Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 554 · 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 bag has 5 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 6 (c) 10 (d) 2
2. 2.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) 42 (b) 84 (c) 48 (d) 13
3. 3.A bag has 2 white, 5 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 4/5 (b) 1/3 (c) 3/10 (d) 7/10
4. 4.Using (a − b)² = a² − 2ab + b², what is 76²? (a) 7056 (b) 6384 (c) 5776 (d) 5786
5. 5.In a class of 34 children, 16 like maths, 18 like science and 6 like both. How many like neither? (a) 7 (b) 12 (c) 0 (d) 6
6. 6.What is the distance between the points (8, 18) and (17, 6)? (a) 16 (b) 225 (c) 21 (d) 15
7. 7.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
8. 8.In a class of 33 children, 19 like mangoes, 15 like bananas and 10 like both. How many like only mangoes? (a) 9 (b) 5 (c) 18 (d) 19
9. 9.What is the mode of 5, 6, 1, 6, 6, 1 and 15? (a) 1 (b) 5 (c) 6 (d) 15
10. 10.If a + b = 9 and ab = 18, what is (a − b)²? (a) 81 (b) 45 (c) 3 (d) 9
11. 11.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 120° (d) 60°
12. 12.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 7 (d) 2
13. 13.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 115° (d) 100°
14. 14.How many prime numbers are there between 30 and 60? (a) 7 (b) 6 (c) 8 (d) 9
15. 15.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 60 (b) 16 (c) 51 (d) 102
16. 16.A bag has 4 white balls and 7 black 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) 8 (d) 5
17. 17.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 155° (b) 120° (c) 25° (d) 85°
18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
19. 19.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2 × 3² × 7³ (c) 2³ × 3² × 7 (d) 2⁴ × 3² × 7
20. 20.How many prime numbers are there between 70 and 90? (a) 7 (b) 6 (c) 4 (d) 5
21. 21.What is the mean of 2, 9, 9 and 12? (a) 7 (b) 10 (c) 8 (d) 9
22. 22.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
23. 23.In which quadrant does the point (−4, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
24. 24.A bag has 8 red balls and 10 yellow 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) 2 (c) 11 (d) 18
25. 25.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 120° (b) 35° (c) 145° (d) 95°
26. 26.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 81 (d) 72
27. 27.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) 66 (b) 63 (c) 21 (d) 189
28. 28.What is the 20th term of the AP 15, 17, 19, 21, …? (a) 38 (b) 53 (c) 55 (d) 40
29. 29.A drawer has lots of green 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) 4 (c) 5 (d) 3
30. 30.How many prime numbers are there between 90 and 100? (a) 2 (b) 3 (c) 1 (d) 0
31. 31.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x − 2)(x − 4) (c) (x + 1)(x + 5) (d) (x + 1)(x + 8)
32. 32.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
34. 34.In a class of 27 children, 16 like mangoes, 17 like bananas and 12 like both. How many like neither? (a) 18 (b) 7 (c) 12 (d) 6
35. 35.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
37. 37.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 1)(x + 63) (c) (x + 7)(x + 9) (d) (x + 1)(x + 15)
38. 38.In which quadrant does the point (8, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 18
40. 40.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 100 sq cm (d) 150 sq cm

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