Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 903 · 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 sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 18 (b) 20 (c) 19 (d) 9
3. 3.A drawer has lots of white, red, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 8 (c) 5 (d) 2
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
5. 5.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
6. 6.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
7. 7.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 25° (c) 65° (d) 335°
8. 8.If a + b = 15 and ab = 56, what is a² + b²? (a) 337 (b) 169 (c) 113 (d) 225
9. 9.If a + b = 5 and ab = 4, what is (a − b)²? (a) 3 (b) 17 (c) 25 (d) 9
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
11. 11.A bag has 3 green, 2 blue and 5 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 1/10 (c) 1/2 (d) 3/5
12. 12.In a class of 39 children, 21 like tea, 28 like coffee and 12 like both. How many like only tea? (a) 11 (b) 16 (c) 21 (d) 9
13. 13.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 55 (d) 22
14. 14.In a class of 34 children, 10 like tea, 23 like coffee and 5 like both. How many like at least one of the two? (a) 23 (b) 28 (c) 33 (d) 34
15. 15.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
16. 16.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 600 (c) 300 (d) 47
17. 17.What is the midpoint of the line joining (3, 6) and (9, 18)? (a) (12, 24) (b) (12, 6) (c) (3, 6) (d) (6, 12)
18. 18.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 182 (d) 196
19. 19.Which term of the AP 9, 14, 19, 24, … is 64? (a) 11th (b) 13th (c) 14th (d) 12th
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
21. 21.What is the median of 3, 7, 16, 35, 5, 2 and 40? (a) 35 (b) 5 (c) 16 (d) 7
22. 22.There are 4 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 16 (c) 12 (d) 8
23. 23.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) 36° (c) 35° (d) 215°
24. 24.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
25. 25.If a + b = 19 and ab = 84, what is (a − b)²? (a) 5 (b) 361 (c) 193 (d) 25
26. 26.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 95° (d) 85°
27. 27.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/3 (c) 1/6 (d) 1/5
28. 28.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
29. 29.A bag has 12 green balls and 3 red 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) 13 (d) 15
30. 30.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x + 1)(x + 42) (c) (x + 6)(x + 7) (d) (x − 6)(x − 7)
31. 31.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 4 (d) 3
32. 32.In a class of 40 children, 18 like cricket, 25 like football and 9 like neither. How many like both? (a) 31 (b) 3 (c) 12 (d) 9
33. 33.In a class of 31 children, 23 like cricket, 9 like football and 3 like both. How many like only cricket? (a) 6 (b) 23 (c) 22 (d) 20
34. 34.The mean of 7 numbers is 25. When the number 41 is added to them, what is the new mean? (a) 28 (b) 25 (c) 27 (d) 33
35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 45 (d) 90
36. 36.If a + b = 10 and ab = 21, what is a² + b²? (a) 58 (b) 100 (c) 142 (d) 79
37. 37.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
38. 38.What is the 39th term of the AP 1, 9, 17, 25, …? (a) 305 (b) 313 (c) 304 (d) 312
39. 39.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
40. 40.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 95° (c) 25° (d) 110°

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