Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 402 · 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.What is the smallest prime factor of 93? (a) 3 (b) 1 (c) 31 (d) 2
2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
3. 3.A bag has 11 yellow balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 20 (c) 2 (d) 12
4. 4.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 70° (d) 20°
5. 5.In a class of 43 children, 25 like mangoes, 21 like bananas and 11 like both. How many like at least one of the two? (a) 43 (b) 24 (c) 46 (d) 35
6. 6.A bag has 4 black balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 2 (c) 6 (d) 5
7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 9 (d) 15
8. 8.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 14 (d) 15
9. 9.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) 72 (b) 207 (c) 23 (d) 69
10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
12. 12.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 110° (c) 70° (d) 290°
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
14. 14.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
15. 15.What is the median of 10, 22, 24, 9 and 20? (a) 17 (b) 20 (c) 22 (d) 24
16. 16.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 35 (c) 30 (d) 11
17. 17.What is the mean of 5, 7, 2, 6, 9 and 19? (a) 9 (b) 7 (c) 10 (d) 8
18. 18.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
19. 19.In a class of 27 children, 12 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 15 (b) 19 (c) 23 (d) 27
20. 20.The mean of 6 numbers is 23. When the number 16 is added to them, what is the new mean? (a) 24 (b) 21 (c) 22 (d) 23
21. 21.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 115° (b) 120° (c) 60° (d) 125°
22. 22.In a class of 34 children, 12 like maths, 22 like science and 7 like both. How many like at least one of the two? (a) 28 (b) 20 (c) 34 (d) 27
23. 23.If a + b = 13 and ab = 36, what is a² + b²? (a) 169 (b) 241 (c) 97 (d) 133
24. 24.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 5 (b) 17 (c) 16 (d) 15
26. 26.A bag has 9 white, 7 red and 4 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 7/13 (c) 7/20 (d) 13/20
27. 27.In a class of 44 children, 22 like dance, 30 like music and 10 like both. How many like neither? (a) 2 (b) 12 (c) 10 (d) 3
28. 28.What is the midpoint of the line joining (2, 19) and (12, 7)? (a) (13, 7) (b) (7, 13) (c) (14, 26) (d) (5, 6)
29. 29.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
30. 30.How many prime numbers are there between 70 and 90? (a) 6 (b) 7 (c) 4 (d) 5
31. 31.In which quadrant does the point (−3, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
32. 32.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 30 (b) 156 (c) 312 (d) 168
33. 33.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 120° (b) 150° (c) 90° (d) 60°
34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 19 (d) 9
35. 35.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
37. 37.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
38. 38.What is the midpoint of the line joining (4, 10) and (8, 18)? (a) (2, 4) (b) (6, 14) (c) (12, 28) (d) (14, 6)
39. 39.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 110° (c) 220° (d) 70°
40. 40.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 3 (d) 5

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