Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 99 · 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.A bag has 8 red, 5 blue and 3 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/11 (b) 11/16 (c) 5/16 (d) 1/3
2. 2.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
3. 3.A bag has 3 green balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 4 (b) 11 (c) 2 (d) 5
4. 4.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 100 sq cm (c) 25 sq cm (d) 125 sq cm
5. 5.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
6. 6.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 150° (d) 145°
7. 7.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
8. 8.What is the mean of 20, 16, 20, 4 and 5? (a) 14 (b) 15 (c) 12 (d) 13
9. 9.How many prime numbers are there between 10 and 40? (a) 8 (b) 7 (c) 9 (d) 10
10. 10.In a class of 25 children, 13 like maths, 12 like science and 4 like both. How many like at least one of the two? (a) 22 (b) 17 (c) 25 (d) 21
11. 11.In a class of 18 children, 11 like dance, 11 like music and 2 like neither. How many like both? (a) 2 (b) 4 (c) 6 (d) 16
12. 12.What is the midpoint of the line joining (9, 8) and (15, 14)? (a) (11, 12) (b) (3, 3) (c) (24, 22) (d) (12, 11)
13. 13.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 3 (d) 1
14. 14.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 40° (d) 70°
15. 15.In which quadrant does the point (−5, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
16. 16.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 145° (c) 80° (d) 100°
17. 17.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
18. 18.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 80° (c) 135° (d) 100°
19. 19.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 115° (d) 50°
20. 20.What is the prime factorisation of 20? (a) 2 × 5² (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5
21. 21.A bag has 5 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 6 (c) 10 (d) 2
22. 22.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
23. 23.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 1225 (b) 2025 (c) 2035 (d) 1625
24. 24.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 85° (c) 86° (d) 95°
25. 25.If a + b = 14 and ab = 45, what is a² + b²? (a) 286 (b) 106 (c) 196 (d) 151
26. 26.A bag has 3 yellow balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 2 (c) 5 (d) 4
27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
28. 28.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
30. 30.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 363 (c) 396 (d) 726
31. 31.Which is the correct factorisation of x² + 9x + 18? (a) (x + 1)(x + 18) (b) (x + 1)(x + 8) (c) (x − 3)(x − 6) (d) (x + 3)(x + 6)
32. 32.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 10° (b) 110° (c) 80° (d) 170°
33. 33.What is the distance between the points (1, 2) and (10, 14)? (a) 16 (b) 225 (c) 15 (d) 21
34. 34.What is the midpoint of the line joining (4, 10) and (16, 14)? (a) (20, 24) (b) (10, 12) (c) (6, 2) (d) (12, 10)
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
36. 36.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 32 (b) 8 (c) 16 (d) 20
37. 37.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
38. 38.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 160° (b) 50° (c) 70° (d) 130°
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 14 (b) 16 (c) 4 (d) 15

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