Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 960 · 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.The mean of 4 numbers is 18. When the number 38 is added to them, what is the new mean? (a) 18 (b) 23 (c) 22 (d) 28
2. 2.In which quadrant does the point (7, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
3. 3.How many factors does 27 have? (a) 2 (b) 3 (c) 5 (d) 4
4. 4.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
5. 5.What is the product of the roots of x² − 10x + 24 = 0? (a) 25 (b) 10 (c) 23 (d) 24
6. 6.A bag has 5 yellow, 7 blue and 6 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 5/18 (c) 5/13 (d) 13/18
7. 7.There are 8 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) 56 (b) 64 (c) 112 (d) 15
8. 8.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 48 (d) 12
9. 9.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 55 (b) 15 (c) 60 (d) 110
10. 10.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 300° (c) 30° (d) 120°
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
12. 12.Which is the correct factorisation of x² + 13x + 40? (a) (x + 5)(x + 8) (b) (x + 1)(x + 12) (c) (x − 5)(x − 8) (d) (x + 1)(x + 40)
13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 15
14. 14.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
15. 15.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 29 (c) 21 (d) 28
16. 16.In a class of 23 children, 15 like maths, 13 like science and 9 like both. How many like at least one of the two? (a) 19 (b) 23 (c) 28 (d) 10
17. 17.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
18. 18.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
19. 19.How many factors does 38 have? (a) 5 (b) 3 (c) 4 (d) 2
20. 20.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2⁴ × 5 (c) 2² × 5 (d) 2 × 5³
21. 21.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 72 (c) 73 (d) 17
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
23. 23.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) 54 (b) 57 (c) 162 (d) 18
24. 24.Which term of the AP 3, 6, 9, 12, … is 108? (a) 37th (b) 36th (c) 35th (d) 38th
25. 25.How many prime numbers are there between 40 and 70? (a) 7 (b) 9 (c) 8 (d) 6
26. 26.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 72 (c) 24 (d) 27
27. 27.Using (a − b)² = a² − 2ab + b², what is 55²? (a) 3575 (b) 4225 (c) 3035 (d) 3025
28. 28.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 33 (b) 27 (c) 25 (d) 26
29. 29.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
30. 30.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
31. 31.In a class of 39 children, 15 like maths, 19 like science and 2 like both. How many like only maths? (a) 15 (b) 17 (c) 13 (d) 20
32. 32.What is the median of 19, 3, 30, 24 and 6? (a) 24 (b) 6 (c) 19 (d) 30
33. 33.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 135° (d) 45°
34. 34.A bag has 5 white, 6 green and 6 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 12/17 (b) 1/3 (c) 5/12 (d) 5/17
35. 35.A bag has 2 green, 8 red and 8 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 11/18 (c) 5/9 (d) 4/9
36. 36.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
38. 38.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 325 (d) 650
39. 39.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
40. 40.A bag has 10 red balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 12 (b) 2 (c) 11 (d) 22

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