Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 589 · 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 factors does 96 have? (a) 10 (b) 11 (c) 12 (d) 13
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
4. 4.In a class of 30 children, 13 like maths, 17 like science and 6 like both. How many like only maths? (a) 13 (b) 11 (c) 7 (d) 6
5. 5.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 30° (d) 25°
6. 6.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
7. 7.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 110° (d) 155°
8. 8.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 165° (b) 15° (c) 100° (d) 95°
9. 9.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 12 (d) 7
10. 10.If a + b = 19 and ab = 90, what is a² + b²? (a) 361 (b) 271 (c) 541 (d) 181
11. 11.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 75° (b) 125° (c) 160° (d) 105°
12. 12.A bag has 8 red balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 9 (c) 11 (d) 4
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
14. 14.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 24 (c) 16 (d) 32
15. 15.How many factors does 62 have? (a) 3 (b) 4 (c) 2 (d) 5
16. 16.What is the distance between the points (2, 11) and (14, 6)? (a) 169 (b) 14 (c) 17 (d) 13
17. 17.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1653 (d) 1711
18. 18.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 2070 (c) 1036 (d) 1035
19. 19.A bag has 7 yellow balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 18 (b) 9 (c) 2 (d) 8
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/6 (c) 5/36 (d) 1/11
21. 21.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 121 (d) 22
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 5/36 (c) 1/9 (d) 1/11
23. 23.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 105 (d) 210
24. 24.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2 × 5 × 7³ (d) 2³ × 5 × 7
25. 25.A drawer has lots of black, yellow, blue, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 6 (c) 2 (d) 10
26. 26.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
27. 27.In which quadrant does the point (−5, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
28. 28.A bag has 3 blue balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 4 (b) 10 (c) 5 (d) 2
29. 29.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 30° (c) 105° (d) 210°
30. 30.What is the mean of 10, 4, 10, 6, 6 and 6? (a) 7 (b) 9 (c) 6 (d) 8
31. 31.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
32. 32.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 99 (c) 33 (d) 11
33. 33.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x − 3)(x − 9) (c) (x + 3)(x + 9) (d) (x + 1)(x + 11)
34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
35. 35.In a class of 40 children, 31 like maths, 14 like science and 6 like neither. How many like both? (a) 5 (b) 11 (c) 34 (d) 6
36. 36.If a + b = 9 and ab = 8, what is (a − b)²? (a) 7 (b) 65 (c) 81 (d) 49
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
38. 38.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3³ × 5 × 7
39. 39.A bag has 5 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 2 (c) 15 (d) 6
40. 40.In a class of 42 children, 16 like cricket, 25 like football and 10 like neither. How many like both? (a) 8 (b) 10 (c) 9 (d) 32

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