Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 896 · 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 an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°
2. 2.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
3. 3.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
4. 4.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) 10 (c) 33 (d) 90
5. 5.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 112 sq cm (c) 56 sq cm (d) 80 sq cm
6. 6.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
7. 7.A bag has 6 blue, 3 yellow and 6 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 4/5 (c) 1/5 (d) 1/4
8. 8.What is the distance between the points (7, 8) and (15, 23)? (a) 289 (b) 17 (c) 23 (d) 18
9. 9.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 230° (b) 130° (c) 100° (d) 50°
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
11. 11.What is the mean of 17, 17, 9, 7 and 15? (a) 14 (b) 12 (c) 15 (d) 13
12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
13. 13.How many factors does 50 have? (a) 7 (b) 6 (c) 5 (d) 4
14. 14.What is the sum of the roots of x² − 15x + 56 = 0? (a) 56 (b) 15 (c) 16 (d) 14
15. 15.In a class of 41 children, 16 like dance, 24 like music and 9 like both. How many like only dance? (a) 16 (b) 7 (c) 15 (d) 17
16. 16.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) 24 (b) 7 (c) 63 (d) 21
17. 17.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) 178 (c) 170 (d) 169
18. 18.In a class of 33 children, 23 like dance, 10 like music and 7 like both. How many like only dance? (a) 23 (b) 3 (c) 7 (d) 16
19. 19.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 6 (b) 7 (c) 5 (d) 4
21. 21.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 100° (d) 115°
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
23. 23.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2 × 3² × 7
24. 24.Which term of the AP 12, 21, 30, 39, … is 129? (a) 15th (b) 16th (c) 14th (d) 13th
25. 25.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 42 (c) 24 (d) 21
26. 26.5 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 20 (c) 15 (d) 10
27. 27.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2⁵ × 3 (d) 2³ × 3
28. 28.In a class of 41 children, 28 like tea, 14 like coffee and 10 like both. How many like only tea? (a) 28 (b) 4 (c) 27 (d) 18
29. 29.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 459 (c) 384 (d) 468
30. 30.What is the mean of 8, 3, 8, 11, 8 and 10? (a) 10 (b) 7 (c) 8 (d) 9
31. 31.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) 36 (c) 37 (d) 25
32. 32.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 20° (d) 30°
33. 33.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 21 (d) 15
34. 34.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 105 (c) 210 (d) 225
35. 35.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
36. 36.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
37. 37.There are 8 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) 80 (b) 40 (c) 13 (d) 48
38. 38.What is the midpoint of the line joining (3, 6) and (5, 18)? (a) (1, 6) (b) (12, 4) (c) (8, 24) (d) (4, 12)
39. 39.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 110° (b) 10° (c) 80° (d) 170°
40. 40.The mean of 6 numbers is 35. When the number 63 is added to them, what is the new mean? (a) 40 (b) 39 (c) 49 (d) 35

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