Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 403 · 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 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 245° (d) 130°
2. 2.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 100° (d) 115°
3. 3.What is the prime factorisation of 21? (a) 3 × 7² (b) 3³ × 7 (c) 3 × 7 (d) 3² × 7
4. 4.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 144 (c) 48 (d) 16
5. 5.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
6. 6.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
8. 8.In which quadrant does the point (−3, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
9. 9.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 19 (b) 25 (c) 20 (d) 18
10. 10.A bag has 11 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 2 (c) 15 (d) 12
11. 11.A bag has 3 yellow, 3 blue and 2 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 3/4 (b) 5/8 (c) 3/8 (d) 1/3
12. 12.A drawer has lots of white, red, yellow, black 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) 10 (b) 5 (c) 6 (d) 2
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
14. 14.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
15. 15.How many factors does 96 have? (a) 11 (b) 10 (c) 12 (d) 13
16. 16.In a class of 36 children, 15 like tea, 23 like coffee and 3 like neither. How many like both? (a) 3 (b) 33 (c) 5 (d) 2
17. 17.A drawer has lots of blue 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) 5 (c) 3 (d) 4
18. 18.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
19. 19.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 150° (b) 100° (c) 110° (d) 30°
20. 20.What is the distance between the points (2, 3) and (10, 9)? (a) 14 (b) 100 (c) 10 (d) 11
21. 21.If a + b = 12 and ab = 20, what is (a − b)²? (a) 104 (b) 64 (c) 8 (d) 144
22. 22.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 16 (d) 28
23. 23.A bag has 4 white balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 16 (c) 5 (d) 6
24. 24.What is the product of the roots of x² − 9x + 18 = 0? (a) 19 (b) 17 (c) 9 (d) 18
25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 5 (b) 3 (c) 6 (d) 4
26. 26.A drawer has lots of red 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) 4 (b) 5 (c) 3 (d) 2
27. 27.What is the distance between the points (3, 10) and (6, 6)? (a) 25 (b) 7 (c) 6 (d) 5
28. 28.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) 4 (b) 3 (c) 2 (d) 5
29. 29.In a class of 25 children, 10 like dance, 15 like music and 6 like both. How many like at least one of the two? (a) 20 (b) 25 (c) 13 (d) 19
30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 21 (d) 19
31. 31.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
32. 32.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 95° (c) 115° (d) 150°
33. 33.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
34. 34.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3698 (c) 3655 (d) 7482
35. 35.Using (a − b)² = a² − 2ab + b², what is 98²? (a) 10404 (b) 9604 (c) 9996 (d) 9614
36. 36.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 70° (b) 110° (c) 250° (d) 125°
37. 37.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
38. 38.If a + b = 20 and ab = 99, what is (a − b)²? (a) 202 (b) 4 (c) 400 (d) 2
39. 39.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 11 (c) 35 (d) 60
40. 40.If a + b = 14 and ab = 48, what is (a − b)²? (a) 100 (b) 196 (c) 2 (d) 4

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