Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 508 · 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.A bag has 12 white balls and 6 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) 18 (c) 13 (d) 7
2. 2.Which term of the AP 9, 18, 27, 36, … is 108? (a) 13th (b) 12th (c) 14th (d) 11th
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
4. 4.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
5. 5.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 7 (c) 8 (d) 15
6. 6.If a + b = 14 and ab = 33, what is a² + b²? (a) 262 (b) 196 (c) 163 (d) 130
7. 7.What is the 29th term of the AP 19, 28, 37, 46, …? (a) 252 (b) 261 (c) 271 (d) 280
8. 8.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 39 (b) 38 (c) 46 (d) 40
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 7/36 (d) 1/11
10. 10.A drawer has lots of blue 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) 2 (c) 3 (d) 5
11. 11.What is the sum of the roots of x² − 15x + 56 = 0? (a) 56 (b) 14 (c) 15 (d) 16
12. 12.In a class of 39 children, 26 like cricket, 17 like football and 10 like both. How many like at least one of the two? (a) 39 (b) 33 (c) 43 (d) 23
13. 13.A bag has 10 black balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 16 (c) 2 (d) 7
14. 14.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
15. 15.In a class of 56 children, 27 like maths, 30 like science and 10 like both. How many like neither? (a) 8 (b) 9 (c) 19 (d) 10
16. 16.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 30 (b) 228 (c) 240 (d) 456
17. 17.How many factors does 103 have? (a) 1 (b) 3 (c) 4 (d) 2
18. 18.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 6 (b) 5 (c) 4 (d) 8
19. 19.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x + 1)(x + 42) (c) (x − 6)(x − 7) (d) (x + 6)(x + 7)
20. 20.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7³
21. 21.In a class of 35 children, 18 like cricket, 17 like football and 3 like neither. How many like both? (a) 32 (b) 2 (c) 4 (d) 3
22. 22.In a class of 45 children, 27 like tea, 21 like coffee and 9 like both. How many like at least one of the two? (a) 30 (b) 45 (c) 39 (d) 48
23. 23.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
24. 24.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 130° (d) 75°
25. 25.What is the mode of 17, 18, 14, 18, 17, 17 and 4? (a) 14 (b) 17 (c) 4 (d) 18
26. 26.In a class of 33 children, 12 like dance, 19 like music and 4 like both. How many like neither? (a) 4 (b) 2 (c) 10 (d) 6
27. 27.A bag has 10 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) 4 (b) 11 (c) 13 (d) 2
28. 28.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
29. 29.How many factors does 74 have? (a) 2 (b) 4 (c) 5 (d) 3
30. 30.In a class of 33 children, 18 like dance, 23 like music and 3 like neither. How many like both? (a) 11 (b) 3 (c) 30 (d) 8
31. 31.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 70 (b) 42 (c) 35 (d) 12
32. 32.How many prime numbers are there between 70 and 90? (a) 5 (b) 6 (c) 7 (d) 4
33. 33.What is the smallest prime factor of 145? (a) 29 (b) 1 (c) 5 (d) 2
34. 34.A bag has 3 red balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 4 (c) 11 (d) 2
35. 35.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 59° (c) 61° (d) 60°
36. 36.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 324 (b) 484 (c) 494 (d) 404
37. 37.A drawer has lots of green 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) 4 (b) 2 (c) 3 (d) 5
38. 38.In which quadrant does the point (4, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
39. 39.In a class of 31 children, 22 like maths, 17 like science and 11 like both. How many like only maths? (a) 11 (b) 14 (c) 6 (d) 22
40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5

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