Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 5 · 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 circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
2. 2.What is the median of 7, 8, 17, 2, 11, 37 and 31? (a) 17 (b) 2 (c) 8 (d) 11
3. 3.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 12) (b) (x + 2)(x + 6) (c) (x + 1)(x + 7) (d) (x − 2)(x − 6)
4. 4.There are 6 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) 60 (b) 36 (c) 30 (d) 11
5. 5.How many factors does 79 have? (a) 1 (b) 2 (c) 4 (d) 3
6. 6.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 18 (c) 57 (d) 54
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
8. 8.Which term of the AP 15, 24, 33, 42, … is 168? (a) 17th (b) 19th (c) 18th (d) 20th
9. 9.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 35° (c) 290° (d) 145°
10. 10.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 135° (b) 85° (c) 95° (d) 130°
11. 11.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 11 (c) 56 (d) 28
12. 12.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 75° (d) 15°
13. 13.A drawer has lots of red, white, green and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 5 (c) 4 (d) 2
14. 14.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2² × 3 (d) 2 × 3³
15. 15.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 98 (c) 106 (d) 88
16. 16.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) 36 (b) 24 (c) 37 (d) 25
17. 17.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 10° (b) 160° (c) 170° (d) 30°
18. 18.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 95° (c) 85° (d) 155°
19. 19.A bag has 3 black balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 2 (c) 10 (d) 12
20. 20.A bag has 9 yellow, 2 green and 3 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 6/7 (b) 3/14 (c) 1/3 (d) 11/14
21. 21.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2² × 7 (c) 2⁴ × 7 (d) 2³ × 7
22. 22.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
23. 23.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
24. 24.Which is the correct factorisation of x² + 11x + 24? (a) (x − 3)(x − 8) (b) (x + 3)(x + 8) (c) (x + 1)(x + 10) (d) (x + 1)(x + 24)
25. 25.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2116 (b) 2916 (c) 2516 (d) 2926
26. 26.What is the distance between the points (5, 8) and (20, 16)? (a) 23 (b) 289 (c) 17 (d) 18
27. 27.A drawer has lots of black, green, white, blue and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 6 (c) 10 (d) 5
28. 28.What is the midpoint of the line joining (0, 15) and (12, 7)? (a) (11, 6) (b) (12, 22) (c) (6, 11) (d) (6, 4)
29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 7 (d) 17
30. 30.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
31. 31.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 45° (b) 135° (c) 115° (d) 110°
32. 32.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 64 cu cm (d) 96 cu cm
33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 21 (d) 121
34. 34.There are 5 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) 25 (b) 40 (c) 20 (d) 9
35. 35.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 46 (b) 572 (c) 308 (d) 286
36. 36.7 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) 9 (b) 21 (c) 28 (d) 14
37. 37.5 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) 15 (b) 7 (c) 20 (d) 10
38. 38.What is the 12th term of the AP 5, 8, 11, 14, …? (a) 38 (b) 33 (c) 36 (d) 41
39. 39.A drawer has lots of white and red 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
40. 40.What is the distance between the points (8, 4) and (20, 9)? (a) 17 (b) 169 (c) 13 (d) 14

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