Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 344 · 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 missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 15 (c) 12 (d) 11
2. 2.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
3. 3.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 120° (c) 60° (d) 30°
4. 4.Which term of the AP 16, 20, 24, 28, … is 80? (a) 18th (b) 20th (c) 16th (d) 17th
5. 5.Using (a − b)² = a² − 2ab + b², what is 17²? (a) 391 (b) 529 (c) 299 (d) 289
6. 6.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 6 (b) 4 (c) 5 (d) 7
7. 7.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 19 (c) 171 (d) 57
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/9 (c) 3/11 (d) 1/11
9. 9.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
11. 11.What is the distance between the points (9, 2) and (33, 9)? (a) 25 (b) 31 (c) 625 (d) 26
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
13. 13.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
14. 14.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) 16 (c) 12 (d) 7
15. 15.A bag has 5 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 6 (d) 7
16. 16.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2² × 3² × 5
17. 17.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
18. 18.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) 207 (b) 23 (c) 69 (d) 72
19. 19.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
20. 20.In a class of 30 children, 14 like dance, 16 like music and 6 like both. How many like at least one of the two? (a) 25 (b) 18 (c) 30 (d) 24
21. 21.A bag has 6 blue balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 11 (c) 2 (d) 16
22. 22.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 904 (b) 1034 (c) 784 (d) 1024
23. 23.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
24. 24.If a + b = 19 and ab = 84, what is a² + b²? (a) 361 (b) 277 (c) 193 (d) 529
25. 25.What is the prime factorisation of 45? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5 (d) 3 × 5²
26. 26.How many factors does 31 have? (a) 3 (b) 1 (c) 4 (d) 2
27. 27.What is the median of 39, 11, 16, 3 and 19? (a) 17 (b) 11 (c) 19 (d) 16
28. 28.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
29. 29.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
30. 30.The mean of 7 numbers is 38. When the number 54 is added to them, what is the new mean? (a) 46 (b) 41 (c) 40 (d) 38
31. 31.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 250° (c) 70° (d) 71°
32. 32.In a class of 26 children, 17 like dance, 17 like music and 12 like both. How many like neither? (a) 5 (b) 16 (c) 12 (d) 4
33. 33.What is the midpoint of the line joining (9, 10) and (11, 8)? (a) (20, 18) (b) (10, 9) (c) (1, 1) (d) (9, 10)
34. 34.What is the distance between the points (8, 0) and (32, 7)? (a) 625 (b) 31 (c) 26 (d) 25
35. 35.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
36. 36.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 16 (d) 12
37. 37.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 135° (b) 105° (c) 60° (d) 120°
38. 38.Using (a − b)² = a² − 2ab + b², what is 18²? (a) 484 (b) 396 (c) 334 (d) 324
39. 39.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 78 (c) 169 (d) 156
40. 40.In which quadrant does the point (5, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

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