Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 478 · 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 median of 5, 26, 38, 19 and 39? (a) 27 (b) 19 (c) 38 (d) 26
2. 2.A bag has 4 green, 7 white and 3 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/14 (b) 1/3 (c) 1/2 (d) 4/7
3. 3.6 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) 9 (b) 36 (c) 24 (d) 18
4. 4.How many factors does 24 have? (a) 7 (b) 6 (c) 8 (d) 9
5. 5.In a class of 45 children, 22 like dance, 26 like music and 11 like both. How many like at least one of the two? (a) 37 (b) 45 (c) 48 (d) 26
6. 6.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 516 (b) 480 (c) 960 (d) 73
7. 7.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 130° (b) 95° (c) 50° (d) 135°
8. 8.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) 10 (b) 90 (c) 33 (d) 30
9. 9.In a class of 45 children, 24 like tea, 29 like coffee and 10 like both. How many like only tea? (a) 14 (b) 19 (c) 16 (d) 24
10. 10.What is the prime factorisation of 560? (a) 2³ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2⁴ × 5 × 7 (d) 2⁵ × 5 × 7
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
12. 12.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 9 (d) 6
13. 13.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2³ × 5 (c) 2² × 5 (d) 2⁴ × 5
14. 14.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
16. 16.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
17. 17.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
18. 18.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
19. 19.In a class of 41 children, 16 like cricket, 31 like football and 6 like neither. How many like both? (a) 6 (b) 35 (c) 13 (d) 12
20. 20.If a + b = 11 and ab = 24, what is (a − b)²? (a) 73 (b) 5 (c) 121 (d) 25
21. 21.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
22. 22.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1369 (b) 1609 (c) 1859 (d) 1849
23. 23.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 1/8 (d) 3/8
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
25. 25.If a + b = 20 and ab = 99, what is a² + b²? (a) 598 (b) 202 (c) 400 (d) 301
26. 26.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 155° (b) 145° (c) 120° (d) 60°
27. 27.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 65° (d) 335°
28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 20 (d) 8
29. 29.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 100° (b) 125° (c) 80° (d) 155°
30. 30.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
31. 31.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 145° (c) 85° (d) 95°
32. 32.What is the mean of 2, 2, 5 and 15? (a) 6 (b) 7 (c) 5 (d) 8
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
34. 34.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
35. 35.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 576 (b) 384 (c) 266 (d) 256
36. 36.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 36 (d) 30
37. 37.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 36 (c) 9 (d) 21
38. 38.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
39. 39.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 75° (d) 160°
40. 40.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 456 (d) 576

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