Maths Olympiad Sample Paper 2 (Practice)
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.
NameDateTime takenScore ___ / 40
- 1.How many prime numbers are there between 80 and 90? (a) 2 (b) 4 (c) 3 (d) 1
- 2.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
- 3.What is the sum of the roots of x² − 13x + 40 = 0? (a) 13 (b) 14 (c) 12 (d) 40
- 4.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
- 5.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
- 6.5 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 20 (b) 15 (c) 10 (d) 7
- 7.How many factors does 78 have? (a) 9 (b) 7 (c) 6 (d) 8
- 8.What is the midpoint of the line joining (0, 3) and (2, 7)? (a) (5, 1) (b) (1, 2) (c) (1, 5) (d) (2, 10)
- 9.What is the distance between the points (3, 17) and (9, 9)? (a) 14 (b) 10 (c) 11 (d) 100
- 10.In a class of 54 children, 29 like mangoes, 30 like bananas and 12 like both. How many like neither? (a) 7 (b) 8 (c) 12 (d) 19
- 11.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
- 12.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 1 (c) 4 (d) 2
- 13.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
- 14.What is the distance between the points (0, 5) and (6, 13)? (a) 14 (b) 11 (c) 10 (d) 100
- 15.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
- 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
- 17.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 204 (b) 208 (c) 202 (d) 198
- 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
- 19.In which quadrant does the point (7, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
- 20.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 190 cu cm (b) 18 cu cm (c) 126 cu cm (d) 14 cu cm
- 21.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 105° (c) 76° (d) 255°
- 22.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 11 (d) 3
- 23.What is the 15th term of the AP 2, 7, 12, 17, …? (a) 70 (b) 72 (c) 75 (d) 77
- 24.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2 × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
- 25.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
- 26.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 15 (c) 14 (d) 56
- 27.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
- 28.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
- 29.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 3 (d) 6
- 30.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 22 (b) 119 (c) 112 (d) 224
- 31.What is the mode of 3, 1, 19, 19, 11, 11 and 11? (a) 19 (b) 11 (c) 3 (d) 1
- 32.What is the distance between the points (9, 0) and (13, 3)? (a) 7 (b) 6 (c) 5 (d) 25
- 33.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 28 (d) 16
- 34.The mean of 3 numbers is 23. When the number 19 is added to them, what is the new mean? (a) 21 (b) 23 (c) 24 (d) 22
- 35.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
- 36.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 28 (b) 108 (c) 186 (d) 93
- 37.What is the mean of 16, 11, 20, 3, 5 and 17? (a) 11 (b) 12 (c) 14 (d) 13
- 38.A bag has 3 yellow, 5 red and 3 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/8 (b) 3/11 (c) 1/3 (d) 8/11
- 39.A drawer has lots of green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
- 40.In a class of 17 children, 11 like dance, 10 like music and 5 like both. How many like neither? (a) 5 (b) 2 (c) 1 (d) 6
Answer key
- 2
- Third quadrant
- 13
- 2² × 3 × 5
- 16 times
- 10
- 8
- (1, 5)
- 10
- 7
- 120
- 3
- 5
- 10
- 3/4
- 88 cm
- 202
- 44 cm
- First quadrant
- 126 cu cm
- 75°
- 11
- 72
- 2 × 3 × 5 × 7
- 2³ × 3 × 7
- 15
- 2
- 17
- 4
- 112
- 11
- 5
- 56
- 22
- 44 cm
- 93
- 12
- 3/11
- 3
- 1
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