Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 610 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
3. 3.What is the midpoint of the line joining (6, 10) and (14, 14)? (a) (20, 24) (b) (12, 10) (c) (10, 12) (d) (4, 2)
4. 4.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
5. 5.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 305° (d) 125°
6. 6.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
7. 7.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) 8 (c) 7 (d) 15
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6
9. 9.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 49 (b) 13 (c) 84 (d) 42
10. 10.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 7)(x + 8) (c) (x − 7)(x − 8) (d) (x + 1)(x + 56)
11. 11.The mean of 9 numbers is 13. When the number 3 is added to them, what is the new mean? (a) 13 (b) 12 (c) 11 (d) 8
12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 5 (b) 2 (c) 3 (d) 4
13. 13.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 45) (b) (x + 1)(x + 13) (c) (x + 5)(x + 9) (d) (x − 5)(x − 9)
14. 14.How many prime numbers are there between 60 and 80? (a) 5 (b) 7 (c) 6 (d) 4
15. 15.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 18 (d) 6
16. 16.What is the 37th term of the AP 9, 11, 13, 15, …? (a) 74 (b) 72 (c) 81 (d) 83
17. 17.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 5 (d) 7
18. 18.If a + b = 13 and ab = 12, what is a² + b²? (a) 169 (b) 193 (c) 157 (d) 145
19. 19.What is the 35th term of the AP 9, 11, 13, 15, …? (a) 79 (b) 77 (c) 68 (d) 70
20. 20.What is the midpoint of the line joining (2, 4) and (8, 6)? (a) (3, 1) (b) (6, 5) (c) (5, 5) (d) (10, 10)
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 1/6 (c) 5/36 (d) 5/11
22. 22.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 310° (d) 130°
23. 23.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 64 cu cm (d) 96 cu cm
24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 14 (d) 3
25. 25.In a class of 49 children, 25 like cricket, 22 like football and 5 like both. How many like only cricket? (a) 25 (b) 17 (c) 27 (d) 20
26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 171 (d) 35
27. 27.If a + b = 19 and ab = 90, what is (a − b)²? (a) 271 (b) 181 (c) 361 (d) 1
28. 28.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7²
29. 29.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 49 sq cm (d) 294 sq cm
30. 30.What is the mode of 5, 4, 15, 5, 15, 15 and 2? (a) 2 (b) 5 (c) 4 (d) 15
31. 31.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 130° (d) 70°
32. 32.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
33. 33.In which quadrant does the point (3, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
34. 34.A bag has 9 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 10 (c) 15 (d) 11
35. 35.In a class of 32 children, 7 like mangoes, 18 like bananas and 3 like both. How many like neither? (a) 10 (b) 3 (c) 13 (d) 7
36. 36.A drawer has lots of white, yellow 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) 6 (b) 3 (c) 2 (d) 4
37. 37.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 8 (b) 9 (c) 10 (d) 13
38. 38.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
39. 39.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 150° (b) 55° (c) 125° (d) 155°
40. 40.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 35° (b) 105° (c) 110° (d) 145°

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