Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 816 · 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 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) 101 (d) 92
2. 2.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
3. 3.In a class of 38 children, 19 like cricket, 18 like football and 5 like both. How many like neither? (a) 11 (b) 5 (c) 1 (d) 6
4. 4.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
5. 5.How many factors does 80 have? (a) 11 (b) 8 (c) 9 (d) 10
6. 6.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 166 (c) 165 (d) 20
7. 7.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 45 (d) 15
8. 8.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
9. 9.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
10. 10.What is the distance between the points (8, 1) and (20, 6)? (a) 13 (b) 17 (c) 14 (d) 169
11. 11.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 21 (d) 22
12. 12.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 45° (c) 100° (d) 125°
13. 13.In which quadrant does the point (−4, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
14. 14.A cuboid is 8 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 32 cu cm (c) 112 cu cm (d) 64 cu cm
15. 15.What is the midpoint of the line joining (4, 13) and (12, 5)? (a) (16, 18) (b) (9, 8) (c) (4, 4) (d) (8, 9)
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 7/36 (d) 1/11
17. 17.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
18. 18.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 28 (c) 24 (d) 10
19. 19.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 30 (b) 35 (c) 29 (d) 28
20. 20.What is the mode of 6, 6, 6, 4, 14, 4 and 5? (a) 4 (b) 6 (c) 14 (d) 5
21. 21.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
22. 22.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 80 cu cm (b) 13 cu cm (c) 112 cu cm (d) 20 cu cm
23. 23.What is the median of 34, 5, 21, 7, 1, 2 and 17? (a) 8 (b) 5 (c) 17 (d) 7
24. 24.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 17 (c) 73 (d) 72
25. 25.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2² × 3⁴ (c) 2³ × 3² (d) 2⁴ × 3²
26. 26.If a + b = 15 and ab = 56, what is (a − b)²? (a) 113 (b) 225 (c) 169 (d) 1
27. 27.How many factors does 61 have? (a) 1 (b) 3 (c) 4 (d) 2
28. 28.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 45° (d) 90°
29. 29.What is the midpoint of the line joining (6, 8) and (14, 6)? (a) (20, 14) (b) (4, 1) (c) (10, 7) (d) (7, 10)
30. 30.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
32. 32.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 95° (d) 10°
33. 33.In a class of 46 children, 24 like maths, 30 like science and 11 like both. How many like at least one of the two? (a) 43 (b) 32 (c) 46 (d) 54
34. 34.If a + b = 17 and ab = 66, what is (a − b)²? (a) 289 (b) 157 (c) 5 (d) 25
35. 35.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 155° (c) 55° (d) 150°
36. 36.What is the mean of 13, 7, 16, 19 and 20? (a) 14 (b) 16 (c) 17 (d) 15
37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
38. 38.What is the midpoint of the line joining (1, 1) and (11, 5)? (a) (3, 6) (b) (5, 2) (c) (6, 3) (d) (12, 6)
39. 39.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 20° (c) 200° (d) 100°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 95° (d) 170°

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