Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 61 · 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.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
3. 3.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) 290° (c) 70° (d) 110°
4. 4.A bag has 6 white balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 7 (c) 13 (d) 2
5. 5.What is the 32nd term of the AP 1, 10, 19, 28, …? (a) 289 (b) 279 (c) 288 (d) 280
6. 6.What is the mean of 2, 11, 14 and 17? (a) 10 (b) 12 (c) 11 (d) 13
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
8. 8.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 24 (d) 66
9. 9.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 15 (c) 21 (d) 22
10. 10.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 144 sq cm (d) 864 sq cm
11. 11.What is the 32nd term of the AP 8, 15, 22, 29, …? (a) 224 (b) 225 (c) 217 (d) 232
12. 12.A bag has 7 green, 3 red and 6 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/9 (b) 1/3 (c) 9/16 (d) 7/16
13. 13.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 42 (c) 13 (d) 39
14. 14.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
15. 15.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) 63 (b) 60 (c) 180 (d) 20
16. 16.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 7 (d) 13
17. 17.There are 3 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) 21 (b) 24 (c) 10 (d) 42
18. 18.A drawer has lots of black, red 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
19. 19.In a class of 28 children, 16 like maths, 19 like science and 8 like both. How many like only maths? (a) 11 (b) 16 (c) 8 (d) 9
20. 20.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 150° (b) 145° (c) 65° (d) 30°
21. 21.A bag has 5 yellow balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 7 (d) 6
22. 22.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5² (c) 2³ × 5 (d) 2 × 5
23. 23.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 15° (c) 16° (d) 30°
24. 24.A bag has 4 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) 4 (b) 7 (c) 5 (d) 2
25. 25.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
26. 26.If a + b = 15 and ab = 56, what is a² + b²? (a) 169 (b) 337 (c) 113 (d) 225
27. 27.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
28. 28.A bag has 6 black balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 15 (c) 2 (d) 10
29. 29.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 105° (d) 145°
30. 30.In which quadrant does the point (7, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
31. 31.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
32. 32.A cuboid is 8 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 360 sq cm (b) 314 sq cm (c) 157 sq cm (d) 628 sq cm
33. 33.In a class of 29 children, 6 like maths, 21 like science and 3 like both. How many like at least one of the two? (a) 27 (b) 29 (c) 24 (d) 21
34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
35. 35.What is the smallest prime factor of 33? (a) 1 (b) 11 (c) 2 (d) 3
36. 36.A bag has 6 yellow balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 7 (c) 18 (d) 8
37. 37.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
38. 38.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 8 (d) 6
39. 39.What is the mode of 10, 17, 17, 5, 10, 10 and 4? (a) 17 (b) 4 (c) 10 (d) 5
40. 40.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 18 (c) 19 (d) 21

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