Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 9 · 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.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 2/3
2. 2.What is the mode of 4, 10, 2, 3, 4, 4 and 3? (a) 3 (b) 4 (c) 2 (d) 10
3. 3.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 132 (d) 24
4. 4.What is the mode of 3, 5, 5, 3, 3, 6 and 13? (a) 5 (b) 3 (c) 13 (d) 6
5. 5.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 1225 (b) 2025 (c) 2035 (d) 1625
6. 6.In a class of 56 children, 31 like dance, 30 like music and 7 like neither. How many like both? (a) 7 (b) 12 (c) 49 (d) 5
7. 7.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7
8. 8.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
9. 9.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 21 (c) 30 (d) 36
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 1/12 (d) 3/11
11. 11.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
12. 12.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 259 (d) 258
13. 13.What is the distance between the points (4, 8) and (7, 4)? (a) 7 (b) 5 (c) 6 (d) 25
14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
15. 15.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) 22 (b) 14 (c) 15 (d) 21
16. 16.A drawer has lots of green, white 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) 6 (c) 2 (d) 4
17. 17.What is the median of 10, 31, 38, 5, 7, 34 and 40? (a) 10 (b) 5 (c) 31 (d) 34
18. 18.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 12 (c) 24 (d) 13
19. 19.A bag has 12 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 5 (c) 2 (d) 16
20. 20.What is the 23rd term of the AP 14, 18, 22, 26, …? (a) 88 (b) 92 (c) 102 (d) 106
21. 21.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
22. 22.Which term of the AP 15, 24, 33, 42, … is 168? (a) 20th (b) 18th (c) 17th (d) 19th
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 1/11 (c) 1/18 (d) 2/11
24. 24.What is the sum of the roots of x² − 15x + 56 = 0? (a) 14 (b) 16 (c) 15 (d) 56
25. 25.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°
26. 26.How many factors does 94 have? (a) 3 (b) 2 (c) 5 (d) 4
27. 27.In which quadrant does the point (−8, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
28. 28.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
29. 29.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 12 cu cm (d) 64 cu cm
30. 30.Using (a + b)² = a² + 2ab + b², what is 64²? (a) 3136 (b) 4096 (c) 4106 (d) 3616
31. 31.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 61 (c) 370 (d) 340
33. 33.In a class of 40 children, 23 like maths, 20 like science and 8 like neither. How many like both? (a) 3 (b) 11 (c) 8 (d) 32
34. 34.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x − 7)(x − 9) (c) (x + 7)(x + 9) (d) (x + 1)(x + 15)
35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 14 (b) 15 (c) 13 (d) 4
36. 36.In which quadrant does the point (−4, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/8 (d) 3/4
38. 38.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 10004 (b) 9604 (c) 10404 (d) 10414
39. 39.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 48 (c) 42 (d) 13
40. 40.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3

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