Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 189 · 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.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 1)(x + 30) (c) (x + 5)(x + 6) (d) (x + 1)(x + 10)
2. 2.In a class of 33 children, 23 like mangoes, 12 like bananas and 7 like both. How many like neither? (a) 7 (b) 12 (c) 6 (d) 5
3. 3.Using (a − b)² = a² − 2ab + b², what is 85²? (a) 7235 (b) 8075 (c) 7225 (d) 9025
4. 4.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) 37 (b) 36 (c) 25 (d) 24
5. 5.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 145° (b) 75° (c) 110° (d) 105°
6. 6.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
7. 7.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 65° (c) 25° (d) 115°
8. 8.In a class of 41 children, 23 like maths, 18 like science and 3 like both. How many like neither? (a) 4 (b) 6 (c) 3 (d) 0
9. 9.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) 8 times (c) 4 times (d) 2 times
10. 10.In a class of 32 children, 14 like dance, 15 like music and 10 like neither. How many like both? (a) 22 (b) 8 (c) 7 (d) 10
11. 11.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 36 (d) 11
12. 12.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 180 cu cm (d) 17 cu cm
13. 13.In which quadrant does the point (3, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
14. 14.In a class of 35 children, 20 like maths, 13 like science and 7 like both. How many like only maths? (a) 6 (b) 22 (c) 13 (d) 20
15. 15.In which quadrant does the point (2, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
16. 16.The mean of 4 numbers is 26. When the number 31 is added to them, what is the new mean? (a) 28 (b) 29 (c) 27 (d) 26
17. 17.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
18. 18.What is the 15th term of the AP 13, 15, 17, 19, …? (a) 30 (b) 41 (c) 43 (d) 28
19. 19.What is the mean of 8, 11, 2 and 7? (a) 9 (b) 8 (c) 7 (d) 6
20. 20.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 155° (b) 110° (c) 95° (d) 85°
21. 21.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 17 (b) 5 (c) 15 (d) 16
23. 23.In a class of 45 children, 21 like maths, 21 like science and 5 like both. How many like at least one of the two? (a) 45 (b) 37 (c) 42 (d) 32
24. 24.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 28 (c) 10 (d) 21
25. 25.In a class of 21 children, 11 like cricket, 8 like football and 6 like neither. How many like both? (a) 15 (b) 4 (c) 5 (d) 6
26. 26.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 266 (b) 384 (c) 256 (d) 576
27. 27.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 165° (b) 15° (c) 50° (d) 145°
28. 28.What is the 38th term of the AP 11, 15, 19, 23, …? (a) 163 (b) 152 (c) 148 (d) 159
29. 29.What is the mean of 3, 2, 3 and 20? (a) 9 (b) 7 (c) 8 (d) 6
30. 30.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 23 (d) 69
31. 31.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 961 (b) 899 (c) 851 (d) 841
32. 32.What is the distance between the points (3, 1) and (12, 13)? (a) 21 (b) 225 (c) 15 (d) 16
33. 33.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 30 (d) 12
34. 34.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
35. 35.What is the midpoint of the line joining (1, 5) and (7, 1)? (a) (3, 4) (b) (8, 6) (c) (4, 3) (d) (3, 2)
36. 36.In which quadrant does the point (−2, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.In a class of 21 children, 15 like cricket, 11 like football and 8 like both. How many like neither? (a) 8 (b) 3 (c) 11 (d) 4
38. 38.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 210 (d) 105
39. 39.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2 × 3 × 7³ (d) 2³ × 3 × 7
40. 40.Using (a − b)² = a² − 2ab + b², what is 58²? (a) 3596 (b) 3374 (c) 3844 (d) 3364

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