Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 860 · 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.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 132 (c) 24 (d) 66
2. 2.A bag has 10 red balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 12 (b) 18 (c) 2 (d) 11
3. 3.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 40° (d) 30°
4. 4.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 130° (b) 100° (c) 260° (d) 80°
5. 5.How many factors does 19 have? (a) 2 (b) 3 (c) 4 (d) 1
6. 6.In which quadrant does the point (−8, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
7. 7.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 3/8 (d) 7/8
8. 8.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
9. 9.In a class of 30 children, 13 like maths, 19 like science and 6 like both. How many like at least one of the two? (a) 30 (b) 26 (c) 32 (d) 20
10. 10.In a class of 48 children, 24 like maths, 27 like science and 12 like both. How many like at least one of the two? (a) 48 (b) 27 (c) 51 (d) 39
11. 11.What is the product of the roots of x² − 14x + 45 = 0? (a) 45 (b) 44 (c) 46 (d) 14
12. 12.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) 153 (b) 51 (c) 17 (d) 54
13. 13.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
14. 14.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
15. 15.A bag has 8 black balls and 9 green 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) 17 (c) 9 (d) 10
16. 16.There are 4 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 9 (c) 24 (d) 40
17. 17.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 420 (c) 456 (d) 840
18. 18.If a + b = 11 and ab = 10, what is a² + b²? (a) 141 (b) 121 (c) 101 (d) 111
19. 19.A bag has 4 blue balls and 12 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) 16 (c) 2 (d) 5
20. 20.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
21. 21.If a + b = 9 and ab = 18, what is a² + b²? (a) 63 (b) 81 (c) 117 (d) 45
22. 22.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 189 (c) 190 (d) 198
23. 23.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 105° (b) 155° (c) 100° (d) 80°
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
25. 25.In a class of 34 children, 16 like maths, 19 like science and 4 like both. How many like neither? (a) 3 (b) 7 (c) 2 (d) 4
26. 26.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
27. 27.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 28 (b) 209 (c) 396 (d) 198
28. 28.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 4 (d) 2
29. 29.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 64 cu cm (d) 65 cu cm
30. 30.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 125° (b) 15° (c) 70° (d) 165°
31. 31.Which term of the AP 20, 23, 26, 29, … is 119? (a) 33rd (b) 34th (c) 36th (d) 35th
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
33. 33.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
34. 34.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 75° (d) 30°
35. 35.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 154 (b) 37 (c) 308 (d) 159
36. 36.In a class of 44 children, 26 like cricket, 17 like football and 9 like neither. How many like both? (a) 9 (b) 35 (c) 8 (d) 7
37. 37.In a class of 26 children, 8 like mangoes, 14 like bananas and 5 like both. How many like at least one of the two? (a) 26 (b) 17 (c) 22 (d) 12
38. 38.What is the midpoint of the line joining (0, 4) and (4, 10)? (a) (4, 14) (b) (7, 2) (c) (2, 3) (d) (2, 7)
39. 39.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7
40. 40.Which term of the AP 17, 21, 25, 29, … is 149? (a) 36th (b) 35th (c) 33rd (d) 34th

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