Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 490 · 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.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) 33 (c) 30 (d) 90
2. 2.What is the smallest prime factor of 57? (a) 1 (b) 3 (c) 19 (d) 2
3. 3.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 2 (d) 1
4. 4.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 115 (c) 116 (d) 106
5. 5.If a + b = 20 and ab = 99, what is a² + b²? (a) 301 (b) 202 (c) 598 (d) 400
6. 6.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 30° (d) 60°
7. 7.A bag has 6 blue, 5 yellow and 6 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 5/12 (b) 1/3 (c) 12/17 (d) 5/17
8. 8.3 T-shirts and 4 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) 15 (c) 7 (d) 12
9. 9.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 235° (c) 56° (d) 55°
10. 10.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 19 (b) 20 (c) 23 (d) 18
11. 11.A drawer has lots of blue 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) 3 (b) 5 (c) 4 (d) 2
12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 19 (d) 17
13. 13.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 65°
14. 14.A bag has 3 red, 2 white and 9 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/7 (b) 6/7 (c) 1/3 (d) 1/6
15. 15.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 80° (b) 120° (c) 160° (d) 60°
16. 16.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 120 (d) 20
17. 17.A drawer has lots of yellow, white, red, black 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) 6 (b) 2 (c) 5 (d) 10
18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 19 (d) 9
19. 19.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/4 (c) 1/8 (d) 7/8
20. 20.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 30° (d) 15°
21. 21.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 80 (b) 13 (c) 40 (d) 48
22. 22.Which term of the AP 18, 27, 36, 45, … is 360? (a) 38th (b) 40th (c) 39th (d) 41st
23. 23.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 14 (c) 15 (d) 7
24. 24.How many factors does 54 have? (a) 7 (b) 6 (c) 9 (d) 8
25. 25.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 55° (b) 125° (c) 105° (d) 130°
26. 26.A bag has 4 yellow balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 6 (c) 5 (d) 2
27. 27.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 270 (c) 252 (d) 261
28. 28.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 576 (b) 266 (c) 384 (d) 256
29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
30. 30.How many factors does 88 have? (a) 8 (b) 7 (c) 6 (d) 9
31. 31.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 10004 (b) 9604 (c) 10414 (d) 10404
32. 32.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 105 (b) 200 (c) 30 (d) 100
33. 33.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
34. 34.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5041 (b) 4761 (c) 4901 (d) 5051
35. 35.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
36. 36.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
37. 37.How many prime numbers are there between 80 and 90? (a) 1 (b) 4 (c) 2 (d) 3
38. 38.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 36 (c) 42 (d) 72
39. 39.A bag has 8 green, 9 yellow and 8 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 9/25 (b) 16/25 (c) 1/3 (d) 17/25
40. 40.What is the 25th term of the AP 16, 22, 28, 34, …? (a) 150 (b) 144 (c) 160 (d) 166

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