Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 612 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
2. 2.In a class of 43 children, 30 like dance, 18 like music and 7 like neither. How many like both? (a) 36 (b) 5 (c) 12 (d) 7
3. 3.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
4. 4.In which quadrant does the point (3, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
6. 6.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 121 (d) 55
7. 7.How many factors does 41 have? (a) 1 (b) 2 (c) 3 (d) 4
8. 8.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 576 cu cm (c) 1728 cu cm (d) 864 cu cm
9. 9.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5² × 7 (d) 5 × 7
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
11. 11.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
12. 12.In a class of 30 children, 10 like cricket, 20 like football and 3 like neither. How many like both? (a) 3 (b) 27 (c) 4 (d) 2
13. 13.What is the mean of 3, 16, 11 and 14? (a) 12 (b) 13 (c) 11 (d) 10
14. 14.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
15. 15.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 18 (d) 72
16. 16.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 55° (b) 155° (c) 150° (d) 25°
17. 17.What is the midpoint of the line joining (5, 12) and (11, 4)? (a) (9, 8) (b) (3, 4) (c) (16, 16) (d) (8, 8)
18. 18.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 21 (c) 18 (d) 54
19. 19.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
20. 20.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 240 (d) 20
21. 21.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 110° (b) 70° (c) 140° (d) 250°
22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
23. 23.If a + b = 8 and ab = 12, what is a² + b²? (a) 40 (b) 64 (c) 52 (d) 88
24. 24.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
25. 25.In a class of 28 children, 8 like tea, 21 like coffee and 3 like both. How many like neither? (a) 5 (b) 3 (c) 1 (d) 2
26. 26.In a class of 31 children, 15 like maths, 19 like science and 12 like both. How many like at least one of the two? (a) 34 (b) 10 (c) 22 (d) 31
27. 27.In a class of 20 children, 14 like tea, 14 like coffee and 9 like both. How many like neither? (a) 1 (b) 2 (c) 9 (d) 10
28. 28.A bag has 7 red balls and 3 yellow 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) 4 (c) 8 (d) 2
29. 29.In a class of 38 children, 17 like dance, 31 like music and 12 like both. How many like only dance? (a) 7 (b) 17 (c) 5 (d) 19
30. 30.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 153 (c) 51 (d) 17
31. 31.In a class of 29 children, 10 like mangoes, 21 like bananas and 7 like both. How many like only mangoes? (a) 14 (b) 10 (c) 3 (d) 8
32. 32.What is the midpoint of the line joining (2, 11) and (10, 1)? (a) (4, 5) (b) (6, 6) (c) (7, 6) (d) (12, 12)
33. 33.What is the 32nd term of the AP 17, 19, 21, 23, …? (a) 81 (b) 62 (c) 79 (d) 64
34. 34.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
35. 35.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 49 (b) 56 (c) 98 (d) 14
36. 36.What is the sum of the roots of x² − 15x + 54 = 0? (a) 14 (b) 16 (c) 15 (d) 54
37. 37.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) 25 times (d) 10 times
38. 38.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 320° (d) 20°
39. 39.What is the 36th term of the AP 18, 22, 26, 30, …? (a) 140 (b) 158 (c) 162 (d) 144
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm

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