Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 636 · 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 area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
2. 2.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 144 (c) 48 (d) 51
3. 3.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 190° (c) 85° (d) 95°
4. 4.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 55° (b) 125° (c) 85° (d) 150°
5. 5.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
6. 6.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/6 (c) 5/6 (d) 1/5
7. 7.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
8. 8.In a class of 19 children, 9 like mangoes, 9 like bananas and 3 like both. How many like only mangoes? (a) 3 (b) 6 (c) 9 (d) 10
9. 9.In a class of 28 children, 19 like cricket, 15 like football and 11 like both. How many like only cricket? (a) 19 (b) 13 (c) 8 (d) 4
10. 10.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10211 (b) 9801 (c) 10201 (d) 10001
11. 11.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 55° (b) 135° (c) 125° (d) 100°
12. 12.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 95° (c) 85° (d) 5°
13. 13.If a + b = 16 and ab = 60, what is a² + b²? (a) 376 (b) 256 (c) 136 (d) 196
14. 14.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) 21 (c) 28 (d) 22
15. 15.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 1)(x + 24) (c) (x + 4)(x + 6) (d) (x − 4)(x − 6)
16. 16.How many factors does 32 have? (a) 5 (b) 4 (c) 7 (d) 6
17. 17.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 198 (d) 66
18. 18.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
21. 21.What is the mean of 15, 19, 13, 19, 19 and 17? (a) 16 (b) 18 (c) 19 (d) 17
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 48 (c) 49 (d) 36
24. 24.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 180 (c) 20 (d) 63
25. 25.A cuboid is 8 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 112 cu cm (b) 64 cu cm (c) 16 cu cm (d) 14 cu cm
26. 26.What are the roots of x² − 8x + 12 = 0? (a) 1 and 12 (b) 1 and 7 (c) 3 and 4 (d) 2 and 6
27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
28. 28.A bag has 7 black balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 8 (c) 9 (d) 2
29. 29.What is the distance between the points (3, 5) and (19, 17)? (a) 20 (b) 21 (c) 28 (d) 400
30. 30.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 1)(x + 15) (c) (x + 7)(x + 9) (d) (x + 1)(x + 63)
31. 31.What is the sum of the roots of x² − 15x + 54 = 0? (a) 14 (b) 15 (c) 16 (d) 54
32. 32.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 48 (c) 24 (d) 32
33. 33.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/4 (c) 1/2 (d) 1/3
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
35. 35.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 484 (c) 483 (d) 474
36. 36.In a class of 25 children, 16 like cricket, 10 like football and 3 like both. How many like neither? (a) 3 (b) 5 (c) 1 (d) 2
37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 378 (d) 53
38. 38.4 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) 12 (b) 8 (c) 16 (d) 6
39. 39.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 72 (c) 8 (d) 24
40. 40.What is the median of 15, 4, 8, 13, 39, 26 and 23? (a) 16 (b) 15 (c) 13 (d) 23

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