Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 92 · 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 factors does 62 have? (a) 5 (b) 3 (c) 2 (d) 4
2. 2.What is the sum of the roots of x² − 13x + 40 = 0? (a) 12 (b) 13 (c) 40 (d) 14
3. 3.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
4. 4.What is the 17th term of the AP 16, 19, 22, 25, …? (a) 67 (b) 48 (c) 51 (d) 64
5. 5.How many factors does 107 have? (a) 1 (b) 4 (c) 3 (d) 2
6. 6.How many factors does 22 have? (a) 5 (b) 2 (c) 3 (d) 4
7. 7.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 315° (c) 136° (d) 135°
8. 8.What is the median of 11, 31, 32, 21 and 33? (a) 30 (b) 31 (c) 32 (d) 21
9. 9.The mean of 3 numbers is 24. When the number 36 is added to them, what is the new mean? (a) 28 (b) 30 (c) 27 (d) 24
10. 10.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 94 (c) 93 (d) 84
11. 11.What is the midpoint of the line joining (2, 4) and (4, 2)? (a) (6, 6) (b) (4, 3) (c) (3, 3) (d) (1, 1)
12. 12.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) 36 (c) 108 (d) 12
13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
14. 14.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
15. 15.How many factors does 115 have? (a) 4 (b) 3 (c) 5 (d) 2
16. 16.The mean of 7 numbers is 31. When the number 39 is added to them, what is the new mean? (a) 33 (b) 32 (c) 35 (d) 31
17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 13 (d) 14
18. 18.If a + b = 8 and ab = 12, what is (a − b)²? (a) 64 (b) 4 (c) 40 (d) 16
19. 19.How many factors does 27 have? (a) 3 (b) 4 (c) 2 (d) 5
20. 20.In a class of 33 children, 22 like tea, 18 like coffee and 2 like neither. How many like both? (a) 31 (b) 7 (c) 2 (d) 9
21. 21.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
22. 22.Which is the correct factorisation of x² + 11x + 28? (a) (x − 4)(x − 7) (b) (x + 1)(x + 28) (c) (x + 1)(x + 10) (d) (x + 4)(x + 7)
23. 23.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 12 (c) 24 (d) 16
24. 24.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 8 (c) 15 (d) 18
25. 25.If a + b = 18 and ab = 80, what is a² + b²? (a) 484 (b) 324 (c) 244 (d) 164
26. 26.Which term of the AP 2, 4, 6, 8, … is 48? (a) 26th (b) 24th (c) 23rd (d) 25th
27. 27.What is the 18th term of the AP 7, 15, 23, 31, …? (a) 151 (b) 136 (c) 144 (d) 143
28. 28.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
29. 29.What is the prime factorisation of 28? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
30. 30.In which quadrant does the point (−6, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
31. 31.In a class of 37 children, 31 like cricket, 17 like football and 1 like neither. How many like both? (a) 11 (b) 36 (c) 1 (d) 12
32. 32.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 70 (c) 12 (d) 35
33. 33.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 27 (c) 9 (d) 30
34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
35. 35.What is the mode of 4, 4, 2, 2, 17, 15 and 2? (a) 4 (b) 15 (c) 17 (d) 2
36. 36.How many prime numbers are there between 30 and 60? (a) 9 (b) 6 (c) 7 (d) 8
37. 37.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 65 (c) 60 (d) 120
38. 38.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) 36 (b) 37 (c) 25 (d) 24
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
40. 40.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4771 (b) 5041 (c) 4899 (d) 4761

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