Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 535 · 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 65° and 85°. What is the third angle? (a) 115° (b) 30° (c) 150° (d) 95°
2. 2.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x + 1)(x + 11) (c) (x − 3)(x − 9) (d) (x + 3)(x + 9)
3. 3.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 72 (c) 16 (d) 18
4. 4.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
5. 5.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
6. 6.What is the distance between the points (7, 8) and (13, 16)? (a) 11 (b) 100 (c) 14 (d) 10
7. 7.Which is the correct factorisation of x² + 11x + 28? (a) (x + 4)(x + 7) (b) (x + 1)(x + 28) (c) (x − 4)(x − 7) (d) (x + 1)(x + 10)
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6
9. 9.If a + b = 14 and ab = 40, what is (a − b)²? (a) 116 (b) 6 (c) 36 (d) 196
10. 10.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 6 (d) 5
11. 11.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 46° (c) 135° (d) 45°
12. 12.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 50° (c) 130° (d) 150°
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
14. 14.In which quadrant does the point (−8, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
15. 15.In a class of 19 children, 6 like cricket, 9 like football and 3 like both. How many like neither? (a) 3 (b) 10 (c) 7 (d) 4
16. 16.In a class of 16 children, 9 like tea, 12 like coffee and 6 like both. How many like neither? (a) 6 (b) 2 (c) 1 (d) 7
17. 17.In a class of 35 children, 15 like cricket, 15 like football and 3 like both. How many like at least one of the two? (a) 30 (b) 35 (c) 24 (d) 27
18. 18.A drawer has lots of green, 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) 3 (b) 6 (c) 4 (d) 2
19. 19.What is the mean of 2, 3, 5, 8 and 17? (a) 7 (b) 6 (c) 9 (d) 8
20. 20.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
21. 21.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
22. 22.What is the midpoint of the line joining (9, 9) and (19, 3)? (a) (28, 12) (b) (14, 6) (c) (6, 14) (d) (5, 3)
23. 23.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x + 1)(x + 12) (c) (x + 1)(x + 42) (d) (x − 6)(x − 7)
24. 24.What is the 34th term of the AP 10, 18, 26, 34, …? (a) 272 (b) 274 (c) 282 (d) 264
25. 25.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 65° (d) 155°
26. 26.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 45° (d) 90°
27. 27.If a + b = 13 and ab = 22, what is a² + b²? (a) 147 (b) 213 (c) 169 (d) 125
28. 28.If the radius of a circle 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
29. 29.Which term of the AP 11, 14, 17, 20, … is 35? (a) 9th (b) 10th (c) 8th (d) 11th
30. 30.In which quadrant does the point (−3, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 91 (d) 78
32. 32.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
33. 33.A bag has 5 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 16 (c) 7 (d) 2
34. 34.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
35. 35.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 100 (d) 90
36. 36.A bag has 12 yellow balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 22 (c) 13 (d) 14
37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 25 (d) 240
38. 38.What is the mean of 10, 5, 4, 3, 5 and 15? (a) 8 (b) 9 (c) 6 (d) 7
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
40. 40.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 21 (b) 22 (c) 20 (d) 19

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