Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 380 · 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.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
2. 2.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
3. 3.A bag has 5 blue balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 17 (b) 7 (c) 6 (d) 2
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
5. 5.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 180 (c) 189 (d) 190
6. 6.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 310° (d) 130°
7. 7.What are the roots of x² − 13x + 36 = 0? (a) 1 and 12 (b) 4 and 9 (c) 2 and 18 (d) 1 and 36
8. 8.What is the mode of 20, 13, 15, 20, 3, 20 and 15? (a) 15 (b) 3 (c) 13 (d) 20
9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 5 (c) 17 (d) 15
10. 10.What is the 39th term of the AP 12, 15, 18, 21, …? (a) 117 (b) 114 (c) 129 (d) 126
11. 11.In a class of 32 children, 19 like mangoes, 20 like bananas and 5 like neither. How many like both? (a) 5 (b) 12 (c) 27 (d) 7
12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
13. 13.In a class of 39 children, 17 like dance, 25 like music and 6 like both. How many like at least one of the two? (a) 30 (b) 42 (c) 39 (d) 36
14. 14.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 352 (c) 36 (d) 176
15. 15.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 9 (d) 3
16. 16.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
17. 17.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 18 (c) 6 (d) 54
18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
19. 19.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
20. 20.In a class of 23 children, 15 like cricket, 9 like football and 3 like both. How many like at least one of the two? (a) 23 (b) 18 (c) 24 (d) 21
21. 21.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2 × 5 × 7³
22. 22.What is the midpoint of the line joining (0, 11) and (10, 3)? (a) (5, 4) (b) (10, 14) (c) (5, 7) (d) (7, 5)
23. 23.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 8 (b) 7 (c) 9 (d) 12
24. 24.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 18 (c) 9 (d) 21
25. 25.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 70° (b) 150° (c) 110° (d) 140°
26. 26.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
27. 27.What is the smallest prime factor of 209? (a) 2 (b) 11 (c) 1 (d) 19
28. 28.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 216 (c) 222 (d) 226
29. 29.If a + b = 5 and ab = 4, what is (a − b)²? (a) 3 (b) 9 (c) 25 (d) 17
30. 30.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
31. 31.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 150° (d) 115°
32. 32.Which term of the AP 10, 12, 14, 16, … is 68? (a) 34th (b) 29th (c) 30th (d) 31st
33. 33.In which quadrant does the point (7, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
34. 34.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
35. 35.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
37. 37.What is the distance between the points (1, 2) and (10, 14)? (a) 21 (b) 16 (c) 15 (d) 225
38. 38.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 903 (c) 946 (d) 1892
39. 39.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 70 (c) 130 (d) 65
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad