Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 363 · 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 28 have? (a) 6 (b) 5 (c) 7 (d) 4
2. 2.Which is the correct factorisation of x² + 9x + 14? (a) (x + 1)(x + 14) (b) (x + 2)(x + 7) (c) (x − 2)(x − 7) (d) (x + 1)(x + 8)
3. 3.What is the mode of 17, 8, 17, 8, 18, 17 and 2? (a) 17 (b) 8 (c) 18 (d) 2
4. 4.If a + b = 4 and ab = 3, what is (a − b)²? (a) 16 (b) 4 (c) 2 (d) 10
5. 5.What is the 19th term of the AP 3, 5, 7, 9, …? (a) 39 (b) 38 (c) 41 (d) 36
6. 6.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
7. 7.If a + b = 9 and ab = 8, what is (a − b)²? (a) 7 (b) 65 (c) 81 (d) 49
8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
9. 9.What is the 30th term of the AP 12, 21, 30, 39, …? (a) 282 (b) 273 (c) 270 (d) 261
10. 10.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 60° (d) 140°
11. 11.In which quadrant does the point (−1, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 1)(x + 12) (c) (x + 6)(x + 7) (d) (x − 6)(x − 7)
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
14. 14.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 4 (d) 2
15. 15.A bag has 8 yellow, 4 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 5/9 (b) 4/5 (c) 1/3 (d) 4/9
16. 16.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 105° (c) 70° (d) 110°
17. 17.A bag has 9 blue, 7 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/11 (b) 7/18 (c) 1/3 (d) 11/18
18. 18.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
19. 19.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2³ × 3 (c) 2⁵ × 3 (d) 2 × 3⁴
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
21. 21.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 63 (b) 12 (c) 126 (d) 64
22. 22.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 91 (d) 78
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
24. 24.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 21 (c) 63 (d) 189
25. 25.What is the distance between the points (8, 2) and (32, 9)? (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) 60° (b) 30° (c) 61° (d) 120°
27. 27.There are 5 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) 50 (b) 30 (c) 10 (d) 25
28. 28.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
29. 29.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 15 (d) 21
30. 30.In a class of 34 children, 26 like mangoes, 13 like bananas and 7 like both. How many like neither? (a) 3 (b) 7 (c) 9 (d) 2
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 5 (b) 7 (c) 4 (d) 6
32. 32.The mean of 8 numbers is 40. When the number 49 is added to them, what is the new mean? (a) 42 (b) 40 (c) 43 (d) 41
33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 16 (d) 17
34. 34.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
35. 35.What are the roots of x² − 11x + 30 = 0? (a) 1 and 10 (b) 1 and 30 (c) 2 and 15 (d) 5 and 6
36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
37. 37.A bag has 9 white, 3 green and 4 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 7/9 (c) 9/16 (d) 7/16
38. 38.If a + b = 19 and ab = 88, what is a² + b²? (a) 185 (b) 537 (c) 273 (d) 361
39. 39.The mean of 7 numbers is 13. When the number 5 is added to them, what is the new mean? (a) 9 (b) 13 (c) 11 (d) 12
40. 40.In a class of 48 children, 28 like cricket, 28 like football and 12 like both. How many like neither? (a) 4 (b) 5 (c) 16 (d) 12

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