Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 238 · 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 9 white balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 14 (c) 2 (d) 10
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
3. 3.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 15 (c) 7 (d) 14
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/18 (d) 1/12
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
7. 7.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 55° (b) 125° (c) 110° (d) 235°
8. 8.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 12 (d) 24
9. 9.How many prime numbers are there between 30 and 50? (a) 5 (b) 6 (c) 4 (d) 7
10. 10.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 165° (b) 60° (c) 15° (d) 135°
11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
12. 12.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 48 (d) 24
13. 13.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4
14. 14.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2³ × 3 × 7 (d) 2 × 3 × 7
15. 15.The mean of 5 numbers is 37. When the number 13 is added to them, what is the new mean? (a) 33 (b) 37 (c) 25 (d) 34
16. 16.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 25 sq cm (c) 150 sq cm (d) 125 sq cm
17. 17.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 10 (c) 90 (d) 33
18. 18.What is the smallest prime factor of 187? (a) 11 (b) 2 (c) 17 (d) 1
19. 19.In a class of 28 children, 10 like maths, 12 like science and 9 like neither. How many like both? (a) 19 (b) 3 (c) 4 (d) 9
20. 20.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 72 (c) 18 (d) 81
21. 21.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5041 (b) 5051 (c) 4761 (d) 4901
22. 22.What is the midpoint of the line joining (9, 3) and (19, 15)? (a) (9, 14) (b) (14, 9) (c) (5, 6) (d) (28, 18)
23. 23.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 55° (b) 95° (c) 140° (d) 125°
24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 7 (b) 8 (c) 5 (d) 6
25. 25.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3969 (b) 3249 (c) 3591 (d) 3259
26. 26.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
27. 27.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 36 (d) 15
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
30. 30.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
31. 31.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
32. 32.How many factors does 32 have? (a) 6 (b) 5 (c) 4 (d) 7
33. 33.What is the median of 39, 19, 3, 29, 38, 16 and 2? (a) 16 (b) 29 (c) 20 (d) 19
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/18 (c) 2/11 (d) 1/11
35. 35.Which is the correct factorisation of x² + 10x + 24? (a) (x + 4)(x + 6) (b) (x + 1)(x + 9) (c) (x + 1)(x + 24) (d) (x − 4)(x − 6)
36. 36.A bag has 10 yellow balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 4 (c) 2 (d) 13
37. 37.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
38. 38.What is the mode of 1, 3, 1, 3, 4, 3 and 11? (a) 11 (b) 3 (c) 4 (d) 1
39. 39.In a class of 31 children, 20 like cricket, 17 like football and 7 like both. How many like neither? (a) 8 (b) 7 (c) 2 (d) 1
40. 40.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3

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