Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 964 · 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 (1, 18) and (11, 8)? (a) (5, 5) (b) (13, 6) (c) (12, 26) (d) (6, 13)
2. 2.A bag has 2 white, 6 yellow and 8 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 7/8 (b) 1/8 (c) 1/7 (d) 1/3
3. 3.A drawer has lots of red, black, green, blue and white 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
4. 4.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
5. 5.A drawer has lots of black, red, 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) 8 (c) 2 (d) 5
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
7. 7.In a class of 43 children, 16 like cricket, 29 like football and 9 like both. How many like only cricket? (a) 20 (b) 16 (c) 14 (d) 7
8. 8.A cuboid is 7 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 120 sq cm (b) 252 sq cm (c) 240 sq cm (d) 480 sq cm
9. 9.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
10. 10.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 1)(x + 6) (c) (x + 2)(x + 3) (d) (x + 1)(x + 4)
11. 11.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
12. 12.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 26 sq cm (b) 24 sq cm (c) 104 sq cm (d) 52 sq cm
13. 13.A drawer has lots of green, yellow, white, black and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
14. 14.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
15. 15.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 30° (d) 75°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
17. 17.A bag has 4 green balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 5 (b) 6 (c) 2 (d) 16
18. 18.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 355 (c) 308 (d) 354
19. 19.What is the midpoint of the line joining (0, 12) and (2, 8)? (a) (10, 1) (b) (2, 20) (c) (1, 10) (d) (1, 2)
20. 20.What is the mean of 4, 9, 8 and 19? (a) 10 (b) 11 (c) 8 (d) 9
21. 21.A drawer has lots of blue, green and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 6 (c) 4 (d) 2
22. 22.Which is the correct factorisation of x² + 9x + 14? (a) (x − 2)(x − 7) (b) (x + 2)(x + 7) (c) (x + 1)(x + 14) (d) (x + 1)(x + 8)
23. 23.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240
24. 24.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 6 (d) 5
25. 25.A bag has 5 red balls and 9 yellow 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) 6 (c) 14 (d) 10
26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
27. 27.What is the midpoint of the line joining (0, 0) and (4, 6)? (a) (4, 6) (b) (3, 2) (c) (3, 3) (d) (2, 3)
28. 28.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 276 (c) 288 (d) 600
29. 29.A drawer has lots of black and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 4 (d) 5
30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 529 (d) 45
31. 31.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
32. 32.A cuboid is 7 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 63 cu cm (b) 13 cu cm (c) 102 cu cm (d) 21 cu cm
33. 33.What is the midpoint of the line joining (3, 0) and (15, 10)? (a) (18, 10) (b) (6, 5) (c) (9, 5) (d) (5, 9)
34. 34.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 7931 (b) 7921 (c) 8099 (d) 8281
35. 35.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 11) (b) (x + 4)(x + 8) (c) (x + 1)(x + 32) (d) (x − 4)(x − 8)
36. 36.There are 4 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 16 (c) 6 (d) 8
37. 37.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 110° (b) 125° (c) 250° (d) 70°
38. 38.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 600 (c) 610 (d) 478
39. 39.How many factors does 75 have? (a) 4 (b) 6 (c) 7 (d) 5
40. 40.In a class of 45 children, 21 like maths, 28 like science and 9 like both. How many like at least one of the two? (a) 45 (b) 31 (c) 40 (d) 49

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