Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 258 · 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.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 110° (d) 140°
2. 2.Using (a − b)² = a² − 2ab + b², what is 66²? (a) 4366 (b) 5476 (c) 4356 (d) 4884
3. 3.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 15° (b) 165° (c) 35° (d) 160°
4. 4.What is the distance between the points (2, 10) and (26, 3)? (a) 25 (b) 31 (c) 625 (d) 26
5. 5.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 280° (d) 140°
6. 6.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 91° (b) 135° (c) 270° (d) 90°
7. 7.In which quadrant does the point (−9, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
8. 8.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 36 (d) 12
9. 9.A drawer has lots of red, blue, green, white and black 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) 10 (c) 5 (d) 6
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
11. 11.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) 22 (b) 15 (c) 14 (d) 21
12. 12.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 15 (c) 56 (d) 14
13. 13.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 140° (d) 40°
14. 14.A drawer has lots of blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 2 (d) 5
15. 15.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 196 (b) 350 (c) 175 (d) 43
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
17. 17.A drawer has lots of red, black, yellow, 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) 6 (c) 5 (d) 10
18. 18.In a class of 33 children, 17 like cricket, 13 like football and 9 like neither. How many like both? (a) 24 (b) 9 (c) 7 (d) 6
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
20. 20.The mean of 3 numbers is 38. When the number 22 is added to them, what is the new mean? (a) 34 (b) 38 (c) 35 (d) 30
21. 21.What is the 24th term of the AP 5, 10, 15, 20, …? (a) 120 (b) 125 (c) 115 (d) 121
22. 22.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
23. 23.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 75° (c) 145° (d) 105°
24. 24.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
25. 25.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 172 (c) 181 (d) 190
26. 26.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 7/8 (c) 1/4 (d) 3/8
27. 27.How many factors does 29 have? (a) 3 (b) 4 (c) 2 (d) 1
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
29. 29.If a + b = 10 and ab = 24, what is (a − b)²? (a) 4 (b) 2 (c) 52 (d) 100
30. 30.In a class of 48 children, 29 like cricket, 30 like football and 12 like both. How many like only cricket? (a) 17 (b) 18 (c) 12 (d) 29
31. 31.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 15 (d) 45
32. 32.How many factors does 51 have? (a) 4 (b) 2 (c) 5 (d) 3
33. 33.A cuboid is 7 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 242 cu cm (b) 210 cu cm (c) 21 cu cm (d) 20 cu cm
34. 34.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 65° (c) 245° (d) 115°
35. 35.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
36. 36.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 4 (d) 3
37. 37.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
38. 38.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
39. 39.What is the mode of 14, 20, 17, 20, 2, 17 and 20? (a) 17 (b) 20 (c) 14 (d) 2
40. 40.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 523 (b) 513 (c) 420 (d) 522

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