Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 245 · 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 a class of 52 children, 27 like cricket, 25 like football and 7 like neither. How many like both? (a) 45 (b) 8 (c) 7 (d) 6
2. 2.In a class of 44 children, 15 like dance, 24 like music and 5 like both. How many like neither? (a) 10 (b) 11 (c) 5 (d) 15
3. 3.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/7 (c) 1/4 (d) 1/8
4. 4.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) 8 (b) 27 (c) 24 (d) 72
5. 5.A bag has 7 black balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 2 (c) 8 (d) 9
6. 6.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 100° (b) 145° (c) 35° (d) 115°
7. 7.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 24 (c) 8 (d) 18
8. 8.In which quadrant does the point (6, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
9. 9.What is the prime factorisation of 12? (a) 2 × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2² × 3
10. 10.What is the distance between the points (2, 10) and (17, 2)? (a) 23 (b) 18 (c) 289 (d) 17
11. 11.In a class of 49 children, 21 like cricket, 26 like football and 8 like both. How many like at least one of the two? (a) 39 (b) 47 (c) 49 (d) 31
12. 12.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 63 (c) 64 (d) 54
13. 13.What is the product of the roots of x² − 17x + 72 = 0? (a) 17 (b) 73 (c) 72 (d) 71
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/6 (c) 5/11 (d) 1/11
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
16. 16.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 100° (d) 155°
17. 17.If a + b = 17 and ab = 72, what is a² + b²? (a) 217 (b) 289 (c) 433 (d) 145
18. 18.What is the product of the roots of x² − 15x + 56 = 0? (a) 15 (b) 55 (c) 56 (d) 57
19. 19.A bag has 5 black balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 4 (c) 8 (d) 6
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
21. 21.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 7)(x + 9) (c) (x + 1)(x + 15) (d) (x + 1)(x + 63)
22. 22.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 140° (c) 250° (d) 70°
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
24. 24.3 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) 7 (b) 12 (c) 15 (d) 24
25. 25.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
26. 26.Which is the correct factorisation of x² + 12x + 27? (a) (x + 3)(x + 9) (b) (x − 3)(x − 9) (c) (x + 1)(x + 11) (d) (x + 1)(x + 27)
27. 27.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 75° (d) 60°
28. 28.How many factors does 46 have? (a) 4 (b) 2 (c) 3 (d) 5
29. 29.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 14 (c) 7 (d) 15
30. 30.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
31. 31.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1681 (b) 1601 (c) 1521 (d) 1691
32. 32.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
33. 33.A drawer has lots of red, blue, green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 8 (c) 4 (d) 2
34. 34.A bag has 12 white balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 13 (c) 20 (d) 9
35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
36. 36.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 12 (d) 16
37. 37.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
38. 38.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 120° (b) 105° (c) 135° (d) 75°
39. 39.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 300 (c) 650 (d) 326
40. 40.In a class of 50 children, 22 like maths, 22 like science and 3 like both. How many like neither? (a) 9 (b) 12 (c) 6 (d) 3

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