Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 755 · 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.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x − 8)(x − 9) (d) (x + 1)(x + 72)
2. 2.A bag has 6 yellow balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 2 (c) 15 (d) 7
3. 3.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2³ × 7 (c) 2 × 7⁴ (d) 2⁴ × 7
4. 4.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 28 (c) 14 (d) 21
5. 5.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 145° (b) 100° (c) 80° (d) 115°
6. 6.What is the mode of 4, 6, 20, 20, 13, 20 and 6? (a) 13 (b) 6 (c) 4 (d) 20
7. 7.What is the distance between the points (7, 16) and (19, 7)? (a) 15 (b) 225 (c) 16 (d) 21
8. 8.What are the roots of x² − 11x + 24 = 0? (a) 1 and 10 (b) 1 and 24 (c) 3 and 8 (d) 2 and 12
9. 9.In which quadrant does the point (−7, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
10. 10.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 6 (c) 21 (d) 18
11. 11.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
12. 12.A bag has 7 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 8 (c) 2 (d) 9
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
14. 14.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
15. 15.What is the median of 31, 18, 28, 14, 36, 16 and 34? (a) 18 (b) 28 (c) 14 (d) 31
16. 16.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 169 (d) 78
17. 17.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
18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
19. 19.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 8 (c) 36 (d) 70
20. 20.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 800 (c) 820 (d) 780
21. 21.The mean of 4 numbers is 30. When the number 45 is added to them, what is the new mean? (a) 30 (b) 32 (c) 34 (d) 33
22. 22.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/7 (c) 1/4 (d) 7/8
23. 23.What is the mode of 18, 18, 11, 19, 11, 9 and 11? (a) 19 (b) 9 (c) 18 (d) 11
24. 24.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 3 (d) 6
25. 25.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 66° (c) 65° (d) 130°
26. 26.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 100° (d) 80°
27. 27.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 25 (c) 24 (d) 36
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 5/36 (d) 1/6
29. 29.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 80° (d) 125°
30. 30.How many factors does 93 have? (a) 5 (b) 2 (c) 3 (d) 4
31. 31.In a class of 24 children, 12 like cricket, 5 like football and 2 like both. How many like only cricket? (a) 12 (b) 19 (c) 3 (d) 10
32. 32.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
33. 33.If a + b = 16 and ab = 63, what is (a − b)²? (a) 2 (b) 256 (c) 130 (d) 4
34. 34.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 10° (d) 50°
35. 35.What is the 39th term of the AP 6, 14, 22, 30, …? (a) 318 (b) 310 (c) 312 (d) 304
36. 36.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 24 (c) 36 (d) 18
37. 37.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 22 (d) 15
38. 38.If a + b = 5 and ab = 4, what is (a − b)²? (a) 3 (b) 17 (c) 25 (d) 9
39. 39.How many factors does 98 have? (a) 6 (b) 4 (c) 7 (d) 5
40. 40.In a class of 38 children, 30 like tea, 17 like coffee and 2 like neither. How many like both? (a) 9 (b) 36 (c) 11 (d) 2

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