Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 777 · 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 two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
2. 2.A drawer has lots of 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) 6 (b) 4 (c) 2 (d) 3
3. 3.How many prime numbers are there between 10 and 30? (a) 6 (b) 5 (c) 8 (d) 7
4. 4.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 64 (c) 56 (d) 28
5. 5.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 30° (c) 210° (d) 150°
6. 6.In a class of 25 children, 15 like tea, 8 like coffee and 2 like both. How many like only tea? (a) 13 (b) 15 (c) 17 (d) 6
7. 7.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 5° (c) 95° (d) 275°
8. 8.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
9. 9.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
10. 10.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 135° (c) 95° (d) 85°
11. 11.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
12. 12.In which quadrant does the point (−8, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
13. 13.What is the distance between the points (1, 12) and (10, 0)? (a) 21 (b) 16 (c) 15 (d) 225
14. 14.What is the midpoint of the line joining (10, 9) and (14, 15)? (a) (13, 12) (b) (24, 24) (c) (12, 12) (d) (2, 3)
15. 15.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
16. 16.What is the mode of 9, 13, 18, 7, 7, 7 and 18? (a) 18 (b) 9 (c) 13 (d) 7
17. 17.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2 × 3² × 7³
18. 18.What is the mean of 5, 8, 20, 15, 20 and 10? (a) 14 (b) 12 (c) 13 (d) 15
19. 19.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
20. 20.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 90° (d) 135°
21. 21.A bag has 4 yellow balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 10 (c) 2 (d) 5
22. 22.What is the prime factorisation of 14? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2 × 7
23. 23.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
24. 24.Which term of the AP 3, 11, 19, 27, … is 67? (a) 8th (b) 11th (c) 10th (d) 9th
25. 25.A bag has 7 white, 2 red and 2 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 4/11 (c) 8/11 (d) 7/11
26. 26.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 50° (c) 130° (d) 105°
27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 5 (c) 4 (d) 7
28. 28.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
29. 29.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
30. 30.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 496 (c) 1056 (d) 512
31. 31.Which term of the AP 15, 22, 29, 36, … is 197? (a) 29th (b) 27th (c) 26th (d) 28th
32. 32.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
33. 33.How many factors does 85 have? (a) 2 (b) 3 (c) 5 (d) 4
34. 34.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
35. 35.A drawer has lots of red, blue, white 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) 2 (b) 4 (c) 8 (d) 5
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/11 (c) 1/12 (d) 1/18
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
38. 38.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
39. 39.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 57 (d) 171
40. 40.The mean of 5 numbers is 23. When the number 17 is added to them, what is the new mean? (a) 22 (b) 21 (c) 23 (d) 20

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