Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 776 · 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.What is the distance between the points (5, 6) and (20, 14)? (a) 17 (b) 18 (c) 23 (d) 289
2. 2.If a + b = 11 and ab = 28, what is (a − b)²? (a) 121 (b) 9 (c) 65 (d) 3
3. 3.In which quadrant does the point (5, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
4. 4.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 50° (d) 40°
5. 5.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 54 (b) 48 (c) 96 (d) 13
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 13 (c) 14 (d) 12
8. 8.A bag has 10 black 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) 13 (d) 2
9. 9.What is the distance between the points (0, 6) and (4, 9)? (a) 25 (b) 5 (c) 6 (d) 7
10. 10.Which term of the AP 13, 17, 21, 25, … is 129? (a) 29th (b) 31st (c) 30th (d) 32nd
11. 11.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 230° (c) 115° (d) 65°
12. 12.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 50° (c) 25° (d) 65°
13. 13.If a + b = 14 and ab = 33, what is a² + b²? (a) 262 (b) 163 (c) 196 (d) 130
14. 14.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 14 (b) 10 (c) 9 (d) 11
15. 15.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 100° (b) 80° (c) 155° (d) 105°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 240° (c) 60° (d) 120°
17. 17.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 40) (b) (x + 1)(x + 12) (c) (x − 5)(x − 8) (d) (x + 5)(x + 8)
18. 18.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 100° (b) 155° (c) 105° (d) 80°
19. 19.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) 20 (b) 8 (c) 32 (d) 16
20. 20.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
21. 21.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 16 (c) 144 (d) 51
22. 22.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 162 (d) 57
23. 23.Which term of the AP 18, 27, 36, 45, … is 198? (a) 21st (b) 22nd (c) 20th (d) 23rd
24. 24.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
26. 26.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
27. 27.In a class of 20 children, 8 like dance, 7 like music and 4 like both. How many like only dance? (a) 4 (b) 13 (c) 8 (d) 3
28. 28.What is the median of 8, 11, 39, 15 and 38? (a) 38 (b) 39 (c) 11 (d) 15
29. 29.In which quadrant does the point (−3, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
30. 30.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
31. 31.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 94 sq cm (b) 47 sq cm (c) 188 sq cm (d) 60 sq cm
32. 32.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
33. 33.3 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) 30 (b) 8 (c) 18 (d) 15
34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 17 (b) 15 (c) 16 (d) 6
35. 35.What are the roots of x² − 17x + 72 = 0? (a) 1 and 72 (b) 1 and 16 (c) 8 and 9 (d) 2 and 36
36. 36.How many factors does 31 have? (a) 4 (b) 1 (c) 2 (d) 3
37. 37.The mean of 7 numbers is 23. When the number 39 is added to them, what is the new mean? (a) 26 (b) 25 (c) 31 (d) 23
38. 38.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 8 (c) 18 (d) 12
39. 39.In which quadrant does the point (7, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
40. 40.What is the mean of 8, 14, 4, 5 and 4? (a) 8 (b) 6 (c) 7 (d) 9

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