Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 386 · 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.There are 5 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 50 (b) 10 (c) 30 (d) 25
2. 2.What is the mean of 13, 12, 4, 14 and 17? (a) 15 (b) 10 (c) 13 (d) 12
3. 3.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 15° (b) 85° (c) 165° (d) 110°
4. 4.If a + b = 15 and ab = 56, what is a² + b²? (a) 337 (b) 225 (c) 113 (d) 169
5. 5.In a class of 36 children, 27 like mangoes, 14 like bananas and 2 like neither. How many like both? (a) 2 (b) 5 (c) 34 (d) 7
6. 6.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 125° (d) 55°
7. 7.What is the median of 1, 25, 28, 5 and 2? (a) 5 (b) 2 (c) 28 (d) 25
8. 8.What is the mean of 18, 12, 4 and 6? (a) 8 (b) 9 (c) 11 (d) 10
9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
10. 10.If a + b = 15 and ab = 56, what is (a − b)²? (a) 113 (b) 169 (c) 225 (d) 1
11. 11.In which quadrant does the point (−4, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
12. 12.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2211 (c) 2145 (d) 4422
13. 13.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 130° (b) 55° (c) 125° (d) 105°
14. 14.In a class of 40 children, 21 like maths, 19 like science and 3 like both. How many like only maths? (a) 21 (b) 18 (c) 3 (d) 16
15. 15.In a class of 36 children, 15 like maths, 24 like science and 5 like both. How many like neither? (a) 5 (b) 7 (c) 3 (d) 2
16. 16.In a class of 29 children, 12 like maths, 14 like science and 4 like both. How many like at least one of the two? (a) 18 (b) 22 (c) 26 (d) 29
17. 17.In a class of 23 children, 8 like tea, 8 like coffee and 3 like both. How many like neither? (a) 13 (b) 3 (c) 10 (d) 7
18. 18.What is the 22nd term of the AP 17, 26, 35, 44, …? (a) 189 (b) 198 (c) 206 (d) 215
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
20. 20.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) 61° (c) 120° (d) 60°
21. 21.What is the mode of 6, 19, 10, 10, 19, 19 and 16? (a) 10 (b) 6 (c) 16 (d) 19
22. 22.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
23. 23.What is the median of 1, 38, 10, 14 and 19? (a) 15 (b) 19 (c) 14 (d) 10
24. 24.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
25. 25.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
26. 26.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6084 (b) 6404 (c) 6734 (d) 6724
27. 27.In a class of 40 children, 19 like cricket, 16 like football and 2 like both. How many like only cricket? (a) 19 (b) 17 (c) 14 (d) 24
28. 28.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 6 cu cm (b) 30 cu cm (c) 62 cu cm (d) 10 cu cm
29. 29.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 140° (d) 155°
30. 30.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 39 (d) 36
31. 31.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 384 (b) 27 (c) 204 (d) 192
32. 32.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 14 (c) 9 (d) 21
33. 33.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 54 (c) 18 (d) 21
34. 34.What is the midpoint of the line joining (7, 11) and (13, 9)? (a) (3, 1) (b) (11, 10) (c) (10, 10) (d) (20, 20)
35. 35.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 145° (d) 105°
36. 36.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 310° (d) 130°
37. 37.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 5 (c) 15 (d) 45
38. 38.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 568 (c) 567 (d) 558
39. 39.A bag has 7 red, 4 green and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 11/16 (c) 5/16 (d) 3/4
40. 40.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm

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