Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 128 · 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 12th term of the AP 8, 13, 18, 23, …? (a) 68 (b) 55 (c) 60 (d) 63
2. 2.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7066 (b) 5776 (c) 6416 (d) 7056
3. 3.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 45° (b) 125° (c) 100° (d) 135°
4. 4.A bag has 7 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 8 (b) 2 (c) 11 (d) 9
5. 5.A bag has 6 blue balls and 3 yellow 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) 4 (c) 7 (d) 2
6. 6.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 78 (c) 156 (d) 91
7. 7.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) 15 (b) 14 (c) 8 (d) 7
8. 8.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 105 (c) 182 (d) 91
9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
10. 10.A bag has 6 yellow, 3 red and 5 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 3/14 (c) 11/14 (d) 6/7
11. 11.How many factors does 20 have? (a) 6 (b) 4 (c) 7 (d) 5
12. 12.In a class of 27 children, 21 like maths, 5 like science and 3 like neither. How many like both? (a) 3 (b) 2 (c) 24 (d) 1
13. 13.In which quadrant does the point (7, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
14. 14.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) 9 times (c) 27 times (d) 6 times
15. 15.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 255° (c) 150° (d) 75°
16. 16.What is the distance between the points (0, 1) and (12, 17)? (a) 400 (b) 20 (c) 21 (d) 28
17. 17.What is the missing term in the AP 14, 23, ?, 41, 50? (a) 32 (b) 31 (c) 41 (d) 33
18. 18.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 1806 (c) 882 (d) 861
19. 19.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
20. 20.A bag has 3 green, 2 yellow and 8 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 11/13 (b) 1/3 (c) 2/13 (d) 2/11
21. 21.What is the mode of 16, 15, 14, 15, 9, 15 and 14? (a) 14 (b) 9 (c) 16 (d) 15
22. 22.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 100° (b) 135° (c) 80° (d) 125°
23. 23.A bag has 7 yellow, 4 blue and 2 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 6/13 (b) 7/13 (c) 1/3 (d) 6/7
24. 24.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 25 (b) 28 (c) 24 (d) 23
25. 25.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
26. 26.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 130° (d) 40°
27. 27.How many factors does 53 have? (a) 3 (b) 2 (c) 4 (d) 1
28. 28.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
29. 29.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/8 (c) 1/4 (d) 1/7
30. 30.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 16 (c) 51 (d) 48
31. 31.What is the median of 12, 21, 4, 22 and 2? (a) 21 (b) 13 (c) 4 (d) 12
32. 32.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
33. 33.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
34. 34.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 132 (d) 144
35. 35.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
37. 37.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 57 (c) 19 (d) 171
38. 38.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
39. 39.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 290° (d) 70°
40. 40.If a + b = 19 and ab = 84, what is (a − b)²? (a) 193 (b) 361 (c) 25 (d) 5

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