Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 536 · 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.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 150° (b) 10° (c) 40° (d) 170°
2. 2.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 35 (b) 36 (c) 37 (d) 44
3. 3.How many factors does 86 have? (a) 4 (b) 2 (c) 5 (d) 3
4. 4.A bag has 8 white, 5 green and 5 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 5/9 (c) 4/5 (d) 4/9
5. 5.In which quadrant does the point (−2, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
6. 6.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
7. 7.What is the mean of 15, 6, 14, 3 and 12? (a) 11 (b) 9 (c) 12 (d) 10
8. 8.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 21 (d) 36
9. 9.In a class of 29 children, 20 like cricket, 11 like football and 1 like neither. How many like both? (a) 3 (b) 1 (c) 2 (d) 28
10. 10.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 19 (d) 57
11. 11.A drawer has lots of white, 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) 3 (b) 6 (c) 4 (d) 2
12. 12.In a class of 42 children, 23 like maths, 24 like science and 7 like both. How many like only maths? (a) 18 (b) 17 (c) 16 (d) 23
13. 13.A bag has 3 green balls and 4 white 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) 4 (c) 7 (d) 5
14. 14.What is the mean of 4, 7, 3, 20 and 11? (a) 10 (b) 9 (c) 11 (d) 8
15. 15.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 25 (c) 24 (d) 13
16. 16.What is the midpoint of the line joining (3, 6) and (5, 10)? (a) (8, 16) (b) (8, 4) (c) (4, 8) (d) (1, 2)
17. 17.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 5° (d) 275°
18. 18.What is the 35th term of the AP 17, 25, 33, 41, …? (a) 297 (b) 280 (c) 272 (d) 289
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
20. 20.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 27 cu cm (d) 54 cu cm
21. 21.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)
22. 22.The mean of 3 numbers is 18. When the number 22 is added to them, what is the new mean? (a) 20 (b) 19 (c) 18 (d) 21
23. 23.How many factors does 101 have? (a) 1 (b) 3 (c) 4 (d) 2
24. 24.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7³
25. 25.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
26. 26.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2 × 7⁴ (c) 2⁴ × 7 (d) 2³ × 7
27. 27.In which quadrant does the point (−2, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
28. 28.What is the mean of 13, 17, 4, 13, 8 and 11? (a) 10 (b) 11 (c) 13 (d) 12
29. 29.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 160° (d) 10°
30. 30.Which term of the AP 6, 10, 14, 18, … is 50? (a) 14th (b) 13th (c) 12th (d) 11th
31. 31.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 135° (c) 270° (d) 90°
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 month? (a) 36 (b) 37 (c) 24 (d) 25
33. 33.Which term of the AP 13, 21, 29, 37, … is 173? (a) 21st (b) 20th (c) 23rd (d) 22nd
34. 34.If a + b = 5 and ab = 4, what is a² + b²? (a) 33 (b) 21 (c) 25 (d) 17
35. 35.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
36. 36.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 10° (b) 60° (c) 130° (d) 170°
37. 37.Which term of the AP 13, 16, 19, 22, … is 70? (a) 22nd (b) 21st (c) 20th (d) 19th
38. 38.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) 5 (b) 9 (c) 12 (d) 6
39. 39.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 11 (d) 42
40. 40.How many factors does 78 have? (a) 7 (b) 6 (c) 8 (d) 9

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