Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 716 · 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.If a + b = 21 and ab = 108, what is (a − b)²? (a) 225 (b) 441 (c) 9 (d) 3
2. 2.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 14 (c) 8 (d) 7
3. 3.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 70° (d) 110°
4. 4.Which term of the AP 2, 7, 12, 17, … is 112? (a) 25th (b) 23rd (c) 22nd (d) 24th
5. 5.In a class of 38 children, 20 like dance, 14 like music and 2 like both. How many like neither? (a) 6 (b) 8 (c) 2 (d) 4
6. 6.What is the 20th term of the AP 4, 11, 18, 25, …? (a) 137 (b) 140 (c) 133 (d) 144
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
9. 9.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 100 (b) 26 (c) 180 (d) 90
10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
11. 11.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 35° (d) 145°
12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 3 (d) 4
13. 13.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
14. 14.Which is the correct factorisation of x² + 13x + 36? (a) (x + 4)(x + 9) (b) (x + 1)(x + 12) (c) (x − 4)(x − 9) (d) (x + 1)(x + 36)
15. 15.What is the median of 15, 23, 13, 17, 34, 4 and 32? (a) 23 (b) 18 (c) 17 (d) 15
16. 16.In which quadrant does the point (8, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
18. 18.The mean of 8 numbers is 40. When the number 31 is added to them, what is the new mean? (a) 38 (b) 41 (c) 39 (d) 40
19. 19.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 125° (d) 305°
20. 20.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
21. 21.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 11 (d) 25
22. 22.A bag has 11 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 13 (c) 14 (d) 2
23. 23.What is the product of the roots of x² − 5x + 6 = 0? (a) 7 (b) 6 (c) 8 (d) 5
24. 24.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 42 (c) 72 (d) 36
25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
26. 26.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 60° (d) 30°
27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
28. 28.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 3 (d) 0
29. 29.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 265° (d) 86°
30. 30.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
31. 31.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 170°
32. 32.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2² × 3⁴ (c) 2⁴ × 3² (d) 2⁵ × 3²
33. 33.What is the median of 4, 30, 40, 12, 19, 33 and 5? (a) 30 (b) 19 (c) 12 (d) 20
34. 34.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
35. 35.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
36. 36.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
37. 37.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
38. 38.Which term of the AP 1, 7, 13, 19, … is 73? (a) 14th (b) 12th (c) 15th (d) 13th
39. 39.What is the sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 16 (c) 15 (d) 17
40. 40.A bag has 3 yellow balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 4 (b) 2 (c) 5 (d) 10

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