Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 116 · 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 sum of the first 12 terms of the AP 9, 12, 15, …? (a) 324 (b) 306 (c) 42 (d) 612
2. 2.What is the sum of the roots of x² − 6x + 8 = 0? (a) 7 (b) 8 (c) 5 (d) 6
3. 3.What is the midpoint of the line joining (8, 5) and (18, 11)? (a) (8, 13) (b) (5, 3) (c) (26, 16) (d) (13, 8)
4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 14 (d) 15
5. 5.What is the 38th term of the AP 7, 10, 13, 16, …? (a) 121 (b) 111 (c) 114 (d) 118
6. 6.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) 1/2 (d) 2/3
7. 7.In a class of 25 children, 19 like tea, 5 like coffee and 3 like neither. How many like both? (a) 1 (b) 22 (c) 3 (d) 2
8. 8.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 160° (d) 130°
9. 9.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 174 (c) 156 (d) 166
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
12. 12.What is the mode of 15, 15, 10, 15, 18, 11 and 10? (a) 11 (b) 15 (c) 18 (d) 10
13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 5 (d) 2
14. 14.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 60° (c) 120° (d) 61°
15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 15 (c) 14 (d) 16
16. 16.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
17. 17.A drawer has lots of white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 5 (d) 4
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
20. 20.If a + b = 16 and ab = 48, what is (a − b)²? (a) 8 (b) 256 (c) 64 (d) 160
21. 21.What is the mean of 14, 15, 20, 18 and 13? (a) 15 (b) 16 (c) 17 (d) 20
22. 22.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
23. 23.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
24. 24.A bag has 5 red balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 9 (c) 7 (d) 2
25. 25.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 90° (d) 91°
26. 26.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3609 (b) 3979 (c) 3969 (d) 3249
27. 27.In a class of 29 children, 9 like mangoes, 15 like bananas and 4 like both. How many like only mangoes? (a) 11 (b) 9 (c) 5 (d) 14
28. 28.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 200° (c) 160° (d) 21°
29. 29.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16
30. 30.What is the mean of 19, 3, 13, 3 and 12? (a) 11 (b) 12 (c) 9 (d) 10
31. 31.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 7 (b) 12 (c) 24 (d) 15
32. 32.A cuboid is 8 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 128 cu cm (b) 192 cu cm (c) 16 cu cm (d) 18 cu cm
33. 33.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) 33 (b) 10 (c) 30 (d) 90
34. 34.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
35. 35.What is the distance between the points (0, 7) and (4, 4)? (a) 5 (b) 25 (c) 6 (d) 7
36. 36.In a class of 47 children, 19 like tea, 27 like coffee and 8 like both. How many like neither? (a) 9 (b) 8 (c) 17 (d) 1
37. 37.In a class of 22 children, 13 like cricket, 6 like football and 2 like both. How many like only cricket? (a) 13 (b) 4 (c) 11 (d) 16
38. 38.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 80° (d) 140°
39. 39.What is the distance between the points (5, 2) and (10, 14)? (a) 169 (b) 13 (c) 14 (d) 17
40. 40.In a class of 25 children, 9 like dance, 19 like music and 5 like both. How many like at least one of the two? (a) 28 (b) 25 (c) 18 (d) 23

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