Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 311 · 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 distance between the points (2, 8) and (6, 11)? (a) 7 (b) 25 (c) 5 (d) 6
2. 2.Which is the correct factorisation of x² + 11x + 18? (a) (x + 1)(x + 18) (b) (x + 1)(x + 10) (c) (x − 2)(x − 9) (d) (x + 2)(x + 9)
3. 3.How many factors does 86 have? (a) 4 (b) 2 (c) 3 (d) 5
4. 4.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 20 (c) 16 (d) 8
5. 5.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 155° (c) 45° (d) 135°
6. 6.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
7. 7.In a class of 41 children, 13 like mangoes, 23 like bananas and 10 like neither. How many like both? (a) 31 (b) 10 (c) 6 (d) 5
8. 8.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 35° (d) 25°
9. 9.If a + b = 9 and ab = 18, what is a² + b²? (a) 63 (b) 81 (c) 45 (d) 117
10. 10.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2² × 7 (c) 2³ × 7 (d) 2⁴ × 7
11. 11.What is the mode of 20, 7, 3, 20, 7, 1 and 7? (a) 7 (b) 3 (c) 1 (d) 20
12. 12.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
13. 13.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 50° (c) 51° (d) 100°
14. 14.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
15. 15.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 30° (b) 150° (c) 100° (d) 110°
16. 16.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 50 (c) 100 (d) 18
17. 17.A bag has 6 green balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 8 (b) 10 (c) 7 (d) 2
18. 18.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 27 sq cm (d) 54 sq cm
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
20. 20.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
21. 21.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 7 (b) 6 (c) 5 (d) 8
22. 22.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
23. 23.In a class of 26 children, 14 like mangoes, 14 like bananas and 6 like both. How many like neither? (a) 5 (b) 4 (c) 10 (d) 6
24. 24.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
25. 25.A bag has 4 white balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 5 (c) 16 (d) 2
26. 26.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 2 (d) 1
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
28. 28.What is the midpoint of the line joining (2, 6) and (12, 12)? (a) (14, 18) (b) (9, 7) (c) (5, 3) (d) (7, 9)
29. 29.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 160° (d) 125°
30. 30.A bag has 4 red, 3 green and 2 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 2/3 (c) 4/9 (d) 1/2
31. 31.A drawer has lots of green, red, yellow and white 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) 5 (c) 4 (d) 8
32. 32.What is the distance between the points (3, 5) and (15, 10)? (a) 169 (b) 14 (c) 17 (d) 13
33. 33.The numbers 18 to 26 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) 22 (c) 66 (d) 198
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
36. 36.What is the sum of the roots of x² − 15x + 54 = 0? (a) 54 (b) 14 (c) 16 (d) 15
37. 37.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 61 (b) 60 (c) 120 (d) 14
38. 38.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 6 (d) 5
40. 40.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 70°

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