Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 697 · 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.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6734 (b) 6404 (c) 6084 (d) 6724
2. 2.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3² × 5 × 7
3. 3.What is the mode of 20, 5, 2, 17, 17, 20 and 17? (a) 20 (b) 5 (c) 2 (d) 17
4. 4.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) 11 (c) 33 (d) 99
5. 5.A bag has 3 yellow balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 15 (b) 4 (c) 2 (d) 5
6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
7. 7.A drawer has lots of blue, yellow, 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) 8 (c) 2 (d) 5
8. 8.4 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) 12 (b) 16 (c) 6 (d) 8
9. 9.If a + b = 13 and ab = 40, what is (a − b)²? (a) 169 (b) 89 (c) 3 (d) 9
10. 10.A bag has 2 white, 4 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 8/9 (c) 2/9 (d) 7/9
11. 11.In which quadrant does the point (−2, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
12. 12.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
13. 13.In a class of 33 children, 20 like cricket, 16 like football and 9 like both. How many like only cricket? (a) 11 (b) 20 (c) 7 (d) 17
14. 14.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
15. 15.In a class of 45 children, 21 like mangoes, 18 like bananas and 3 like both. How many like only mangoes? (a) 18 (b) 21 (c) 15 (d) 27
16. 16.A bag has 10 blue balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 12 (c) 16 (d) 11
17. 17.What is the midpoint of the line joining (4, 5) and (12, 7)? (a) (16, 12) (b) (6, 8) (c) (8, 6) (d) (4, 1)
18. 18.In a class of 25 children, 15 like dance, 17 like music and 12 like both. How many like only dance? (a) 5 (b) 3 (c) 8 (d) 15
19. 19.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 702 (d) 351
21. 21.What is the mean of 9, 10, 3, 17, 16 and 11? (a) 13 (b) 12 (c) 11 (d) 10
22. 22.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 4 (d) 2
23. 23.A bag has 5 black balls and 11 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) 16 (c) 6 (d) 12
24. 24.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 75° (d) 50°
25. 25.What is the distance between the points (9, 8) and (17, 2)? (a) 10 (b) 14 (c) 100 (d) 11
26. 26.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 30° (d) 75°
27. 27.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 11) (b) (x − 5)(x − 7) (c) (x + 1)(x + 35) (d) (x + 5)(x + 7)
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
29. 29.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 4 (b) 2 (c) 5 (d) 3
30. 30.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
31. 31.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2601 (b) 2499 (c) 2411 (d) 2401
32. 32.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
34. 34.In a class of 33 children, 25 like dance, 14 like music and 8 like both. How many like only dance? (a) 6 (b) 19 (c) 17 (d) 25
35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 15 (d) 16
37. 37.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 589 (c) 588 (d) 579
38. 38.What is the mean of 2, 19, 18, 18, 7 and 20? (a) 14 (b) 12 (c) 15 (d) 13
39. 39.What are the roots of x² − 17x + 72 = 0? (a) 1 and 72 (b) 8 and 9 (c) 1 and 16 (d) 2 and 36
40. 40.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 100° (d) 80°

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