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CBSE Class 9 Pre Board 2019 : Mathematics (St Xavier's Sr. Sec. School, Delhi)

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Annual Examination in MATHEMATICS Std. 9 25-2-2019 Time : 3 hrs. Max. Marks : 80 General Instructions: i) All questions are compulsory. ii) The question paper consists of 30 questions divided into four sections A, B, C & D. Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each & Section D comprises of 8 questions of 4 marks each. SECTION A (1 x 6 = 6 marks) 1. Find the perpendicular distance of the point (-5, 7) from the y-axis. 2. Write an equation in two variables that passes through the point (3, -5). 3. If a cube has surface area and volume numerically equal. Find the edge of such a cube. (OR) The curved surface area of a cylinder is 1210cm2 and its diameter is 20cm. Find its height. 4. Expand ( 2x 3 3y)2. 1 5. Simplify: ( 6. In ABC, If AB = AC, B = 55o, then find the measure of A. 27 ) -2 3 (OR) Find the value of 4 12 12 27 SECTION B (2 x 6 = 12 marks) 7. In the given fig., ABC = 25 . Then find AOC. B O C A 8. Find the remainder when f(x) = 9x3 3x2 +14x 3 is divided by g(x) = 3x 1, using remainder theorem. (OR) 1 If one of the zeroes of polynomial 2x2 + 3x + a is , find the value of a. 2 9. The lateral surface area of a cube is 100m2. Find the volume of the cube. 10. In the given fig., if AC = BD, show that AB = CD. State the Euclid s postulate/axiom used for the same. 11. A B If two lines intersect each other, then prove that the vertically opposite angles are equal. (OR) C D Find the measure of BOD in the given figure. 56 3x - 8 x + 20 A Std. 9 D C -2- O B MATHEMATICS 12. A bag contains 5 red, 6 blue and 3 green balls. A ball is drawn at random. Find the probability of getting (i) a non green ball (ii) a ball of any colour. Section C (3 x 10 = 30 marks) 13. A triangle and a parallelogram have the same base and same area. If the sides of the triangle are 9cm, 12cm and 15cm and parallelogram stands on the base 9cm. Find the height of the parallelogram. 14. Simplify and factorize : (a + b + c)2 (a b c)2 + 4b2 4c2 (OR) Show that 2 and 5 2 are the zeroes of the polynomial 2x3 3x2 17x + 30. 15. Plot the points A(4, 2), B(4, -1), C(-2, -1) and D(-2, 2). Write the name of the figure obtained after joining A, B, C and D in order. Hence find the coordinates of the point where diagonals AC and BD intersect. 16. Prove that median of a triangle divides it into two triangles of equal area. 17. In a class there are x girls and y boys. Number of boys are 5 more than twice the number of girls. Write this information in the form of a linear equation in two variables. Represent it graphically. 18. Factorize: 19. In ABC, the sides AB and AC are produced upto points E and D respectively. If bisectors BO and CO of CBE and BCD respectively meet at point O, 6x3 + 23x2 + 9x - 18. then prove that BOC = 90 - 1 2 A A B E C O D (OR) If two parallel lines are intersected by a transversal, prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles. 20. The volume of a vessel in the form of right circular cylinder is 448 cm3 and its height is 7cm. Find the radius of its base. Also, find its curved surface area. (OR) Marbles of diameter 1.4cm are dropped into a beaker containing some water and are fully submerged. The diameter of the beaker is 7cm. Find how many marbles have been dropped in it if water rises by 56cm? 21. If two non parallel sides of a trapezium are equal, then prove that it is cyclic. (OR) If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords. 22. Represent 12.5 on the number line. Section D 23. Std. 9 Prove that 1 2 + 3 + 2 5 - 3 + 1 2 - 5 (4 x 8 = 32 marks) = 0. -3- MATHEMATICS 24. Draw the graph of x + y = 3 and 2x + 2y = 8 on the same graph sheet. What does the graph of these lines represent? 25. Show that the bisectors of angles of parallelogram form a rectangle. (OR) Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles then it is a square. 26. The following table shows the ages of the patients of economically weaker sections of society provided free treatment in a private hospital during a year. Ages (in years) No. of patients 5 15 6 15 25 11 25 35 21 35 45 23 45 55 14 55 65 5 Represent this information by constructing a histogram and frequency polygon on the same axes. 27. Construct PQR in which QR = 6cm, Q = 30 and PQ PR = 3.5cm. (OR) Construct PQR, where QR = 7cm, Q = 75 and PQ + PR = 14cm. 28. In the given fig. D is a point on side BC of ABC such that AD = AC. Show that AB > AD. A B 29. D C Given below is the frequency distribution of salary (in Rs) of 80 workers in a factory. Salary (in Rs) No of workers 1000 2000 12 2000 3000 18 3000 4000 28 4000 5000 22 If a worker is selected at random, find the probability that his salary is i) Less than Rs 3000 ii) more than or equal to Rs 1000 iii) More than Rs 5000 iv) more than or equal to Rs 1000 but less than Rs 3000. 30. The radius and height of a right circular cone are in the ratio of 5:12, its volume is 2512 cm3. Find the curved surface area of the cone. ( = 3.14). (OR) How many meters of cloth 2.5m wide, will be required to make conical tent whose base radius is 7m and height 24m? -x-x-x-x-x-x-

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