Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 717 · 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 KITE be arranged? (a) 24 (b) 48 (c) 12 (d) 16
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/12 (c) 1/18 (d) 1/11
3. 3.4 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) 24 (b) 12 (c) 16 (d) 7
4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
5. 5.A drawer has lots of green, red, black, white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 5 (d) 6
6. 6.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 15 (b) 198 (c) 99 (d) 100
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
8. 8.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
9. 9.A bag has 5 blue balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 7 (c) 6 (d) 15
10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 17 (b) 6 (c) 15 (d) 16
11. 11.A bag has 8 green balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 9 (c) 15 (d) 10
12. 12.In which quadrant does the point (5, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
14. 14.A bag has 5 blue, 5 red and 4 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/7 (b) 5/14 (c) 1/3 (d) 9/14
15. 15.A drawer has lots of yellow, green, red and blue 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) 4 (c) 8 (d) 2
16. 16.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 64 cu cm (d) 96 cu cm
17. 17.Using (a + b)² = a² + 2ab + b², what is 72²? (a) 4624 (b) 5184 (c) 4904 (d) 5194
18. 18.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) 28 (b) 22 (c) 29 (d) 21
19. 19.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 80 (c) 72 (d) 62
20. 20.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 240 (d) 20
21. 21.4 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) 11 (b) 32 (c) 28 (d) 56
22. 22.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 150° (d) 30°
23. 23.There are 6 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) 72 (b) 36 (c) 12 (d) 42
24. 24.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 18
26. 26.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 12 (b) 11 (c) 10 (d) 9
27. 27.The numbers 19 to 27 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) 23 (c) 69 (d) 207
28. 28.What is the 12th term of the AP 15, 24, 33, 42, …? (a) 114 (b) 108 (c) 123 (d) 99
29. 29.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 240° (b) 61° (c) 120° (d) 60°
30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
31. 31.In a class of 28 children, 11 like mangoes, 18 like bananas and 8 like both. How many like only mangoes? (a) 11 (b) 10 (c) 8 (d) 3
32. 32.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 325° (c) 55° (d) 145°
33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
34. 34.A drawer has lots of black, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 3 (d) 4
35. 35.If a + b = 19 and ab = 90, what is (a − b)²? (a) 271 (b) 1 (c) 181 (d) 361
36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 5 (d) 4
37. 37.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
38. 38.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
39. 39.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 255° (c) 76° (d) 75°
40. 40.What is the mode of 19, 3, 8, 19, 19, 16 and 16? (a) 19 (b) 16 (c) 3 (d) 8

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