Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 96 · 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 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
2. 2.What is the midpoint of the line joining (7, 17) and (19, 5)? (a) (13, 11) (b) (26, 22) (c) (11, 13) (d) (6, 6)
3. 3.What is the midpoint of the line joining (2, 12) and (14, 2)? (a) (7, 8) (b) (16, 14) (c) (6, 5) (d) (8, 7)
4. 4.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
5. 5.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 24 (d) 72
6. 6.What are the roots of x² − 5x + 6 = 0? (a) 2 and 3 (b) 2 and 4 (c) 1 and 4 (d) 1 and 6
7. 7.What is the distance between the points (2, 5) and (7, 17)? (a) 169 (b) 17 (c) 13 (d) 14
8. 8.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3
9. 9.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 49 (d) 42
10. 10.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/4 (b) 2/3 (c) 5/6 (d) 1/3
11. 11.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 217 cu cm (d) 216 cu cm
12. 12.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) 32 (c) 16 (d) 8
13. 13.What are the roots of x² − 10x + 16 = 0? (a) 3 and 7 (b) 2 and 8 (c) 1 and 9 (d) 1 and 16
14. 14.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 50° (c) 230° (d) 130°
15. 15.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
16. 16.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
17. 17.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
18. 18.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 85° (c) 265° (d) 95°
19. 19.What is the distance between the points (0, 8) and (6, 16)? (a) 100 (b) 11 (c) 14 (d) 10
20. 20.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
21. 21.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 20 (c) 8 (d) 15
22. 22.The mean of 8 numbers is 39. When the number 30 is added to them, what is the new mean? (a) 38 (b) 39 (c) 37 (d) 40
23. 23.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times
24. 24.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
25. 25.In a class of 53 children, 26 like mangoes, 32 like bananas and 7 like neither. How many like both? (a) 5 (b) 7 (c) 46 (d) 12
26. 26.A cuboid is 7 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 21 cu cm (b) 242 cu cm (c) 210 cu cm (d) 20 cu cm
27. 27.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 1/8 (d) 3/8
28. 28.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 28 (c) 56 (d) 32
29. 29.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 24 sq cm (d) 4 sq cm
30. 30.A bag has 11 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 6 (c) 12 (d) 2
31. 31.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 460 (c) 459 (d) 450
32. 32.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 21 (b) 17 (c) 16 (d) 18
33. 33.A drawer has lots of red, 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) 2 (b) 6 (c) 3 (d) 4
34. 34.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 244 (c) 243 (d) 351
35. 35.A bag has 5 red balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 4 (c) 2 (d) 8
36. 36.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
37. 37.In which quadrant does the point (−8, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
38. 38.In a class of 20 children, 11 like maths, 10 like science and 4 like both. How many like at least one of the two? (a) 21 (b) 13 (c) 17 (d) 20
39. 39.What is the 37th term of the AP 19, 22, 25, 28, …? (a) 127 (b) 130 (c) 108 (d) 111
40. 40.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15

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