Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 366 · 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.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 4 sq cm (c) 8 sq cm (d) 16 sq cm
2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 4 (d) 1
3. 3.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 140° (c) 160° (d) 20°
4. 4.A bag has 4 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 6 (c) 15 (d) 5
5. 5.In which quadrant does the point (−6, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
6. 6.A drawer has lots of yellow, white, red, black and blue 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) 5 (d) 10
7. 7.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 148 sq cm (b) 296 sq cm (c) 120 sq cm (d) 74 sq cm
8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 2 (d) 5
9. 9.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 105° (b) 75° (c) 150° (d) 135°
10. 10.What is the midpoint of the line joining (7, 16) and (11, 8)? (a) (2, 4) (b) (12, 9) (c) (18, 24) (d) (9, 12)
11. 11.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 64 (d) 56
12. 12.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 4422 (c) 2145 (d) 2178
13. 13.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
14. 14.In a class of 40 children, 22 like cricket, 23 like football and 4 like neither. How many like both? (a) 4 (b) 9 (c) 36 (d) 5
15. 15.A drawer has lots of green, blue, 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) 6 (b) 2 (c) 10 (d) 5
16. 16.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 63 (c) 66 (d) 189
17. 17.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
19. 19.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
20. 20.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 110 (d) 22
21. 21.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 9216 (b) 10826 (c) 10816 (d) 10016
22. 22.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 15 (b) 70 (c) 126 (d) 63
23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 9 (d) 12
24. 24.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 5 (b) 15 (c) 16 (d) 14
26. 26.A bag has 4 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 5 (d) 7
27. 27.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
28. 28.What are the roots of x² − 14x + 48 = 0? (a) 1 and 48 (b) 6 and 8 (c) 1 and 13 (d) 2 and 24
29. 29.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/4 (c) 1/2 (d) 1/3
30. 30.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
31. 31.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 36 (c) 49 (d) 37
32. 32.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
33. 33.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 16 (c) 24 (d) 10
34. 34.The mean of 9 numbers is 38. When the number 68 is added to them, what is the new mean? (a) 41 (b) 42 (c) 38 (d) 53
35. 35.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 18 (c) 6 (d) 54
36. 36.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
37. 37.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 42 (c) 28 (d) 21
38. 38.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
39. 39.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 794 (b) 1024 (c) 784 (d) 896
40. 40.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 160 (c) 25 (d) 170

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