Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 792 · 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 missing term in the AP 16, ?, 32, 40, 48? (a) 23 (b) 24 (c) 25 (d) 32
2. 2.There are 4 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 24 (c) 20 (d) 40
3. 3.In a class of 32 children, 15 like maths, 25 like science and 9 like both. How many like neither? (a) 1 (b) 10 (c) 2 (d) 9
4. 4.What is the mean of 3, 8, 17, 8, 8 and 16? (a) 9 (b) 10 (c) 11 (d) 12
5. 5.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
6. 6.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/4 (c) 7/8 (d) 1/8
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
8. 8.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 1 (d) 11
9. 9.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 120° (d) 145°
10. 10.A bag has 3 yellow, 2 blue and 2 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 2/7 (b) 1/3 (c) 5/7 (d) 6/7
11. 11.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 155° (d) 125°
12. 12.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 130° (b) 125° (c) 55° (d) 105°
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
14. 14.A bag has 12 white balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 23 (b) 14 (c) 13 (d) 2
15. 15.What is the midpoint of the line joining (3, 14) and (13, 6)? (a) (10, 8) (b) (5, 4) (c) (16, 20) (d) (8, 10)
16. 16.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 16 (d) 28
17. 17.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
18. 18.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3⁴
19. 19.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 85° (d) 170°
20. 20.What is the midpoint of the line joining (4, 1) and (10, 11)? (a) (3, 5) (b) (14, 12) (c) (6, 7) (d) (7, 6)
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
22. 22.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 24 (d) 144
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 3/11 (d) 1/12
24. 24.What is the distance between the points (4, 20) and (9, 8)? (a) 169 (b) 17 (c) 13 (d) 14
25. 25.What is the distance between the points (0, 8) and (12, 24)? (a) 400 (b) 21 (c) 28 (d) 20
26. 26.What is the mode of 13, 15, 7, 8, 15, 15 and 8? (a) 15 (b) 7 (c) 8 (d) 13
27. 27.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
28. 28.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 420 (d) 210
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/36 (d) 1/11
31. 31.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3969 (b) 3591 (c) 3249 (d) 3259
32. 32.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
33. 33.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 20° (c) 40° (d) 160°
34. 34.What are the roots of x² − 14x + 45 = 0? (a) 3 and 15 (b) 5 and 9 (c) 1 and 13 (d) 1 and 45
35. 35.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
36. 36.What is the midpoint of the line joining (2, 2) and (10, 10)? (a) (12, 12) (b) (6, 6) (c) (4, 4) (d) (7, 6)
37. 37.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 45 (c) 72 (d) 81
38. 38.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
39. 39.Which is the correct factorisation of x² + 12x + 32? (a) (x + 4)(x + 8) (b) (x − 4)(x − 8) (c) (x + 1)(x + 32) (d) (x + 1)(x + 11)
40. 40.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 75° (c) 150° (d) 105°

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