Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 183 · 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 book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 28 (c) 37 (d) 46
2. 2.What is the midpoint of the line joining (8, 1) and (16, 3)? (a) (4, 1) (b) (2, 12) (c) (24, 4) (d) (12, 2)
3. 3.What is the mean of 19, 20, 20 and 13? (a) 24 (b) 18 (c) 19 (d) 17
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
5. 5.In a class of 20 children, 11 like tea, 12 like coffee and 8 like both. How many like only tea? (a) 3 (b) 8 (c) 4 (d) 11
6. 6.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
8. 8.A bag has 12 white balls and 6 blue 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) 7 (d) 18
9. 9.What is the 17th term of the AP 1, 8, 15, 22, …? (a) 119 (b) 112 (c) 113 (d) 120
10. 10.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
11. 11.In which quadrant does the point (7, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
13. 13.In a class of 24 children, 6 like tea, 17 like coffee and 2 like both. How many like at least one of the two? (a) 23 (b) 21 (c) 24 (d) 19
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
15. 15.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 25 (c) 12 (d) 24
16. 16.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 12 (c) 36 (d) 108
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
18. 18.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
19. 19.What is the mean of 17, 17, 17, 19, 8 and 6? (a) 14 (b) 12 (c) 13 (d) 15
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 19 (c) 9 (d) 20
21. 21.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 135°
22. 22.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 142 (c) 150 (d) 141
23. 23.What is the mean of 12, 5, 5, 3, 3 and 2? (a) 7 (b) 5 (c) 4 (d) 6
24. 24.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 9 (c) 6 (d) 12
25. 25.What is the sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 16 (c) 15 (d) 17
26. 26.A drawer has lots of black, green, red, blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 10 (c) 6 (d) 5
27. 27.What is the sum of the roots of x² − 11x + 28 = 0? (a) 12 (b) 28 (c) 10 (d) 11
28. 28.In a class of 25 children, 15 like maths, 13 like science and 6 like both. How many like only maths? (a) 9 (b) 12 (c) 15 (d) 7
29. 29.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
30. 30.How many prime numbers are there between 90 and 120? (a) 6 (b) 7 (c) 5 (d) 8
31. 31.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 140 (b) 26 (c) 70 (d) 85
32. 32.What is the smallest prime factor of 35? (a) 5 (b) 2 (c) 1 (d) 7
33. 33.The mean of 6 numbers is 22. When the number 43 is added to them, what is the new mean? (a) 25 (b) 26 (c) 22 (d) 24
34. 34.A drawer has lots of blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 2 (d) 3
35. 35.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 60° (b) 40° (c) 160° (d) 140°
36. 36.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
38. 38.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 170° (b) 150° (c) 10° (d) 40°
39. 39.What is the median of 30, 11, 17, 34 and 23? (a) 23 (b) 17 (c) 24 (d) 30
40. 40.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4

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