Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 434 · 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.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
2. 2.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 25 (d) 20
3. 3.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
4. 4.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 28 (c) 9 (d) 21
5. 5.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
6. 6.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 50°
7. 7.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 18 (d) 45
8. 8.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
9. 9.What is the midpoint of the line joining (1, 16) and (3, 6)? (a) (2, 11) (b) (11, 2) (c) (1, 5) (d) (4, 22)
10. 10.A bag has 3 yellow balls and 4 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) 2 (c) 4 (d) 5
11. 11.How many prime numbers are there between 30 and 40? (a) 2 (b) 3 (c) 1 (d) 4
12. 12.What are the roots of x² − 7x + 10 = 0? (a) 3 and 4 (b) 1 and 10 (c) 2 and 5 (d) 1 and 6
13. 13.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 32 (b) 8 (c) 16 (d) 20
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
16. 16.What is the distance between the points (8, 8) and (20, 24)? (a) 21 (b) 400 (c) 20 (d) 28
17. 17.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 465 (c) 456 (d) 382
18. 18.In a class of 42 children, 26 like tea, 16 like coffee and 8 like both. How many like neither? (a) 16 (b) 8 (c) 9 (d) 0
19. 19.What is the distance between the points (4, 3) and (13, 15)? (a) 16 (b) 21 (c) 225 (d) 15
20. 20.In a class of 33 children, 21 like tea, 19 like coffee and 9 like both. How many like neither? (a) 2 (b) 9 (c) 3 (d) 11
21. 21.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 280 (c) 303 (d) 313
22. 22.In a class of 32 children, 19 like maths, 11 like science and 6 like neither. How many like both? (a) 26 (b) 5 (c) 6 (d) 4
23. 23.In a class of 42 children, 24 like tea, 20 like coffee and 10 like both. How many like at least one of the two? (a) 42 (b) 24 (c) 34 (d) 44
24. 24.In a class of 33 children, 18 like cricket, 21 like football and 9 like both. How many like only cricket? (a) 18 (b) 12 (c) 10 (d) 9
25. 25.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) 9 (b) 12 (c) 18 (d) 6
26. 26.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
27. 27.In a class of 25 children, 9 like dance, 16 like music and 3 like both. How many like neither? (a) 6 (b) 3 (c) 4 (d) 0
28. 28.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 81 (c) 36 (d) 45
29. 29.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 36° (d) 145°
30. 30.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
31. 31.What is the distance between the points (8, 9) and (20, 0)? (a) 15 (b) 16 (c) 21 (d) 225
32. 32.A bag has 3 white balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 13 (d) 4
33. 33.What is the midpoint of the line joining (7, 0) and (15, 12)? (a) (22, 12) (b) (11, 6) (c) (4, 6) (d) (6, 11)
34. 34.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
35. 35.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 30° (d) 120°
36. 36.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 20 (d) 120
37. 37.A bag has 3 blue balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 4 (c) 5 (d) 2
38. 38.A bag has 6 white balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 13 (c) 8 (d) 7
39. 39.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 315 (c) 316 (d) 306
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 16 (d) 17

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