Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 60 · 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.If a + b = 18 and ab = 80, what is (a − b)²? (a) 164 (b) 2 (c) 4 (d) 324
2. 2.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
3. 3.What is the 34th term of the AP 9, 18, 27, 36, …? (a) 297 (b) 315 (c) 307 (d) 306
4. 4.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
5. 5.In a class of 32 children, 13 like mangoes, 19 like bananas and 7 like neither. How many like both? (a) 25 (b) 6 (c) 8 (d) 7
6. 6.How many factors does 20 have? (a) 6 (b) 4 (c) 7 (d) 5
7. 7.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 80° (c) 135° (d) 100°
8. 8.The mean of 6 numbers is 27. When the number 34 is added to them, what is the new mean? (a) 29 (b) 27 (c) 30 (d) 28
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
10. 10.What is the product of the roots of x² − 13x + 36 = 0? (a) 37 (b) 13 (c) 36 (d) 35
11. 11.In a class of 38 children, 14 like maths, 27 like science and 7 like neither. How many like both? (a) 10 (b) 3 (c) 7 (d) 31
12. 12.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 174 cu cm (b) 17 cu cm (c) 135 cu cm (d) 15 cu cm
13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
14. 14.A bag has 11 red balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 19 (c) 9 (d) 12
15. 15.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 295° (c) 115° (d) 25°
16. 16.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 145° (d) 110°
17. 17.How many prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 8 (d) 9
18. 18.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
19. 19.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 7 (d) 24
20. 20.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
21. 21.In which quadrant does the point (−3, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
22. 22.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 3 (d) 6
23. 23.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 1/4 (c) 2/3 (d) 5/6
24. 24.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 40 (c) 80 (d) 48
25. 25.What is the 34th term of the AP 19, 26, 33, 40, …? (a) 257 (b) 238 (c) 231 (d) 250
26. 26.A drawer has lots of green, red, white, black 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) 5 (c) 6 (d) 10
27. 27.A drawer has lots of white, green, 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) 8 (b) 4 (c) 5 (d) 2
28. 28.What is the midpoint of the line joining (7, 0) and (19, 2)? (a) (26, 2) (b) (1, 13) (c) (13, 1) (d) (6, 1)
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
30. 30.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
31. 31.In which quadrant does the point (−6, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
32. 32.How many factors does 86 have? (a) 3 (b) 2 (c) 5 (d) 4
33. 33.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 24 (d) 12
34. 34.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
36. 36.What is the prime factorisation of 36? (a) 2² × 3² (b) 2² × 3³ (c) 2³ × 3² (d) 2 × 3²
37. 37.What is the product of the roots of x² − 13x + 42 = 0? (a) 43 (b) 41 (c) 42 (d) 13
38. 38.What is the 30th term of the AP 18, 22, 26, 30, …? (a) 138 (b) 134 (c) 116 (d) 120
39. 39.How many factors does 35 have? (a) 3 (b) 5 (c) 4 (d) 2
40. 40.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1609 (b) 1369 (c) 1859 (d) 1849

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