Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 735 · 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 6 green balls and 8 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) 14 (c) 7 (d) 2
2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
3. 3.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 22 (d) 29
4. 4.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 56 (d) 28
5. 5.Using (a − b)² = a² − 2ab + b², what is 86²? (a) 7396 (b) 8084 (c) 8836 (d) 7406
6. 6.In which quadrant does the point (1, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 21 (d) 15
8. 8.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 1)(x + 56) (c) (x + 7)(x + 8) (d) (x − 7)(x − 8)
9. 9.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 7 (b) 5 (c) 10 (d) 6
10. 10.How many prime numbers are there between 80 and 100? (a) 3 (b) 4 (c) 2 (d) 5
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 5/36 (c) 4/11 (d) 1/11
13. 13.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3486 (c) 6972 (d) 3403
14. 14.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 325° (c) 145° (d) 55°
15. 15.What is the midpoint of the line joining (8, 7) and (16, 1)? (a) (4, 12) (b) (12, 4) (c) (4, 3) (d) (24, 8)
16. 16.What is the smallest prime factor of 209? (a) 11 (b) 2 (c) 19 (d) 1
17. 17.A bag has 7 green balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 8 (c) 2 (d) 9
18. 18.A drawer has lots of red, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 4 (d) 3
19. 19.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 207 (c) 72 (d) 69
20. 20.What is the prime factorisation of 63? (a) 3 × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3² × 7
21. 21.Which term of the AP 5, 12, 19, 26, … is 110? (a) 16th (b) 18th (c) 15th (d) 17th
22. 22.In a class of 29 children, 17 like maths, 16 like science and 10 like both. How many like at least one of the two? (a) 29 (b) 13 (c) 23 (d) 33
23. 23.The mean of 3 numbers is 26. When the number 18 is added to them, what is the new mean? (a) 22 (b) 24 (c) 26 (d) 25
24. 24.What is the distance between the points (3, 8) and (9, 0)? (a) 100 (b) 11 (c) 10 (d) 14
25. 25.In a class of 38 children, 22 like tea, 23 like coffee and 8 like both. How many like only tea? (a) 14 (b) 15 (c) 8 (d) 22
26. 26.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 70° (d) 110°
27. 27.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 1)(x + 12) (c) (x + 1)(x + 42) (d) (x + 6)(x + 7)
28. 28.A drawer has lots of blue, red, green, yellow and black 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) 10 (c) 6 (d) 5
29. 29.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4608 (c) 4656 (d) 4560
30. 30.What is the median of 16, 14, 29, 26 and 34? (a) 29 (b) 27 (c) 16 (d) 26
31. 31.A bag has 3 white balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 5 (b) 4 (c) 2 (d) 7
32. 32.In which quadrant does the point (9, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
33. 33.A bag has 9 blue balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 10 (c) 11 (d) 2
34. 34.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
35. 35.A bag has 11 blue balls and 8 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) 12 (c) 2 (d) 19
36. 36.What is the mode of 20, 20, 3, 3, 12, 20 and 15? (a) 3 (b) 15 (c) 20 (d) 12
37. 37.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
38. 38.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
40. 40.If a + b = 12 and ab = 32, what is a² + b²? (a) 112 (b) 80 (c) 144 (d) 208

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