Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 369 · 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.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 676 (b) 1166 (c) 916 (d) 1156
2. 2.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 66 (d) 24
3. 3.In a class of 23 children, 9 like maths, 13 like science and 4 like both. How many like neither? (a) 5 (b) 1 (c) 4 (d) 9
4. 4.What is the smallest prime factor of 49? (a) 1 (b) 2 (c) 3 (d) 7
5. 5.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
6. 6.In a class of 25 children, 13 like maths, 14 like science and 7 like both. How many like neither? (a) 6 (b) 5 (c) 12 (d) 7
7. 7.What is the product of the roots of x² − 10x + 24 = 0? (a) 25 (b) 23 (c) 10 (d) 24
8. 8.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 115° (d) 120°
9. 9.What is the median of 32, 30, 34, 23, 20, 39 and 17? (a) 23 (b) 32 (c) 30 (d) 31
10. 10.In a class of 43 children, 20 like tea, 21 like coffee and 8 like neither. How many like both? (a) 6 (b) 8 (c) 35 (d) 7
11. 11.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
12. 12.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 190 (c) 191 (d) 380
13. 13.A bag has 6 yellow balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 2 (c) 8 (d) 7
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
15. 15.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
16. 16.What is the mean of 2, 9, 12, 5, 15 and 5? (a) 8 (b) 10 (c) 9 (d) 7
17. 17.In which quadrant does the point (4, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
18. 18.How many factors does 96 have? (a) 12 (b) 11 (c) 13 (d) 10
19. 19.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
20. 20.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 64 (d) 28
21. 21.A bag has 12 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 16 (b) 14 (c) 2 (d) 13
22. 22.How many factors does 77 have? (a) 2 (b) 4 (c) 5 (d) 3
23. 23.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
24. 24.A bag has 9 red, 9 yellow and 9 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 10/27 (b) 2/3 (c) 1/3 (d) 1/2
25. 25.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 280° (c) 10° (d) 80°
26. 26.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) 26° (c) 205° (d) 155°
27. 27.What is the prime factorisation of 252? (a) 2³ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
28. 28.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 30° (c) 210° (d) 150°
29. 29.What is the prime factorisation of 56? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7³ (d) 2⁴ × 7
30. 30.A bag has 12 red balls and 3 green 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) 13 (c) 4 (d) 15
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
32. 32.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 9 (d) 27
33. 33.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 296 (b) 29 (c) 148 (d) 160
34. 34.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 50° (d) 130°
35. 35.What is the 38th term of the AP 15, 18, 21, 24, …? (a) 114 (b) 111 (c) 129 (d) 126
36. 36.What is the midpoint of the line joining (5, 8) and (9, 18)? (a) (14, 26) (b) (7, 13) (c) (2, 5) (d) (13, 7)
37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
38. 38.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
39. 39.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
40. 40.A bag has 4 green balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 2 (c) 6 (d) 5

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