Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 603 · 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 distance between the points (3, 16) and (11, 1)? (a) 23 (b) 289 (c) 18 (d) 17
2. 2.A bag has 9 red balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 10 (c) 2 (d) 19
3. 3.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 10° (c) 100° (d) 80°
4. 4.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 85° (d) 265°
5. 5.A bag has 12 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 5 (d) 16
6. 6.A cuboid is 9 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 45 cu cm (b) 135 cu cm (c) 174 cu cm (d) 17 cu cm
7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
8. 8.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
9. 9.What is the product of the roots of x² − 16x + 63 = 0? (a) 64 (b) 63 (c) 16 (d) 62
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 5/36 (c) 1/11 (d) 1/6
11. 11.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 633 (c) 500 (d) 642
12. 12.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 3/4 (d) 1/2
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
14. 14.Which term of the AP 5, 10, 15, 20, … is 100? (a) 19th (b) 22nd (c) 20th (d) 21st
15. 15.In a class of 37 children, 16 like dance, 25 like music and 6 like both. How many like at least one of the two? (a) 41 (b) 37 (c) 35 (d) 29
16. 16.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 351 (c) 342 (d) 306
17. 17.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 264 (b) 22 (c) 132 (d) 143
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
19. 19.What is the 27th term of the AP 16, 18, 20, 22, …? (a) 54 (b) 52 (c) 68 (d) 70
20. 20.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 17 (b) 15 (c) 16 (d) 20
21. 21.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2² × 3 × 5
22. 22.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 100° (c) 135° (d) 80°
23. 23.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 220° (b) 40° (c) 140° (d) 80°
24. 24.A bag has 7 blue balls and 8 yellow 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) 15 (d) 9
25. 25.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 155° (b) 150° (c) 125° (d) 55°
26. 26.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
27. 27.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
28. 28.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 196 (c) 98 (d) 101
29. 29.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 851 (b) 841 (c) 961 (d) 899
30. 30.In a class of 30 children, 15 like mangoes, 7 like bananas and 2 like both. How many like at least one of the two? (a) 20 (b) 22 (c) 30 (d) 18
31. 31.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
32. 32.What is the midpoint of the line joining (5, 13) and (17, 3)? (a) (6, 5) (b) (11, 8) (c) (22, 16) (d) (8, 11)
33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
35. 35.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 8 (c) 30 (d) 15
36. 36.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 72 (d) 15
37. 37.In a class of 40 children, 21 like cricket, 18 like football and 6 like neither. How many like both? (a) 5 (b) 4 (c) 34 (d) 6
38. 38.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
40. 40.In a class of 29 children, 14 like mangoes, 17 like bananas and 7 like both. How many like neither? (a) 6 (b) 7 (c) 12 (d) 5

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