Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 217 · 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 canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 56 (c) 14 (d) 96
2. 2.What is the mode of 17, 3, 17, 8, 13, 13 and 17? (a) 8 (b) 13 (c) 17 (d) 3
3. 3.A bag has 12 blue balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 13 (d) 20
4. 4.What is the mean of 5, 8, 2, 4 and 6? (a) 6 (b) 5 (c) 4 (d) 7
5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
6. 6.In a class of 25 children, 7 like maths, 12 like science and 4 like both. How many like neither? (a) 4 (b) 6 (c) 14 (d) 10
7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 6 (c) 7 (d) 5
8. 8.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 23 (c) 75 (d) 150
9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 11 (b) 10 (c) 8 (d) 5
10. 10.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 150° (b) 145° (c) 30° (d) 65°
11. 11.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 36 sq cm (d) 9 sq cm
12. 12.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
15. 15.What is the median of 24, 5, 39, 16, 31, 3 and 29? (a) 24 (b) 16 (c) 29 (d) 21
16. 16.In a class of 39 children, 17 like maths, 18 like science and 4 like both. How many like only maths? (a) 14 (b) 17 (c) 13 (d) 21
17. 17.What is the midpoint of the line joining (3, 10) and (7, 18)? (a) (10, 28) (b) (2, 4) (c) (14, 5) (d) (5, 14)
18. 18.If a + b = 19 and ab = 90, what is (a − b)²? (a) 361 (b) 271 (c) 181 (d) 1
19. 19.Which term of the AP 4, 10, 16, 22, … is 88? (a) 15th (b) 17th (c) 16th (d) 14th
20. 20.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 130° (b) 50° (c) 230° (d) 115°
21. 21.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 6 (b) 9 (c) 8 (d) 7
22. 22.A bag has 5 green balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 11 (d) 7
23. 23.In a class of 32 children, 9 like tea, 16 like coffee and 3 like both. How many like at least one of the two? (a) 22 (b) 32 (c) 25 (d) 19
24. 24.A bag has 3 white, 2 yellow and 5 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/2 (b) 1/10 (c) 3/5 (d) 1/3
25. 25.A bag has 8 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 2 (c) 9 (d) 10
26. 26.In a class of 43 children, 16 like mangoes, 32 like bananas and 7 like neither. How many like both? (a) 12 (b) 36 (c) 7 (d) 5
27. 27.If a + b = 17 and ab = 70, what is a² + b²? (a) 289 (b) 219 (c) 429 (d) 149
28. 28.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 3 (d) 5
29. 29.In which quadrant does the point (8, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
30. 30.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 115° (b) 135° (c) 110° (d) 70°
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 8 (b) 7 (c) 9 (d) 6
32. 32.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 37 (c) 36 (d) 24
33. 33.What is the median of 24, 19, 26, 3, 9, 40 and 5? (a) 3 (b) 18 (c) 19 (d) 24
34. 34.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 72 (c) 27 (d) 8
35. 35.Which is the correct factorisation of x² + 14x + 48? (a) (x + 6)(x + 8) (b) (x + 1)(x + 48) (c) (x − 6)(x − 8) (d) (x + 1)(x + 13)
36. 36.What is the median of 7, 1, 22, 19, 5, 16 and 3? (a) 19 (b) 16 (c) 5 (d) 7
37. 37.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 526 (c) 516 (d) 525
38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
39. 39.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 180 (c) 162 (d) 172
40. 40.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12

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