Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 481 · 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.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
2. 2.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁵ × 7 (c) 2⁴ × 7 (d) 2³ × 7
3. 3.A bag has 6 red, 9 white and 7 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/11 (b) 17/22 (c) 1/3 (d) 3/11
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
5. 5.What is the mode of 1, 10, 1, 8, 10, 16 and 1? (a) 1 (b) 8 (c) 16 (d) 10
6. 6.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 70° (d) 20°
7. 7.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 372 (c) 382 (d) 381
8. 8.In a class of 34 children, 19 like dance, 18 like music and 9 like both. How many like neither? (a) 15 (b) 9 (c) 7 (d) 6
9. 9.If a + b = 8 and ab = 12, what is a² + b²? (a) 52 (b) 40 (c) 64 (d) 88
10. 10.What is the smallest prime factor of 21? (a) 1 (b) 7 (c) 2 (d) 3
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
12. 12.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 416 (b) 256 (c) 586 (d) 576
13. 13.In a class of 29 children, 16 like mangoes, 20 like bananas and 9 like both. How many like at least one of the two? (a) 18 (b) 36 (c) 27 (d) 29
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
15. 15.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 11 (d) 25
16. 16.A drawer has lots of red, white, blue 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) 8 (b) 5 (c) 4 (d) 2
17. 17.A bag has 3 yellow 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) 11 (b) 2 (c) 4 (d) 9
18. 18.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 216 (c) 24 (d) 75
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
20. 20.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 308 (b) 34 (c) 168 (d) 154
21. 21.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 20° (d) 160°
22. 22.What is the mean of 13, 6, 17, 8, 16 and 6? (a) 11 (b) 12 (c) 10 (d) 13
23. 23.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
24. 24.A bag has 3 yellow, 2 white and 3 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 3/4 (b) 3/8 (c) 5/8 (d) 1/3
25. 25.A bag has 3 yellow balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 4 (b) 8 (c) 2 (d) 5
26. 26.In a class of 47 children, 25 like maths, 27 like science and 7 like both. How many like at least one of the two? (a) 38 (b) 45 (c) 47 (d) 52
27. 27.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 270° (c) 120° (d) 90°
28. 28.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 40° (d) 220°
29. 29.A bag has 8 white balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 2 (c) 15 (d) 9
30. 30.How many prime numbers are there between 30 and 50? (a) 5 (b) 4 (c) 7 (d) 6
31. 31.What is the 28th term of the AP 6, 8, 10, 12, …? (a) 54 (b) 60 (c) 62 (d) 56
32. 32.What is the distance between the points (1, 1) and (9, 7)? (a) 14 (b) 100 (c) 11 (d) 10
33. 33.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 12 (d) 48
34. 34.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 32 (c) 11 (d) 28
35. 35.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 130° (d) 50°
36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 2 (c) 3 (d) 4
37. 37.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7³
38. 38.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
39. 39.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) 9 times (c) 3 times (d) 27 times
40. 40.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)

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