Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 861 · 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.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
2. 2.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
4. 4.In a class of 42 children, 19 like maths, 26 like science and 6 like both. How many like only maths? (a) 13 (b) 20 (c) 19 (d) 16
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
6. 6.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
7. 7.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x − 7)(x − 9) (c) (x + 1)(x + 15) (d) (x + 7)(x + 9)
8. 8.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 215° (c) 36° (d) 35°
9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 4 (b) 5 (c) 3 (d) 6
10. 10.A bag has 8 white balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 10 (c) 11 (d) 2
11. 11.If a + b = 13 and ab = 42, what is (a − b)²? (a) 127 (b) 1 (c) 169 (d) 85
12. 12.What is the midpoint of the line joining (1, 5) and (9, 7)? (a) (5, 6) (b) (6, 5) (c) (4, 1) (d) (10, 12)
13. 13.What is the distance between the points (6, 20) and (14, 5)? (a) 289 (b) 23 (c) 17 (d) 18
14. 14.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 66 (c) 21 (d) 63
15. 15.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 10 (c) 7 (d) 20
16. 16.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) 15 (b) 7 (c) 14 (d) 8
17. 17.What is the mode of 16, 17, 19, 4, 17, 19 and 17? (a) 16 (b) 17 (c) 19 (d) 4
18. 18.What is the product of the roots of x² − 15x + 54 = 0? (a) 53 (b) 55 (c) 54 (d) 15
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
20. 20.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
21. 21.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 145° (c) 35° (d) 65°
22. 22.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 168 (c) 150 (d) 159
23. 23.What are the roots of x² − 13x + 36 = 0? (a) 1 and 36 (b) 2 and 18 (c) 4 and 9 (d) 1 and 12
24. 24.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7 (c) 2³ × 7 (d) 2 × 7²
25. 25.How many factors does 43 have? (a) 2 (b) 3 (c) 4 (d) 1
26. 26.A drawer has lots of yellow, black, 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) 8 (d) 4
27. 27.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
28. 28.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 1/4 (c) 5/8 (d) 3/8
29. 29.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 13 (b) 12 (c) 11 (d) 14
30. 30.In a class of 34 children, 25 like maths, 14 like science and 6 like both. How many like only maths? (a) 25 (b) 20 (c) 19 (d) 8
31. 31.How many prime numbers are there between 70 and 90? (a) 4 (b) 6 (c) 5 (d) 7
32. 32.A bag has 11 black balls and 3 blue 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) 2 (c) 14 (d) 12
33. 33.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 30 (d) 27
34. 34.What is the mean of 7, 5, 14 and 6? (a) 10 (b) 7 (c) 9 (d) 8
35. 35.What is the mean of 6, 18, 14 and 14? (a) 15 (b) 12 (c) 14 (d) 13
36. 36.What is the median of 10, 37, 4, 39, 17, 1 and 2? (a) 17 (b) 4 (c) 39 (d) 10
37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 5 (b) 2 (c) 4 (d) 3
38. 38.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 145° (d) 36°
39. 39.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 1/6 (d) 7/36

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