Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 198 · 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 25° and 25°. What is the third angle? (a) 50° (b) 155° (c) 310° (d) 130°
2. 2.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9
4. 4.If a + b = 12 and ab = 20, what is (a − b)²? (a) 104 (b) 144 (c) 64 (d) 8
5. 5.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/11 (c) 1/6 (d) 5/11
7. 7.What is the 38th term of the AP 12, 14, 16, 18, …? (a) 76 (b) 74 (c) 86 (d) 88
8. 8.A bag has 2 blue, 9 red and 5 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/8 (b) 1/3 (c) 7/8 (d) 1/7
9. 9.In a class of 45 children, 16 like cricket, 26 like football and 10 like neither. How many like both? (a) 10 (b) 8 (c) 35 (d) 7
10. 10.A cuboid is 8 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 384 cu cm (b) 22 cu cm (c) 320 cu cm (d) 48 cu cm
11. 11.If a + b = 4 and ab = 3, what is a² + b²? (a) 10 (b) 16 (c) 22 (d) 13
12. 12.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) 15 (b) 8 (c) 7 (d) 14
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
14. 14.A drawer has lots of 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) 5 (b) 2 (c) 4 (d) 3
15. 15.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 250° (c) 70° (d) 125°
16. 16.Which term of the AP 16, 22, 28, 34, … is 178? (a) 28th (b) 29th (c) 27th (d) 30th
17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
18. 18.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
19. 19.In which quadrant does the point (−7, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
20. 20.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
21. 21.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
22. 22.What is the midpoint of the line joining (5, 17) and (15, 7)? (a) (5, 5) (b) (12, 10) (c) (20, 24) (d) (10, 12)
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/11 (c) 1/36 (d) 1/12
24. 24.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
25. 25.What is the product of the roots of x² − 8x + 12 = 0? (a) 13 (b) 11 (c) 12 (d) 8
26. 26.Which term of the AP 3, 11, 19, 27, … is 147? (a) 20th (b) 19th (c) 18th (d) 21st
27. 27.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 220° (c) 40° (d) 140°
28. 28.A bag has 11 black balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 15 (b) 12 (c) 13 (d) 2
29. 29.How many factors does 65 have? (a) 3 (b) 2 (c) 5 (d) 4
30. 30.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 5 (b) 3 (c) 2 (d) 4
31. 31.What is the midpoint of the line joining (10, 2) and (18, 4)? (a) (4, 1) (b) (28, 6) (c) (14, 3) (d) (3, 14)
32. 32.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
33. 33.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
34. 34.A bag has 9 green, 9 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/8 (b) 3/8 (c) 2/3 (d) 1/3
35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16
36. 36.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
37. 37.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 125° (b) 55° (c) 120° (d) 115°
38. 38.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
39. 39.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 792 (b) 429 (c) 66 (d) 396
40. 40.What is the median of 28, 27, 11, 37, 5, 35 and 16? (a) 16 (b) 37 (c) 28 (d) 27

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