Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 465 · 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 mean of 19, 12, 2, 7 and 15? (a) 11 (b) 12 (c) 13 (d) 10
2. 2.How many factors does 108 have? (a) 13 (b) 10 (c) 11 (d) 12
3. 3.What is the mode of 2, 6, 7, 2, 20, 20 and 20? (a) 7 (b) 6 (c) 20 (d) 2
4. 4.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
5. 5.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
6. 6.Which is the correct factorisation of x² + 13x + 36? (a) (x + 4)(x + 9) (b) (x + 1)(x + 36) (c) (x − 4)(x − 9) (d) (x + 1)(x + 12)
7. 7.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
8. 8.The mean of 5 numbers is 35. When the number 29 is added to them, what is the new mean? (a) 32 (b) 34 (c) 35 (d) 33
9. 9.What is the 39th term of the AP 18, 22, 26, 30, …? (a) 170 (b) 174 (c) 152 (d) 156
10. 10.A cuboid is 8 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 584 sq cm (b) 146 sq cm (c) 292 sq cm (d) 336 sq cm
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
12. 12.How many factors does 46 have? (a) 2 (b) 5 (c) 4 (d) 3
13. 13.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
14. 14.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) 8 (c) 15 (d) 7
15. 15.If a + b = 21 and ab = 108, what is a² + b²? (a) 441 (b) 333 (c) 225 (d) 657
16. 16.What is the mode of 4, 15, 17, 3, 4, 4 and 15? (a) 15 (b) 4 (c) 3 (d) 17
17. 17.What is the mean of 12, 14, 10 and 16? (a) 14 (b) 12 (c) 15 (d) 13
18. 18.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 145° (b) 95° (c) 60° (d) 120°
19. 19.Which is the correct factorisation of x² + 15x + 54? (a) (x − 6)(x − 9) (b) (x + 1)(x + 14) (c) (x + 1)(x + 54) (d) (x + 6)(x + 9)
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) 7 (b) 24 (c) 21 (d) 63
21. 21.In a class of 26 children, 14 like dance, 20 like music and 9 like both. How many like at least one of the two? (a) 16 (b) 26 (c) 34 (d) 25
22. 22.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 125° (b) 70° (c) 110° (d) 250°
23. 23.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 160° (b) 260° (c) 100° (d) 80°
24. 24.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 15 (c) 30 (d) 20
25. 25.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 36 (c) 12 (d) 72
26. 26.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 16 (b) 15 (c) 13 (d) 14
27. 27.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 375 (b) 625 (c) 235 (d) 225
28. 28.In a class of 38 children, 17 like cricket, 22 like football and 2 like both. How many like only cricket? (a) 16 (b) 20 (c) 17 (d) 15
29. 29.What is the mode of 2, 16, 16, 2, 2, 17 and 19? (a) 19 (b) 16 (c) 17 (d) 2
30. 30.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
31. 31.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
32. 32.What is the median of 35, 4, 24, 23 and 1? (a) 22 (b) 4 (c) 24 (d) 23
33. 33.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 48 (d) 12
34. 34.What is the mode of 18, 18, 10, 18, 9, 13 and 13? (a) 13 (b) 10 (c) 9 (d) 18
35. 35.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
36. 36.In a class of 28 children, 20 like dance, 17 like music and 12 like both. How many like at least one of the two? (a) 13 (b) 28 (c) 37 (d) 25
37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 25 (d) 240
38. 38.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 70°
39. 39.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2484 (b) 2916 (c) 2126 (d) 2116
40. 40.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°

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