Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 94 · 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.What is the midpoint of the line joining (2, 10) and (14, 4)? (a) (16, 14) (b) (7, 8) (c) (6, 3) (d) (8, 7)
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
3. 3.In a class of 37 children, 23 like mangoes, 7 like bananas and 3 like both. How many like at least one of the two? (a) 30 (b) 37 (c) 24 (d) 27
4. 4.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
5. 5.What is the smallest prime factor of 91? (a) 7 (b) 2 (c) 1 (d) 13
6. 6.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 30 (d) 36
7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
8. 8.How many prime numbers are there between 80 and 100? (a) 4 (b) 5 (c) 2 (d) 3
9. 9.Which term of the AP 14, 16, 18, 20, … is 56? (a) 23rd (b) 28th (c) 21st (d) 22nd
10. 10.What is the prime factorisation of 28? (a) 2 × 7² (b) 2 × 7 (c) 2³ × 7 (d) 2² × 7
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
12. 12.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 135° (c) 90° (d) 46°
13. 13.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 10° (d) 50°
14. 14.Which term of the AP 18, 25, 32, 39, … is 130? (a) 18th (b) 16th (c) 17th (d) 19th
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 16 (d) 6
16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
17. 17.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) 24 (b) 8 (c) 27 (d) 72
18. 18.In a class of 16 children, 8 like cricket, 12 like football and 5 like both. How many like at least one of the two? (a) 10 (b) 16 (c) 15 (d) 20
19. 19.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
20. 20.In a class of 33 children, 11 like maths, 26 like science and 7 like both. How many like neither? (a) 7 (b) 10 (c) 4 (d) 3
21. 21.In which quadrant does the point (−7, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
22. 22.What is the smallest prime factor of 155? (a) 31 (b) 1 (c) 2 (d) 5
23. 23.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 24 (c) 72 (d) 216
24. 24.What is the median of 31, 35, 27, 29, 19, 33 and 22? (a) 27 (b) 29 (c) 31 (d) 28
25. 25.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 150° (c) 30° (d) 60°
26. 26.What is the distance between the points (0, 6) and (4, 3)? (a) 5 (b) 25 (c) 7 (d) 6
27. 27.A drawer has lots of white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 4 (c) 3 (d) 5
28. 28.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 28 (d) 49
29. 29.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 382 (c) 326 (d) 381
30. 30.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) 8 (b) 15 (c) 7 (d) 14
31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 1
32. 32.What is the product of the roots of x² − 17x + 72 = 0? (a) 72 (b) 17 (c) 73 (d) 71
33. 33.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 170° (c) 11° (d) 10°
34. 34.In a class of 42 children, 25 like maths, 17 like science and 9 like both. How many like at least one of the two? (a) 42 (b) 34 (c) 24 (d) 33
35. 35.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 320° (c) 160° (d) 20°
36. 36.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
37. 37.How many factors does 30 have? (a) 8 (b) 9 (c) 6 (d) 7
38. 38.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9811 (b) 9801 (c) 10201 (d) 9999
39. 39.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
40. 40.If a + b = 15 and ab = 44, what is a² + b²? (a) 313 (b) 181 (c) 137 (d) 225

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