Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 893 · 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. 1.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 40 (c) 35 (d) 70
2. 2.How many prime numbers are there between 80 and 110? (a) 9 (b) 8 (c) 6 (d) 7
3. 3.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 230° (c) 115° (d) 50°
4. 4.What is the mean of 10, 19, 6, 19, 4 and 14? (a) 13 (b) 14 (c) 12 (d) 11
5. 5.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) 29 (b) 21 (c) 28 (d) 22
6. 6.In which quadrant does the point (−8, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
7. 7.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
8. 8.In a class of 29 children, 7 like maths, 19 like science and 3 like both. How many like only maths? (a) 10 (b) 4 (c) 16 (d) 7
9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 12 (b) 11 (c) 9 (d) 7
10. 10.There are 4 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) 24 (b) 12 (c) 16 (d) 7
11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 240 (c) 120 (d) 25
12. 12.In a class of 41 children, 22 like dance, 13 like music and 2 like both. How many like neither? (a) 6 (b) 8 (c) 2 (d) 10
13. 13.The mean of 8 numbers is 13. When the number 40 is added to them, what is the new mean? (a) 17 (b) 16 (c) 15 (d) 13
14. 14.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 55° (d) 46°
15. 15.What is the mode of 5, 7, 5, 7, 5, 14 and 15? (a) 14 (b) 7 (c) 15 (d) 5
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) 14 (b) 7 (c) 15 (d) 8
17. 17.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 1/4 (d) 7/8
18. 18.What is the median of 16, 36, 3, 40, 15, 35 and 29? (a) 16 (b) 35 (c) 29 (d) 40
19. 19.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
20. 20.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 7 (d) 21
21. 21.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 1)(x + 12) (c) (x − 6)(x − 7) (d) (x + 6)(x + 7)
22. 22.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
23. 23.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 1/4 (d) 3/5
24. 24.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
25. 25.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
26. 26.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
27. 27.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 160° (b) 145° (c) 55° (d) 20°
28. 28.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 25 (c) 24 (d) 12
29. 29.What is the 15th term of the AP 17, 25, 33, 41, …? (a) 112 (b) 120 (c) 137 (d) 129
30. 30.If a + b = 13 and ab = 30, what is (a − b)²? (a) 49 (b) 109 (c) 169 (d) 7
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 15 (d) 14
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
33. 33.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
34. 34.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
35. 35.In a class of 39 children, 22 like maths, 14 like science and 5 like both. How many like neither? (a) 5 (b) 13 (c) 8 (d) 3
36. 36.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°
37. 37.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 150° (b) 100° (c) 130° (d) 80°
38. 38.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 7 (d) 1
39. 39.In a class of 22 children, 13 like tea, 17 like coffee and 10 like both. How many like only tea? (a) 5 (b) 3 (c) 13 (d) 7
40. 40.What is the distance between the points (4, 8) and (8, 11)? (a) 7 (b) 25 (c) 5 (d) 6

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