Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 313 · 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.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
2. 2.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 51 (c) 48 (d) 16
3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 200 (c) 210 (d) 190
4. 4.A bag has 5 red, 3 blue and 5 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/13 (b) 9/13 (c) 8/13 (d) 1/3
5. 5.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 145° (b) 45° (c) 170° (d) 10°
6. 6.What is the distance between the points (5, 17) and (13, 2)? (a) 23 (b) 289 (c) 17 (d) 18
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 14 (b) 4 (c) 15 (d) 16
8. 8.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) 25 times (c) 10 times (d) 5 times
9. 9.A bag has 9 green balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 2 (c) 21 (d) 11
10. 10.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 21 (b) 22 (c) 19 (d) 20
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
12. 12.A bag has 12 yellow 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) 6 (c) 17 (d) 13
13. 13.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 110° (c) 71° (d) 70°
14. 14.How many factors does 76 have? (a) 5 (b) 6 (c) 7 (d) 4
15. 15.What is the 22nd term of the AP 10, 13, 16, 19, …? (a) 66 (b) 76 (c) 73 (d) 63
16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 4 (d) 7
17. 17.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 70° (d) 110°
18. 18.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 145° (c) 120° (d) 155°
19. 19.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 25° (b) 55° (c) 150° (d) 155°
20. 20.What is the smallest prime factor of 57? (a) 2 (b) 1 (c) 3 (d) 19
21. 21.How many factors does 120 have? (a) 15 (b) 14 (c) 17 (d) 16
22. 22.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 20° (c) 10° (d) 11°
23. 23.What is the product of the roots of x² − 15x + 56 = 0? (a) 57 (b) 15 (c) 56 (d) 55
24. 24.How many prime numbers are there between 70 and 80? (a) 3 (b) 5 (c) 2 (d) 4
25. 25.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 376 (b) 41 (c) 208 (d) 188
26. 26.What is the product of the roots of x² − 16x + 63 = 0? (a) 16 (b) 64 (c) 62 (d) 63
27. 27.A bag has 4 green balls and 3 black 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) 5 (c) 7 (d) 2
28. 28.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 90 (d) 30
29. 29.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 95° (b) 145° (c) 120° (d) 85°
30. 30.If a + b = 21 and ab = 108, what is (a − b)²? (a) 441 (b) 3 (c) 225 (d) 9
31. 31.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2⁴ × 3² × 7
32. 32.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 80° (c) 200° (d) 20°
33. 33.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 2 (d) 3
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
35. 35.A drawer has lots of blue, black, green, 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) 10 (b) 5 (c) 6 (d) 2
36. 36.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
37. 37.What is the mean of 8, 19, 13, 17 and 8? (a) 12 (b) 15 (c) 14 (d) 13
38. 38.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
39. 39.What is the midpoint of the line joining (5, 9) and (11, 19)? (a) (16, 28) (b) (8, 14) (c) (14, 8) (d) (3, 5)
40. 40.What is the mean of 19, 12, 14, 3 and 12? (a) 10 (b) 15 (c) 12 (d) 13

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