Grade: 8 Mathematics Olympiad Qualifier Set: 2
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1 Grade: 8 Mathematics Olympiad Qualifier Set: Max Marks: 60 Test ID: Time Allotted: 40 Mins Instructions: Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Each question carries 2 Marks. There is no negative marking 1. Which of the following set of numbers is closed under subtraction? A. Fractions B. Negative integers C. Natural numbers D. Rational numbers 2. If x = 2, then x is equal to. 7 A. 2 7 B. 2 7 C. 0 D Solve for x: 6x 7 = 3x+1 2x+1 x+5 A. 2 B. -2 C. 18 D In a quadrilateral ABCD, B = 90 and AD 2 = AB 2 + BC 2 + CD 2 then ACD is equal to A. 90 B. 60 C. 30 Page 1 of 6
2 5. If Mohammad has two children and he truthfully answers yes to the question "Is at least one of your children a girl?" The probability that both his children are girls is A. 1 3 B. 1 2 C. 2 3 D If 3(x 3) = 5(2x + 1) and y 8 = y 3, then the value of (2x + 3y)(2x 3y) is. 3 2 A. 425 B. 425 C. 160 D Each interior angle of a regular polygon lies between 136 and 142, then the number of sides of the polygon is. A. 6 B. 9 C. 10 D The square root of a perfect square containing 'n' digits has digits. A. n+1 2 B. n 2 C. A or B 9. If 0 < x < 1, then A. (x + 1 ) > 2 x B. (x + 1 x ) < 2 C. (x + 1 x ) > 4 D. (x + 1 x ) < 4 Page 2 of 6
3 10. If x y = y x, then ( x y ) x y is equal to. x A. xy x B. xy 1 C. x y x D. x y x A motor boat covers a distance downstream in a river in five hours. It covers the same distance upstream in five hours and a half. The speed of the water is 1.5 km/hr. The speed of the boat in still water is. A. 30 km/hr B km/hr C km/hr D. 20 km/hr 12. To construct a convex quadrilateral, which of the following cases is not correct? A. When the lengths of the four sides and one diagonal are given. B. When the lengths of the three sides and the two diagonals are given. C. When the lengths of four sides and one angle are given. D. When the lengths of the two sides and two included angles are given. 13. If p and q both are perfect squares, then p q is always a rational number (q 0). Is the statement true? A. Yes B. No C. Cannot be determined 14. Three cubes whose edges are 3cm, 4cm and 5cm respectively are melted without any loss of metal into a single cube. The edge of the new cube is. A. 6cm B. 12cm C. 9cm D. 10cm 15. One of the factors of (a 2 b 2 )(c 2 d 2 ) 4abcd is. A. (ac bd + bc + ad) B. ac + bd + bc + ad C. Cannot be determined D. ab + bd bc ad Page 3 of 6
4 16. If the sum and product of two numbers are 12 and 35, respectively. Then, the sum of their reciprocals is A. 7 5 B C D. None of the above 17. If 4 x + 4 x + 4 x + 4 x + 4 x + 4 x + 4 x + 4 x = 1 512, then the value of 3 x is A. 0.5 B. 8 C D If a = and b = 2 1, then the value of expression a2 ab+b 2 a 2 +ab+b 2 is A B C. 0 D If m, n and p are the three sums of money such that n is simple interest on m and p is the simple interest on n for the same time and at the same rate of interest. The relation among m, n and p is given by A. n 2 = mp B. m 2 = np C. p 2 = nm D. p = nm 25 a If = x a 8 a4. Then, the value of x is A. 5 3 B. 5 4 C D Factorization of 7x 2 8x 12 is: A. (x + 12)(3x 20) B. (x 2)(6x + 7) C. (x 4)(3x 4) D. (x 2)(7x + 6) Page 4 of 6
5 22. Three containers have their volumes in the ratio 3: 4: 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4: 1), (3: 1) and (5: 2) respectively. The ratio of milk and water in the fourth container contains all the above three mixtures is: A. 4: 1 B. 151: 48 C. 157: 53 D. 5: The value of ( ) 5 4 (0.04) 5 4 is: A B C If two cubes of dimension 3cm by 3cm by 3cm are placed side by side, what would be the dimensions of the resulting cuboid be? A. 6cm 6cm 6cm B. 12cm 12cm 12cm C. 9cm 6cm 3cm D. 6cm 3cm 3cm 25. If quotient = 3x 2 2x + 1, remainder = 2x 5 and divisor = x + 2 then the dividend is: A. 3x 3 4x 2 + x 3 B. 3x 3 4x 2 x + 3 C. 3x 3 + 4x 2 x + 3 D. 3x 3 + 4x 2 x In the last three months, Mr. Qureshi lost kg, gained kg and then lost kg respectively in each month. If he now weighs 95 kg, how much did Mr. Qureshi weigh to begin with? A. 100 kg B. 102 kg C. 89 kg D. 104 kg 27. The ratio of the sides of two regular polygons is 1: 2 and their interior angles are in the ratio 3: 4, then the number of sides in each polygon is A. 6,12 B. 5,10 C. 12,6 D. 10,5 Page 5 of 6
6 28. To show the distribution of proteins and other dry elements in the human body, the arc of the circle should subtend at the center of an angle of A. 54 B. 126 C. 108 D The cube root of A. 12 and 13 B. 13 and 14 C. 14 and 15 D. 15 and 16 lies between 30. Choose incorrect statement. A. 1,9, x, y, xy and 9xy are the only possible factors of 9xy. B. 36x 2 + 2xy + 3 is a quadratic polynomial. C. The factors of (y x)a + (x y)b are (x y)(b a). D. On factorization of x 2 + 6x 27, we get (x 9)(x + 3). Page 6 of 6
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