Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 956 · 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 area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
2. 2.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 29 (d) 3
3. 3.What is the 19th term of the AP 6, 15, 24, 33, …? (a) 171 (b) 177 (c) 168 (d) 162
4. 4.How many factors does 13 have? (a) 1 (b) 4 (c) 3 (d) 2
5. 5.The mean of 9 numbers is 25. When the number 55 is added to them, what is the new mean? (a) 40 (b) 29 (c) 25 (d) 28
6. 6.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
8. 8.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 2 (d) 3
9. 9.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 15 (c) 25 (d) 10
10. 10.A bag has 9 black balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 10 (c) 2 (d) 7
11. 11.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
12. 12.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 168 (c) 147 (d) 39
13. 13.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 17 (c) 18 (d) 16
14. 14.A drawer has lots of white, blue, red and yellow 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
15. 15.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
16. 16.What is the distance between the points (2, 14) and (7, 2)? (a) 13 (b) 14 (c) 169 (d) 17
17. 17.Which is the correct factorisation of x² + 9x + 20? (a) (x − 4)(x − 5) (b) (x + 4)(x + 5) (c) (x + 1)(x + 8) (d) (x + 1)(x + 20)
18. 18.A drawer has lots of black, white, yellow and green 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) 4 (c) 5 (d) 2
19. 19.A bag has 8 black 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) 9 (b) 17 (c) 10 (d) 2
20. 20.A bag has 10 yellow balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 19 (b) 2 (c) 11 (d) 12
21. 21.What is the 39th term of the AP 2, 4, 6, 8, …? (a) 80 (b) 78 (c) 76 (d) 79
22. 22.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
23. 23.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
24. 24.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 15 (b) 4 (c) 16 (d) 14
26. 26.In a class of 37 children, 22 like dance, 21 like music and 1 like neither. How many like both? (a) 36 (b) 7 (c) 6 (d) 1
27. 27.A bag has 2 yellow, 9 red and 5 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/9 (b) 1/3 (c) 9/16 (d) 7/16
28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
29. 29.In a class of 35 children, 18 like mangoes, 15 like bananas and 5 like both. How many like only mangoes? (a) 18 (b) 20 (c) 10 (d) 13
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
31. 31.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6399 (b) 6241 (c) 6251 (d) 6561
32. 32.What is the median of 33, 3, 31, 19 and 7? (a) 20 (b) 31 (c) 7 (d) 19
33. 33.How many factors does 82 have? (a) 5 (b) 3 (c) 2 (d) 4
34. 34.If a + b = 20 and ab = 96, what is (a − b)²? (a) 16 (b) 208 (c) 4 (d) 400
35. 35.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 607 (c) 606 (d) 476
36. 36.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
37. 37.A bag has 9 white balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 10 (c) 5 (d) 2
38. 38.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 42 (d) 13
39. 39.How many prime numbers are there between 60 and 90? (a) 6 (b) 7 (c) 9 (d) 8
40. 40.A drawer has lots of blue, red 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) 6 (b) 2 (c) 3 (d) 4

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