Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 928 · 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.In a class of 19 children, 10 like tea, 11 like coffee and 4 like both. How many like only tea? (a) 8 (b) 7 (c) 10 (d) 6
2. 2.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 4 (c) 324 (d) 16
3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/11 (c) 1/18 (d) 1/12
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 1/12 (c) 2/11 (d) 1/11
6. 6.The mean of 3 numbers is 17. When the number 25 is added to them, what is the new mean? (a) 20 (b) 19 (c) 21 (d) 17
7. 7.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
9. 9.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 42 (c) 70 (d) 12
10. 10.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 10° (d) 160°
11. 11.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
12. 12.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2³ × 3² × 7
13. 13.A bag has 6 blue balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 13 (c) 8 (d) 2
14. 14.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 80° (c) 100° (d) 20°
15. 15.A bag has 11 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 18 (b) 12 (c) 13 (d) 2
16. 16.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 18 (c) 72 (d) 16
17. 17.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 139 (c) 130 (d) 148
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
19. 19.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
20. 20.What is the distance between the points (9, 24) and (21, 8)? (a) 400 (b) 21 (c) 28 (d) 20
21. 21.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 327 (c) 290 (d) 318
22. 22.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 511 (b) 510 (c) 412 (d) 501
23. 23.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) 25 (b) 13 (c) 24 (d) 12
24. 24.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
25. 25.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 31 (b) 38 (c) 29 (d) 30
26. 26.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 385 (b) 770 (c) 60 (d) 390
27. 27.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 16 (b) 132 (c) 126 (d) 252
28. 28.How many factors does 41 have? (a) 1 (b) 4 (c) 2 (d) 3
29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 14 (d) 12
30. 30.Which term of the AP 8, 10, 12, 14, … is 70? (a) 31st (b) 32nd (c) 33rd (d) 35th
31. 31.If the radius of a circle 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
32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
33. 33.How many prime numbers are there between 90 and 110? (a) 4 (b) 7 (c) 5 (d) 6
34. 34.9 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
35. 35.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 100 (d) 20
36. 36.What is the median of 35, 30, 17, 11, 39, 31 and 19? (a) 31 (b) 30 (c) 26 (d) 11
37. 37.What is the distance between the points (3, 11) and (6, 7)? (a) 7 (b) 6 (c) 5 (d) 25
38. 38.In a class of 25 children, 18 like dance, 7 like music and 2 like both. How many like only dance? (a) 5 (b) 2 (c) 16 (d) 18
39. 39.What is the 17th term of the AP 18, 21, 24, 27, …? (a) 48 (b) 69 (c) 66 (d) 51
40. 40.A bag has 2 red, 5 green and 8 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/15 (b) 13/15 (c) 2/13 (d) 1/3

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