Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 675 · 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.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
2. 2.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 66 (d) 144
3. 3.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 5/6 (d) 1/4
4. 4.What is the sum of the roots of x² − 13x + 36 = 0? (a) 13 (b) 14 (c) 36 (d) 12
5. 5.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
6. 6.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
7. 7.How many prime numbers are there between 10 and 40? (a) 7 (b) 8 (c) 10 (d) 9
8. 8.What is the 29th term of the AP 8, 10, 12, 14, …? (a) 58 (b) 66 (c) 64 (d) 56
9. 9.What is the median of 24, 16, 21, 1 and 4? (a) 4 (b) 17 (c) 21 (d) 16
10. 10.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 45° (c) 140° (d) 135°
11. 11.What is the mode of 4, 2, 19, 14, 19, 14 and 14? (a) 4 (b) 2 (c) 19 (d) 14
12. 12.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 205° (d) 26°
13. 13.What is the distance between the points (7, 5) and (15, 11)? (a) 10 (b) 11 (c) 14 (d) 100
14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
15. 15.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7 (c) 2³ × 7 (d) 2 × 7²
16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
17. 17.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 24 (c) 25 (d) 37
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
19. 19.What is the 32nd term of the AP 2, 5, 8, 11, …? (a) 98 (b) 93 (c) 96 (d) 95
20. 20.What is the median of 31, 37, 35, 29, 25, 9 and 11? (a) 31 (b) 25 (c) 30 (d) 29
21. 21.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 150° (d) 115°
22. 22.What is the sum of the roots of x² − 11x + 18 = 0? (a) 18 (b) 10 (c) 11 (d) 12
23. 23.What is the 22nd term of the AP 1, 5, 9, 13, …? (a) 85 (b) 84 (c) 88 (d) 89
24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 20 (d) 9
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
26. 26.What is the mean of 12, 6, 13, 13 and 11? (a) 13 (b) 10 (c) 12 (d) 11
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
28. 28.The mean of 8 numbers is 27. When the number 45 is added to them, what is the new mean? (a) 27 (b) 36 (c) 29 (d) 30
29. 29.In which quadrant does the point (−3, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
30. 30.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 50° (d) 130°
31. 31.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 25 (d) 20
32. 32.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5051 (b) 4761 (c) 4901 (d) 5041
33. 33.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 36 (c) 48 (d) 37
34. 34.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
35. 35.What is the sum of the roots of x² − 13x + 40 = 0? (a) 14 (b) 13 (c) 12 (d) 40
36. 36.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 160° (b) 155° (c) 45° (d) 135°
37. 37.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/8 (c) 3/4 (d) 1/4
38. 38.If a + b = 12 and ab = 35, what is (a − b)²? (a) 2 (b) 74 (c) 144 (d) 4
39. 39.What are the roots of x² − 12x + 32 = 0? (a) 1 and 11 (b) 2 and 16 (c) 1 and 32 (d) 4 and 8
40. 40.If a + b = 15 and ab = 56, what is (a − b)²? (a) 169 (b) 113 (c) 225 (d) 1

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