Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 747 · 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.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 8125 (b) 9035 (c) 7225 (d) 9025
2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
3. 3.The mean of 3 numbers is 24. When the number 36 is added to them, what is the new mean? (a) 24 (b) 28 (c) 27 (d) 30
4. 4.What is the 40th term of the AP 7, 15, 23, 31, …? (a) 320 (b) 319 (c) 312 (d) 327
5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 20 (d) 8
6. 6.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
7. 7.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2557 (c) 2485 (d) 5112
8. 8.What is the 10th term of the AP 13, 19, 25, 31, …? (a) 60 (b) 54 (c) 67 (d) 73
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
10. 10.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
12. 12.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
13. 13.What is the midpoint of the line joining (6, 6) and (18, 8)? (a) (12, 7) (b) (24, 14) (c) (6, 1) (d) (7, 12)
14. 14.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 210° (b) 150° (c) 30° (d) 105°
15. 15.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
16. 16.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 7 (d) 27
17. 17.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 160 (c) 159 (d) 150
18. 18.A bag has 8 green balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 9 (c) 10 (d) 14
19. 19.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 682 (b) 56 (c) 346 (d) 341
20. 20.What is the distance between the points (4, 4) and (13, 16)? (a) 16 (b) 21 (c) 225 (d) 15
21. 21.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 11 (c) 99 (d) 33
22. 22.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
23. 23.A bag has 7 blue balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 18 (d) 12
24. 24.What is the mode of 19, 18, 5, 14, 14, 5 and 14? (a) 14 (b) 18 (c) 5 (d) 19
25. 25.What is the 34th term of the AP 8, 12, 16, 20, …? (a) 136 (b) 132 (c) 144 (d) 140
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 17 (d) 16
27. 27.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 48 (d) 12
28. 28.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
29. 29.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 150° (b) 120° (c) 60° (d) 300°
30. 30.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 18 (b) 19 (c) 25 (d) 20
31. 31.What is the product of the roots of x² − 17x + 72 = 0? (a) 72 (b) 71 (c) 17 (d) 73
32. 32.What is the midpoint of the line joining (7, 0) and (15, 8)? (a) (11, 4) (b) (4, 4) (c) (22, 8) (d) (4, 11)
33. 33.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 29 (d) 22
34. 34.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
35. 35.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
36. 36.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
37. 37.What is the mode of 4, 13, 20, 20, 17, 20 and 4? (a) 4 (b) 13 (c) 20 (d) 17
38. 38.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 8 (d) 10
39. 39.In a class of 42 children, 19 like maths, 21 like science and 6 like both. How many like neither? (a) 2 (b) 14 (c) 6 (d) 8
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm

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