Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 519 · 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.In a class of 31 children, 21 like maths, 15 like science and 11 like both. How many like only maths? (a) 10 (b) 21 (c) 4 (d) 16
2. 2.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
3. 3.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 20° (c) 40° (d) 140°
4. 4.How many factors does 79 have? (a) 1 (b) 3 (c) 4 (d) 2
5. 5.How many factors does 116 have? (a) 6 (b) 5 (c) 7 (d) 4
6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
7. 7.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 7 (c) 6 (d) 5
8. 8.A bag has 12 green balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 2 (c) 13 (d) 7
9. 9.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 54 (d) 153
10. 10.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
11. 11.In which quadrant does the point (−2, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
12. 12.What is the midpoint of the line joining (4, 6) and (6, 16)? (a) (5, 11) (b) (10, 22) (c) (11, 5) (d) (1, 5)
13. 13.A drawer has lots of black 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) 4 (b) 3 (c) 2 (d) 5
14. 14.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 60° (b) 30° (c) 210° (d) 150°
15. 15.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 20 (d) 120
16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
17. 17.If a + b = 16 and ab = 55, what is a² + b²? (a) 256 (b) 366 (c) 201 (d) 146
18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 18 (d) 17
19. 19.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
20. 20.In a class of 23 children, 9 like dance, 7 like music and 3 like both. How many like only dance? (a) 6 (b) 4 (c) 16 (d) 9
21. 21.A bag has 3 black balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 4 (b) 5 (c) 2 (d) 9
22. 22.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
23. 23.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 12 (b) 13 (c) 14 (d) 20
24. 24.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
25. 25.In a class of 22 children, 9 like mangoes, 14 like bananas and 1 like neither. How many like both? (a) 1 (b) 21 (c) 3 (d) 2
26. 26.What is the smallest prime factor of 69? (a) 3 (b) 2 (c) 1 (d) 23
27. 27.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 5486 (b) 5476 (c) 4916 (d) 4356
28. 28.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 70° (d) 35°
29. 29.If a + b = 19 and ab = 90, what is (a − b)²? (a) 181 (b) 361 (c) 271 (d) 1
30. 30.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/11 (c) 5/36 (d) 1/6
32. 32.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 130° (b) 145° (c) 35° (d) 85°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 21° (c) 40° (d) 20°
34. 34.6 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) 24 (c) 8 (d) 18
35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
36. 36.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 7744 (b) 8464 (c) 8474 (d) 8104
37. 37.What is the distance between the points (8, 2) and (17, 14)? (a) 225 (b) 15 (c) 21 (d) 16
38. 38.What is the mean of 10, 8, 10, 7, 9 and 16? (a) 9 (b) 11 (c) 10 (d) 12
39. 39.What is the mode of 17, 17, 4, 20, 14, 4 and 17? (a) 4 (b) 14 (c) 17 (d) 20
40. 40.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 22 (d) 15

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