Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 64 · 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 + 9x + 20? (a) (x + 1)(x + 8) (b) (x + 4)(x + 5) (c) (x − 4)(x − 5) (d) (x + 1)(x + 20)
2. 2.A bag has 3 red balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 4 (c) 6 (d) 5
3. 3.What is the smallest prime factor of 69? (a) 23 (b) 2 (c) 3 (d) 1
4. 4.A drawer has lots of yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 4 (c) 5 (d) 3
5. 5.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 196 (d) 182
6. 6.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) 28 (c) 22 (d) 21
7. 7.What is the 22nd term of the AP 3, 11, 19, 27, …? (a) 171 (b) 176 (c) 179 (d) 168
8. 8.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1444 (b) 1774 (c) 1764 (d) 1604
9. 9.A drawer has lots of white, blue and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 4 (d) 6
10. 10.If a + b = 17 and ab = 60, what is a² + b²? (a) 289 (b) 169 (c) 409 (d) 229
11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 7 (d) 16
12. 12.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 72 (c) 207 (d) 69
13. 13.In which quadrant does the point (3, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
14. 14.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 21 (c) 10 (d) 24
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
16. 16.How many factors does 88 have? (a) 7 (b) 8 (c) 6 (d) 9
17. 17.A bag has 8 white, 4 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/7 (b) 1/3 (c) 9/14 (d) 4/7
18. 18.What is the smallest prime factor of 55? (a) 5 (b) 1 (c) 11 (d) 2
19. 19.What is the mean of 8, 15, 9, 2 and 11? (a) 10 (b) 8 (c) 11 (d) 9
20. 20.What is the distance between the points (6, 1) and (14, 7)? (a) 11 (b) 10 (c) 14 (d) 100
21. 21.A bag has 10 red balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 12 (b) 11 (c) 2 (d) 18
22. 22.In a class of 35 children, 23 like dance, 9 like music and 3 like both. How many like at least one of the two? (a) 26 (b) 32 (c) 29 (d) 35
23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
24. 24.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 576 (b) 46 (c) 288 (d) 312
25. 25.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
26. 26.How many prime numbers are there between 90 and 110? (a) 4 (b) 7 (c) 6 (d) 5
27. 27.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 120 (d) 25
28. 28.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x − 2)(x − 8) (c) (x + 1)(x + 16) (d) (x + 2)(x + 8)
29. 29.In which quadrant does the point (5, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
30. 30.How many factors does 117 have? (a) 7 (b) 4 (c) 5 (d) 6
31. 31.How many factors does 58 have? (a) 4 (b) 2 (c) 3 (d) 5
32. 32.If a + b = 17 and ab = 66, what is a² + b²? (a) 289 (b) 157 (c) 421 (d) 223
33. 33.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 85° (b) 40° (c) 140° (d) 135°
34. 34.What is the mode of 20, 18, 12, 8, 8, 20 and 20? (a) 12 (b) 8 (c) 18 (d) 20
35. 35.In a class of 33 children, 17 like dance, 11 like music and 2 like both. How many like neither? (a) 2 (b) 7 (c) 9 (d) 5
36. 36.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2³ × 3 × 7
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
38. 38.What is the midpoint of the line joining (5, 6) and (15, 8)? (a) (10, 7) (b) (5, 1) (c) (20, 14) (d) (7, 10)
39. 39.What is the 19th term of the AP 15, 23, 31, 39, …? (a) 152 (b) 167 (c) 144 (d) 159
40. 40.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)

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