Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 863 · 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 how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 20 (d) 240
2. 2.Which is the correct factorisation of x² + 15x + 54? (a) (x + 6)(x + 9) (b) (x + 1)(x + 54) (c) (x − 6)(x − 9) (d) (x + 1)(x + 14)
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
4. 4.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
7. 7.What is the midpoint of the line joining (3, 0) and (5, 4)? (a) (2, 4) (b) (4, 2) (c) (1, 2) (d) (8, 4)
8. 8.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 85° (b) 145° (c) 130° (d) 35°
9. 9.If a + b = 16 and ab = 63, what is a² + b²? (a) 256 (b) 130 (c) 382 (d) 193
10. 10.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 1 (d) 3
11. 11.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 120° (d) 45°
12. 12.In a class of 28 children, 13 like mangoes, 18 like bananas and 4 like both. How many like only mangoes? (a) 13 (b) 9 (c) 10 (d) 14
13. 13.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 30 (c) 35 (d) 60
14. 14.What is the mean of 13, 13, 12 and 6? (a) 11 (b) 10 (c) 13 (d) 12
15. 15.What is the distance between the points (2, 3) and (14, 12)? (a) 16 (b) 21 (c) 15 (d) 225
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
17. 17.Which term of the AP 17, 21, 25, 29, … is 73? (a) 14th (b) 15th (c) 16th (d) 17th
18. 18.If a + b = 7 and ab = 12, what is (a − b)²? (a) 49 (b) 25 (c) 1 (d) 37
19. 19.In a class of 30 children, 23 like cricket, 11 like football and 7 like both. How many like at least one of the two? (a) 27 (b) 34 (c) 20 (d) 30
20. 20.What is the mean of 16, 5, 12 and 19? (a) 12 (b) 13 (c) 14 (d) 15
21. 21.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 150° (d) 90°
22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 21 (d) 20
23. 23.In a class of 38 children, 16 like maths, 25 like science and 12 like both. How many like at least one of the two? (a) 17 (b) 38 (c) 29 (d) 41
24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
25. 25.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 2/3 (d) 1/4
26. 26.What is the mode of 13, 13, 9, 13, 11, 12 and 11? (a) 11 (b) 12 (c) 9 (d) 13
27. 27.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 95° (b) 115° (c) 85° (d) 150°
28. 28.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
29. 29.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
30. 30.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 35° (c) 70° (d) 110°
31. 31.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 703 (c) 1482 (d) 741
32. 32.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 75 (c) 66 (d) 84
33. 33.Which is the correct factorisation of x² + 11x + 28? (a) (x − 4)(x − 7) (b) (x + 1)(x + 28) (c) (x + 1)(x + 10) (d) (x + 4)(x + 7)
34. 34.In which quadrant does the point (7, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
35. 35.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
36. 36.A drawer has lots of red, 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) 4 (b) 6 (c) 3 (d) 2
37. 37.4 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) 6 (b) 12 (c) 16 (d) 8
38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
39. 39.A bag has 3 green balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 12 (c) 2 (d) 4
40. 40.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm

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