Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 588 · 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 sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 870 (d) 57
2. 2.What is the midpoint of the line joining (8, 9) and (10, 5)? (a) (9, 7) (b) (18, 14) (c) (7, 9) (d) (1, 2)
3. 3.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) 15 (c) 8 (d) 7
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 21 (d) 20
5. 5.What is the smallest prime factor of 169? (a) 2 (b) 13 (c) 3 (d) 1
6. 6.What is the 32nd term of the AP 11, 16, 21, 26, …? (a) 166 (b) 160 (c) 155 (d) 171
7. 7.In a class of 28 children, 11 like cricket, 19 like football and 5 like neither. How many like both? (a) 7 (b) 5 (c) 2 (d) 23
8. 8.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
10. 10.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 115° (d) 110°
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
12. 12.In which quadrant does the point (1, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
13. 13.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 270° (d) 125°
14. 14.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
15. 15.Which term of the AP 4, 7, 10, 13, … is 106? (a) 35th (b) 36th (c) 37th (d) 34th
16. 16.What is the 33rd term of the AP 4, 6, 8, 10, …? (a) 70 (b) 64 (c) 68 (d) 66
17. 17.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 1225 (b) 2025 (c) 2035 (d) 1625
18. 18.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 72 (c) 16 (d) 17
19. 19.In a class of 35 children, 19 like maths, 15 like science and 5 like both. How many like only maths? (a) 10 (b) 14 (c) 19 (d) 20
20. 20.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 4 sq cm (d) 24 sq cm
21. 21.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
22. 22.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
23. 23.What is the midpoint of the line joining (7, 15) and (15, 5)? (a) (4, 5) (b) (10, 11) (c) (22, 20) (d) (11, 10)
24. 24.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 20° (c) 340° (d) 160°
25. 25.The mean of 3 numbers is 21. When the number 29 is added to them, what is the new mean? (a) 23 (b) 24 (c) 25 (d) 21
26. 26.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11025 (b) 10025 (c) 9025 (d) 11035
27. 27.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1681 (b) 1521 (c) 1599 (d) 1531
28. 28.A bag has 4 white, 4 blue and 2 green balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 2/5 (b) 1/3 (c) 7/10 (d) 3/5
29. 29.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 11 (c) 24 (d) 32
30. 30.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
31. 31.What is the mean of 12, 10, 20, 11 and 17? (a) 15 (b) 14 (c) 16 (d) 13
32. 32.What is the distance between the points (4, 12) and (13, 0)? (a) 16 (b) 225 (c) 21 (d) 15
33. 33.What is the distance between the points (1, 14) and (9, 8)? (a) 100 (b) 11 (c) 14 (d) 10
34. 34.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 36 (d) 12
35. 35.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2³ × 3² × 7
36. 36.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) 28 (b) 22 (c) 29 (d) 21
37. 37.The numbers 20 to 28 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) 72 (c) 216 (d) 75
38. 38.What is the mode of 3, 20, 11, 20, 11, 11 and 12? (a) 12 (b) 20 (c) 3 (d) 11
39. 39.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 5/6 (c) 1/3 (d) 1/6
40. 40.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) 69 (b) 72 (c) 23 (d) 207

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