Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 591 · 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.How many prime numbers are there between 30 and 50? (a) 6 (b) 5 (c) 7 (d) 4
2. 2.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 5 (c) 9 (d) 12
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
5. 5.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 6 (d) 9
6. 6.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 90° (b) 45° (c) 135° (d) 225°
7. 7.There are 4 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 16 (c) 6 (d) 8
8. 8.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 2 (d) 1
9. 9.What is the median of 14, 27, 33, 21, 2, 28 and 8? (a) 27 (b) 14 (c) 21 (d) 19
10. 10.In which quadrant does the point (4, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
11. 11.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 1)(x + 5) (c) (x + 1)(x + 8) (d) (x + 2)(x + 4)
12. 12.Which term of the AP 7, 14, 21, 28, … is 245? (a) 34th (b) 35th (c) 36th (d) 37th
13. 13.A bag has 10 yellow balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 17 (b) 12 (c) 11 (d) 2
14. 14.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
15. 15.There are 4 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) 24 (b) 16 (c) 12 (d) 7
16. 16.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 135° (d) 45°
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
18. 18.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2² × 5 (d) 2³ × 5
19. 19.The mean of 3 numbers is 16. When the number 24 is added to them, what is the new mean? (a) 19 (b) 16 (c) 18 (d) 20
20. 20.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)
21. 21.What is the prime factorisation of 21? (a) 3 × 7² (b) 3 × 7 (c) 3³ × 7 (d) 3² × 7
22. 22.How many factors does 36 have? (a) 8 (b) 7 (c) 10 (d) 9
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
24. 24.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 65°
25. 25.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 8)(x + 9) (c) (x − 8)(x − 9) (d) (x + 1)(x + 16)
26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
27. 27.A drawer has lots of black, yellow, blue, green and red 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) 5 (c) 10 (d) 6
28. 28.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 48 (c) 30 (d) 24
29. 29.In a class of 26 children, 14 like mangoes, 18 like bananas and 11 like both. How many like at least one of the two? (a) 26 (b) 32 (c) 10 (d) 21
30. 30.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 156 (c) 169 (d) 91
31. 31.A bag has 9 blue balls and 8 green 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) 17 (c) 2 (d) 10
32. 32.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
33. 33.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
34. 34.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
35. 35.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 5 (c) 9 (d) 6
36. 36.If a + b = 8 and ab = 15, what is a² + b²? (a) 94 (b) 64 (c) 49 (d) 34
37. 37.What is the product of the roots of x² − 17x + 72 = 0? (a) 17 (b) 71 (c) 72 (d) 73
38. 38.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 210° (c) 30° (d) 105°
39. 39.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
40. 40.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 408 (c) 505 (d) 504

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