 8 (d) 6
15. 15.What is the sum of the roots of x² − 9x + 18 = 0? (a) 10 (b) 9 (c) 18 (d) 8
16. 16.In a class of 30 children, 15 like maths, 17 like science and 8 like both. How many like at least one of the two? (a) 32 (b) 30 (c) 16 (d) 24
17. 17.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
18. 18.A bag has 4 red, 4 blue and 5 green balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 9/13 (c) 10/13 (d) 4/13
19. 19.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 3/5 (c) 5/8 (d) 1/4
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
21. 21.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 411 (c) 412 (d) 346
22. 22.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1653 (c) 1654 (d) 1596
23. 23.In a class of 29 children, 24 like dance, 9 like music and 2 like neither. How many like both? (a) 2 (b) 27 (c) 4 (d) 6
24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 18 (d) 8
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
26. 26.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 125° (b) 50° (c) 130° (d) 105°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 75° (d) 76°
28. 28.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 4 (d) 6
29. 29.What is the mode of 13, 19, 7, 13, 3, 3 and 13? (a) 13 (b) 3 (c) 19 (d) 7
30. 30.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
31. 31.A bag has 3 black balls and 5 red 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) 2 (c) 6 (d) 8
32. 32.In a class of 24 children, 10 like dance, 15 like music and 4 like neither. How many like both? (a) 20 (b) 1 (c) 5 (d) 4
33. 33.In a class of 40 children, 20 like maths, 19 like science and 7 like neither. How many like both? (a) 5 (b) 7 (c) 6 (d) 33
34. 34.A bag has 6 yellow balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 8 (c) 2 (d) 7
35. 35.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 25 (d) 20
36. 36.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 110 (c) 118 (d) 100
37. 37.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
38. 38.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 330° (d) 150°
39. 39.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 92 (d) 101
40. 40.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66

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