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KENDRIYA VIDYALAYA SANGATHAN(HYDERABAD REGION)SUMMATIVE ASSESSMENT – 1 (2016)CLASS: X MAX.MARKS: 90Subject: Mathematics Time : 3 hrs General Instructions: All questions are compulsory.The question paper consists of 31 questions divided into four sections A, B, C and D.Section A contains 4 multiple-choice questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 11 questions of 4 marks each.Use of calculator is not permitted.SECTION A1.The perimeter of two similar triangles ABC and LMN are 60cm and 48cm respectively. If LM = 8cm, then find the length of AB.2. For which value of k does the pair of equations 2x + 3y – 5 = 0 and kx – 6y – 8 = 0 has unique solution.3.If tan(3x + 300) = 1, then find the value of x. 4. Find mode, using an empirical relation, when it is given that mean and median are 10.5 and 9.6 respectively. SECTION B5.Find the HCF of 867 and 255 by using Euclid’s Division algorithm.6.Find the least number that is divisible by all the numbers from 1 to 10.7.Find a quadratic polynomial, the sum and product of whose zeroes are ? and -1, respectively.8.Solve the following equations for x and y:mx – ny = m2 + n2x + y = 2m9.A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.10. Find the mode of the following data: Class Interval5 - 1515 - 2525 - 3535- 45 45 - 5555 - 65frequency 6112123145 SECTION C11.Prove that 5 is an irrational number.12.Find the zeroes of the quadratic polynomial 2x2 – (2√3 – 1)x - √3 and verify the relationship between the zeroes and the coefficients.13.The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?14.If secA = 1312 , than calculate all other trigonometric ratios. 15.If tan2A = cot(A + 600), find the value of A, where 2A is an acute angle.16.Prove that (sinA + cosecA)2 + (cosA + secA)2 = 7 + tan2A + cot2A 17.In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that42989508191500ar(ABC)ar(DBC)= AODO18.In an equilateral triangle ABC, D is a point on side BC such that BD = 13 BC. Prove that 9AD2 = 7 AB2.19.Find the mean of the following frequency distribution using step deviation method.Class interval0 - 55 - 1010 - 1515 - 2020 - 25frequency3573220.A survey was conducted regarding the heights of students of class X in a school and the recorded is as follows. Find the median of the data.Height (in cm)135 - 140140 - 145145 - 150150 - 155155 - 160160 - 165Number of students47201165 SECTION D21.Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. 22.Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.23.24.Obtain all other zeroes of 3x4 + 6x3- 2x2 -10x – 5, if two of its zeroes are 53 and-53 .25.Prove that If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.26.In the figure, O is any point inside a rectangle ABCD. Prove that OB2 + OD2 = OA2 + OC2.3194050965200027.Show that : tanθ1-cotθ+ cotθ1-tanθ=1+secθcosecθ28.Find the value of y if: 4sec2590θ-cot23103-2sin9003+3tan2560tan2340= y329.Prove that:secθsecθ+tanθ+ tanθsecθ-tanθ= secθsecθ-tanθ- tanθsecθ+tanθ= 1+sin2θ1-sin2θ 30.The following distribution gives the daily income of 50 workers of a factory:Daily income (in Rs)100-120120-140140-160160-180180-200No.of workers28122438Convert the distribution above to a less than type Cumulative frequency distribution, and draw its Ogive.31.If the median of the distribution given below is 28.5, find the values of x and y.Class interval0-1010-2020-3030-4040-5050-60Totalfrequency5x2015y560 ********************* ................
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