Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 42 · 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.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) 24 (b) 25 (c) 37 (d) 36
2. 2.A bag has 4 white balls and 7 red 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) 5 (c) 8 (d) 11
3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
5. 5.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
6. 6.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 630 (c) 639 (d) 498
7. 7.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 16 (b) 18 (c) 20 (d) 17
8. 8.In which quadrant does the point (−9, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
9. 9.A bag has 7 blue, 4 white and 9 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 9/20 (b) 3/5 (c) 11/20 (d) 1/3
10. 10.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 321 (c) 330 (d) 331
11. 11.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
12. 12.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) 30 (b) 27 (c) 9 (d) 81
13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
14. 14.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 169 (c) 178 (d) 170
15. 15.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5³ (c) 2³ × 3 × 5 (d) 2² × 3 × 5
16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
18. 18.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 105 (d) 120
19. 19.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
20. 20.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 55 (c) 90 (d) 100
21. 21.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 143 (c) 132 (d) 264
22. 22.What is the mode of 16, 11, 16, 8, 11, 4 and 11? (a) 16 (b) 4 (c) 8 (d) 11
23. 23.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
24. 24.In a class of 29 children, 21 like cricket, 10 like football and 6 like both. How many like at least one of the two? (a) 31 (b) 29 (c) 19 (d) 25
25. 25.In a class of 29 children, 18 like mangoes, 14 like bananas and 8 like both. How many like at least one of the two? (a) 16 (b) 29 (c) 32 (d) 24
26. 26.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 160° (c) 110° (d) 20°
27. 27.What are the roots of x² − 16x + 63 = 0? (a) 7 and 9 (b) 1 and 15 (c) 3 and 21 (d) 1 and 63
28. 28.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
29. 29.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) 7 (b) 63 (c) 21 (d) 24
30. 30.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 270 (b) 47 (c) 245 (d) 490
31. 31.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
32. 32.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) 30 (b) 90 (c) 10 (d) 33
33. 33.In which quadrant does the point (9, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
34. 34.In a class of 28 children, 22 like tea, 11 like coffee and 7 like both. How many like only tea? (a) 4 (b) 22 (c) 17 (d) 15
35. 35.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
36. 36.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3591 (b) 3259 (c) 3969 (d) 3249
37. 37.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 85° (d) 95°
38. 38.A bag has 5 blue balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 7 (b) 8 (c) 6 (d) 2
39. 39.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 3/8 (d) 1/4
40. 40.A bag has 2 white, 8 red and 7 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 9/17 (b) 1/3 (c) 8/17 (d) 8/9

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