Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 445 · 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.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
2. 2.What is the smallest prime factor of 155? (a) 31 (b) 1 (c) 5 (d) 2
3. 3.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 120° (b) 115° (c) 125° (d) 55°
4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 121 (d) 132
5. 5.What is the median of 14, 22, 2, 7, 3, 12 and 40? (a) 13 (b) 12 (c) 14 (d) 7
6. 6.What is the median of 27, 36, 39, 10 and 19? (a) 39 (b) 36 (c) 27 (d) 19
7. 7.A bag has 11 yellow balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 13 (c) 14 (d) 2
8. 8.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 70° (c) 36° (d) 145°
9. 9.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 50° (d) 140°
10. 10.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) 189 (b) 63 (c) 66 (d) 21
11. 11.In a class of 40 children, 21 like maths, 23 like science and 3 like neither. How many like both? (a) 4 (b) 7 (c) 3 (d) 37
12. 12.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
13. 13.What is the 39th term of the AP 8, 13, 18, 23, …? (a) 195 (b) 203 (c) 190 (d) 198
14. 14.A drawer has lots of green, blue, yellow, 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) 2 (c) 10 (d) 6
15. 15.In a class of 30 children, 19 like tea, 13 like coffee and 3 like both. How many like at least one of the two? (a) 30 (b) 32 (c) 29 (d) 26
16. 16.What is the 19th term of the AP 2, 9, 16, 23, …? (a) 135 (b) 133 (c) 126 (d) 128
17. 17.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
18. 18.A bag has 11 white balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 18 (d) 8
19. 19.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 48 (c) 32 (d) 24
20. 20.What is the midpoint of the line joining (6, 9) and (10, 1)? (a) (2, 4) (b) (16, 10) (c) (5, 8) (d) (8, 5)
21. 21.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2 × 3³ (c) 2² × 3 (d) 2³ × 3
22. 22.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 63 (d) 60
23. 23.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 22 (d) 55
24. 24.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
25. 25.What is the 27th term of the AP 16, 25, 34, 43, …? (a) 234 (b) 250 (c) 243 (d) 259
26. 26.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
27. 27.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
28. 28.In which quadrant does the point (−3, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
29. 29.In a class of 43 children, 24 like tea, 22 like coffee and 11 like both. How many like only tea? (a) 24 (b) 21 (c) 13 (d) 11
30. 30.A drawer has lots of red 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) 4 (b) 2 (c) 5 (d) 3
31. 31.In a class of 28 children, 13 like maths, 17 like science and 8 like both. How many like neither? (a) 7 (b) 6 (c) 8 (d) 14
32. 32.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 12 (c) 7 (d) 16
33. 33.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
34. 34.A bag has 3 red, 6 green and 7 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 7/16 (b) 9/16 (c) 5/8 (d) 1/3
35. 35.What is the mode of 9, 9, 19, 19, 18, 19 and 3? (a) 3 (b) 9 (c) 18 (d) 19
36. 36.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
37. 37.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
38. 38.A drawer has lots of blue 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) 3 (c) 5 (d) 4
39. 39.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
40. 40.There are 6 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 60 (c) 30 (d) 36

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