Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 704 · 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 an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 155° (d) 25°
2. 2.Using (a − b)² = a² − 2ab + b², what is 59²? (a) 3721 (b) 3599 (c) 3491 (d) 3481
3. 3.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 16 (c) 8 (d) 32
4. 4.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
5. 5.In a class of 39 children, 24 like tea, 19 like coffee and 12 like both. How many like only tea? (a) 20 (b) 24 (c) 7 (d) 12
6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 19 (d) 18
7. 7.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 30 (c) 60 (d) 11
8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
9. 9.In a class of 26 children, 11 like maths, 10 like science and 7 like neither. How many like both? (a) 19 (b) 7 (c) 2 (d) 3
10. 10.What is the distance between the points (6, 15) and (18, 6)? (a) 16 (b) 21 (c) 15 (d) 225
11. 11.What is the mean of 4, 3, 14, 18 and 21? (a) 10 (b) 15 (c) 13 (d) 12
12. 12.What is the smallest prime factor of 21? (a) 2 (b) 3 (c) 7 (d) 1
13. 13.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 3004 (c) 6006 (d) 2926
14. 14.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
15. 15.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 990 (c) 968 (d) 1980
16. 16.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 45 (c) 5 (d) 15
17. 17.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
18. 18.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 120 (d) 20
19. 19.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 15 (b) 60 (c) 66 (d) 120
20. 20.A drawer has lots of blue, yellow 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) 4 (b) 2 (c) 3 (d) 6
21. 21.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 24 (c) 48 (d) 16
22. 22.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 120° (b) 105° (c) 135° (d) 60°
23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 15
24. 24.If a + b = 19 and ab = 84, what is a² + b²? (a) 529 (b) 193 (c) 277 (d) 361
25. 25.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
26. 26.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 35° (c) 115° (d) 145°
27. 27.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 112 (c) 64 (d) 56
28. 28.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) 21 (b) 29 (c) 28 (d) 22
29. 29.How many factors does 109 have? (a) 2 (b) 1 (c) 4 (d) 3
30. 30.If a + b = 20 and ab = 99, what is a² + b²? (a) 400 (b) 301 (c) 202 (d) 598
31. 31.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
32. 32.How many prime numbers are there between 30 and 40? (a) 4 (b) 1 (c) 2 (d) 3
33. 33.What is the 37th term of the AP 10, 16, 22, 28, …? (a) 222 (b) 226 (c) 216 (d) 232
34. 34.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/12 (c) 1/9 (d) 3/11
36. 36.A bag has 9 blue, 6 yellow and 9 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 7/24 (b) 1/4 (c) 3/4 (d) 1/3
37. 37.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 63 (c) 64 (d) 11
38. 38.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 35 (b) 336 (c) 168 (d) 184
39. 39.What is the 37th term of the AP 14, 23, 32, 41, …? (a) 338 (b) 324 (c) 333 (d) 347
40. 40.In a class of 36 children, 17 like tea, 24 like coffee and 11 like both. How many like only tea? (a) 12 (b) 13 (c) 6 (d) 17

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