Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 187 · 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.If a + b = 10 and ab = 16, what is a² + b²? (a) 132 (b) 84 (c) 100 (d) 68
2. 2.There are 5 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) 20 (b) 7 (c) 15 (d) 10
3. 3.How many factors does 24 have? (a) 8 (b) 7 (c) 6 (d) 9
4. 4.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 240 (d) 20
5. 5.What is the 22nd term of the AP 20, 22, 24, 26, …? (a) 42 (b) 64 (c) 44 (d) 62
6. 6.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
7. 7.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
9. 9.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
10. 10.A drawer has lots of black, yellow, red 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) 5 (b) 2 (c) 4 (d) 8
11. 11.What is the mode of 7, 6, 3, 7, 6, 16 and 7? (a) 3 (b) 7 (c) 6 (d) 16
12. 12.How many factors does 106 have? (a) 2 (b) 4 (c) 3 (d) 5
13. 13.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 7 (d) 5
14. 14.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 1166 (b) 916 (c) 676 (d) 1156
15. 15.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
16. 16.How many factors does 116 have? (a) 4 (b) 5 (c) 7 (d) 6
17. 17.How many factors does 40 have? (a) 7 (b) 6 (c) 9 (d) 8
18. 18.A bag has 3 green balls and 5 black 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) 4 (c) 8 (d) 6
19. 19.What is the 18th term of the AP 2, 7, 12, 17, …? (a) 85 (b) 87 (c) 92 (d) 90
20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
21. 21.What is the distance between the points (7, 6) and (11, 3)? (a) 7 (b) 6 (c) 25 (d) 5
22. 22.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
23. 23.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
24. 24.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 539 (b) 289 (c) 529 (d) 409
25. 25.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 899 (b) 851 (c) 961 (d) 841
26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 20
27. 27.Which is the correct factorisation of x² + 9x + 14? (a) (x + 1)(x + 14) (b) (x − 2)(x − 7) (c) (x + 1)(x + 8) (d) (x + 2)(x + 7)
28. 28.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
29. 29.A bag has 4 yellow balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 6 (c) 9 (d) 2
30. 30.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
31. 31.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁵ × 3
32. 32.In a class of 21 children, 9 like maths, 9 like science and 2 like both. How many like at least one of the two? (a) 18 (b) 14 (c) 16 (d) 21
33. 33.A drawer has lots of green, 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) 4 (c) 6 (d) 3
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
35. 35.What is the smallest prime factor of 95? (a) 1 (b) 5 (c) 19 (d) 2
36. 36.A cuboid is 8 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 288 sq cm (b) 576 sq cm (c) 320 sq cm (d) 144 sq cm
37. 37.A drawer has lots of 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) 2 (b) 5 (c) 3 (d) 4
38. 38.What is the product of the roots of x² − 15x + 56 = 0? (a) 56 (b) 15 (c) 55 (d) 57
39. 39.In which quadrant does the point (9, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
40. 40.What is the median of 5, 27, 34, 16 and 17? (a) 27 (b) 16 (c) 17 (d) 34

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