Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 37 · 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 smallest prime factor of 143? (a) 2 (b) 13 (c) 1 (d) 11
2. 2.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
3. 3.What is the midpoint of the line joining (10, 15) and (14, 3)? (a) (9, 12) (b) (12, 9) (c) (24, 18) (d) (2, 6)
4. 4.In a class of 36 children, 25 like maths, 19 like science and 10 like both. How many like only maths? (a) 17 (b) 25 (c) 15 (d) 9
5. 5.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
6. 6.A bag has 9 red, 2 blue and 2 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/11 (b) 1/3 (c) 2/13 (d) 11/13
7. 7.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
8. 8.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 80° (c) 81° (d) 160°
9. 9.The mean of 9 numbers is 22. When the number 2 is added to them, what is the new mean? (a) 12 (b) 22 (c) 20 (d) 21
10. 10.In a class of 41 children, 18 like cricket, 24 like football and 5 like both. How many like neither? (a) 9 (b) 5 (c) 4 (d) 3
11. 11.Which is the correct factorisation of x² + 13x + 40? (a) (x + 5)(x + 8) (b) (x − 5)(x − 8) (c) (x + 1)(x + 12) (d) (x + 1)(x + 40)
12. 12.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
14. 14.In a class of 38 children, 20 like dance, 19 like music and 2 like neither. How many like both? (a) 1 (b) 3 (c) 2 (d) 36
15. 15.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2² × 3² (c) 2³ × 3² (d) 2⁴ × 3²
16. 16.A bag has 8 green balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 9 (c) 10 (d) 2
17. 17.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 246 (b) 33 (c) 123 (d) 138
18. 18.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 7921 (b) 8281 (c) 8101 (d) 8291
19. 19.Which is the correct factorisation of x² + 14x + 48? (a) (x − 6)(x − 8) (b) (x + 1)(x + 48) (c) (x + 1)(x + 13) (d) (x + 6)(x + 8)
20. 20.What is the distance between the points (6, 1) and (11, 13)? (a) 13 (b) 169 (c) 17 (d) 14
21. 21.What is the mean of 6, 14, 11, 19, 6 and 4? (a) 11 (b) 9 (c) 12 (d) 10
22. 22.If a + b = 17 and ab = 66, what is a² + b²? (a) 289 (b) 223 (c) 421 (d) 157
23. 23.A bag has 8 blue, 7 red and 3 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/9 (b) 1/3 (c) 4/5 (d) 4/9
24. 24.What is the 39th term of the AP 1, 4, 7, 10, …? (a) 118 (b) 115 (c) 117 (d) 114
25. 25.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 16 (d) 48
26. 26.What are the roots of x² − 15x + 54 = 0? (a) 2 and 27 (b) 1 and 14 (c) 1 and 54 (d) 6 and 9
27. 27.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 12 (d) 48
28. 28.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
29. 29.A bag has 7 yellow balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 8 (b) 2 (c) 16 (d) 9
30. 30.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 49 (d) 14
31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 20 (d) 240
32. 32.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 155° (c) 150° (d) 55°
33. 33.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2 × 3⁴ (c) 2⁴ × 3 (d) 2⁵ × 3
34. 34.What is the mode of 10, 7, 10, 7, 14, 11 and 7? (a) 7 (b) 14 (c) 10 (d) 11
35. 35.A bag has 4 black balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 11 (c) 5 (d) 8
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
38. 38.How many prime numbers are there between 50 and 70? (a) 4 (b) 6 (c) 3 (d) 5
39. 39.What is the distance between the points (8, 4) and (14, 12)? (a) 10 (b) 11 (c) 14 (d) 100
40. 40.In a class of 44 children, 28 like tea, 19 like coffee and 7 like neither. How many like both? (a) 10 (b) 7 (c) 37 (d) 3

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