Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 975 · 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.In a class of 37 children, 12 like maths, 23 like science and 8 like both. How many like neither? (a) 2 (b) 18 (c) 8 (d) 10
2. 2.In a class of 46 children, 21 like cricket, 21 like football and 6 like both. How many like neither? (a) 10 (b) 16 (c) 4 (d) 6
3. 3.If a + b = 13 and ab = 42, what is a² + b²? (a) 85 (b) 127 (c) 169 (d) 253
4. 4.A bag has 5 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 8 (c) 12 (d) 2
5. 5.A bag has 2 red, 4 blue and 8 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/7 (b) 1/3 (c) 6/7 (d) 1/6
6. 6.In a class of 38 children, 30 like cricket, 15 like football and 12 like both. How many like only cricket? (a) 3 (b) 18 (c) 23 (d) 30
7. 7.In a class of 36 children, 15 like maths, 17 like science and 4 like both. How many like at least one of the two? (a) 32 (b) 36 (c) 24 (d) 28
8. 8.How many factors does 117 have? (a) 6 (b) 7 (c) 4 (d) 5
9. 9.What is the mode of 14, 9, 14, 20, 20, 7 and 14? (a) 20 (b) 9 (c) 7 (d) 14
10. 10.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 85° (c) 130° (d) 95°
11. 11.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
12. 12.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 294 sq cm (d) 49 sq cm
13. 13.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 153 (c) 54 (d) 51
14. 14.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
15. 15.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 8 (c) 14 (d) 7
16. 16.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 140° (d) 95°
17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
18. 18.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
19. 19.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 580 (c) 570 (d) 458
20. 20.What is the median of 36, 33, 37, 18, 15, 22 and 10? (a) 22 (b) 18 (c) 33 (d) 23
21. 21.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 22 (b) 140 (c) 260 (d) 130
22. 22.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/4 (c) 1/8 (d) 3/8
23. 23.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 30° (c) 150° (d) 31°
24. 24.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
25. 25.What is the 35th term of the AP 4, 8, 12, 16, …? (a) 144 (b) 136 (c) 140 (d) 141
26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
28. 28.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 4 (c) 16 (d) 324
29. 29.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 95 (c) 96 (d) 104
30. 30.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁴ × 3² (c) 2⁵ × 3² (d) 2³ × 3²
31. 31.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 120 (d) 240
32. 32.If a + b = 15 and ab = 56, what is (a − b)²? (a) 113 (b) 1 (c) 169 (d) 225
33. 33.What is the product of the roots of x² − 9x + 14 = 0? (a) 15 (b) 14 (c) 13 (d) 9
34. 34.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 8125 (b) 9025 (c) 9035 (d) 7225
35. 35.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 21 (b) 22 (c) 26 (d) 23
36. 36.In which quadrant does the point (1, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
38. 38.A bag has 9 red balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 15 (c) 10 (d) 11
39. 39.What is the 27th term of the AP 2, 8, 14, 20, …? (a) 164 (b) 158 (c) 162 (d) 156
40. 40.Which term of the AP 15, 20, 25, 30, … is 50? (a) 10th (b) 8th (c) 9th (d) 7th

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