Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 423 · 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.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 56) (c) (x + 1)(x + 14) (d) (x + 7)(x + 8)
2. 2.In a class of 31 children, 19 like mangoes, 19 like bananas and 10 like both. How many like at least one of the two? (a) 28 (b) 18 (c) 38 (d) 31
3. 3.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) 5 times (c) 4 times (d) 8 times
4. 4.A drawer has lots of yellow, red, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 2 (d) 5
5. 5.What is the 36th term of the AP 12, 20, 28, 36, …? (a) 300 (b) 280 (c) 288 (d) 292
6. 6.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 324 (d) 342
7. 7.A bag has 4 blue, 4 yellow and 4 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 3/4 (b) 2/3 (c) 1/3 (d) 1/12
8. 8.In a class of 29 children, 12 like mangoes, 12 like bananas and 5 like both. How many like at least one of the two? (a) 14 (b) 29 (c) 19 (d) 24
9. 9.What is the mode of 12, 12, 13, 16, 3, 3 and 3? (a) 12 (b) 3 (c) 13 (d) 16
10. 10.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 65° (d) 140°
11. 11.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
12. 12.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
13. 13.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 1432 (d) 2862
14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
15. 15.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 3/8 (d) 5/8
16. 16.In which quadrant does the point (−2, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
18. 18.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
19. 19.Which is the correct factorisation of x² + 15x + 54? (a) (x − 6)(x − 9) (b) (x + 1)(x + 14) (c) (x + 1)(x + 54) (d) (x + 6)(x + 9)
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
21. 21.A bag has 7 yellow, 5 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 11/15 (b) 1/3 (c) 1/15 (d) 2/3
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/11 (d) 1/36
23. 23.How many prime numbers are there between 30 and 60? (a) 6 (b) 9 (c) 7 (d) 8
24. 24.A bag has 4 yellow, 4 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 2/3 (c) 1/12 (d) 3/4
25. 25.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
26. 26.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
27. 27.A bag has 10 blue balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 2 (c) 21 (d) 12
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
29. 29.How many factors does 39 have? (a) 5 (b) 3 (c) 2 (d) 4
30. 30.How many factors does 82 have? (a) 3 (b) 2 (c) 4 (d) 5
31. 31.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
32. 32.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
33. 33.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 462 (c) 210 (d) 232
34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 4 (d) 1
35. 35.What is the mean of 12, 17, 16 and 15? (a) 15 (b) 12 (c) 20 (d) 16
36. 36.A bag has 8 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 11 (c) 9 (d) 18
37. 37.What is the median of 8, 25, 19, 7, 31, 15 and 32? (a) 15 (b) 19 (c) 7 (d) 25
38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 19 (d) 17
39. 39.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
40. 40.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 12 (d) 16

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