Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 832 · 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 + 13x + 36? (a) (x + 1)(x + 36) (b) (x − 4)(x − 9) (c) (x + 4)(x + 9) (d) (x + 1)(x + 12)
2. 2.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 424 (c) 529 (d) 528
3. 3.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 160° (c) 35° (d) 15°
4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 18 (d) 19
5. 5.A drawer has lots of yellow, black, green, white 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) 5 (b) 6 (c) 2 (d) 10
6. 6.The mean of 6 numbers is 34. When the number 48 is added to them, what is the new mean? (a) 41 (b) 37 (c) 34 (d) 36
7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
8. 8.In a class of 20 children, 12 like tea, 15 like coffee and 8 like both. How many like at least one of the two? (a) 19 (b) 20 (c) 11 (d) 27
9. 9.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
10. 10.What is the sum of the roots of x² − 11x + 18 = 0? (a) 18 (b) 10 (c) 12 (d) 11
11. 11.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 140° (d) 60°
12. 12.The mean of 3 numbers is 14. When the number 18 is added to them, what is the new mean? (a) 14 (b) 16 (c) 17 (d) 15
13. 13.A bag has 9 black balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 2 (c) 13 (d) 10
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 5/36 (d) 1/11
15. 15.What is the median of 5, 7, 40, 19 and 33? (a) 19 (b) 40 (c) 7 (d) 33
16. 16.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 120 (d) 20
17. 17.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 75° (b) 135° (c) 30° (d) 150°
18. 18.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
19. 19.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
20. 20.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
21. 21.In which quadrant does the point (9, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
22. 22.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7
23. 23.A bag has 5 green balls and 4 black 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) 6 (d) 5
24. 24.In which quadrant does the point (7, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
25. 25.A bag has 6 green, 6 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 9/14 (c) 4/7 (d) 3/7
26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
27. 27.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
28. 28.In a class of 17 children, 10 like maths, 6 like science and 2 like both. How many like neither? (a) 3 (b) 2 (c) 1 (d) 5
29. 29.A drawer has lots of blue, black, 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) 8 (b) 5 (c) 4 (d) 2
30. 30.A bag has 11 yellow balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 19 (c) 12 (d) 2
31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
32. 32.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 16 (c) 6 (d) 8
33. 33.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 55 (d) 121
34. 34.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 35 (d) 26
35. 35.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 65° (b) 85° (c) 115° (d) 160°
36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
37. 37.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 18 (c) 15 (d) 5
38. 38.What is the midpoint of the line joining (1, 6) and (9, 2)? (a) (5, 4) (b) (4, 5) (c) (4, 2) (d) (10, 8)
39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100

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