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KENDRIYA VIDYALAYA SANGATHAN(HYDERABAD REGION)SUMMATIVE ASSESSMENT – 1 (2015-16)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 A2568575286385001.The graph of y = p(x) is given in the figure, for some polynomial p(x). Find the number of zeroes of p(x). 2. Find the value of (tan1° tan2° tan3° ... tan89°).3.In the Fig., ?ODC ~ ?OBA, BOC = 125° and CDO = 70°. Find OAB. 4. For the following distribution, find the modal class: MarksBelow 10Below 20Below 30Below 40Below 50No. of students312275775 SECTION B5.Using Euclid’s division algorithm, find whether the following pair of numbers is co-prime or not.231, 396. 6.If p and q are the zeroes of the polynomial 2x2 – 7x +3, find p2 + q2. 7.For which value of k will the following pair of linear equations have no solution? 3x + y =1(2k -1)x + (k – 1)y = 2k + 13681730-106045008.In the Fig., if LM || CB and LN || CD, prove thatAMAB= ANAD 9.Evaluate: 2 tan2 45° + cos2 30° – sin2 60°10. Find the mode of the following data:Family size1-33-55-77-99-11No. of families78221 SECTION C11.Prove that 2+5 is an irrational number.12.Solve the following pair of linear equations graphically. 3x – 2y – 1 = 0 2x – 3y + 6 = 0Shade the region bounded by the lines and x-axis.13.Find the zeroes of the polynomial x2 + 7x + 10 and verify the relationship between the zeroes and the coefficients.14.Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.15.In an equilateral triangle ABC, D is a point on side BC such that BD = 13 BC. Prove that 9AD2 = 7 AB2.16.Prove that (sin4– cos4 +1) cosec2 = 2 17.Without using trigonometric tables, evaluate of the following: sin?(900 - θ)sinθtanθ + sin2 200+sin2 700cos2 200+cos2 700 + cos(900 - θ)cosθcotθ18.If A, B and C are interior angles of a triangle ABC, then show that sinB+C2=cosA2.19.Find the mean for the following data: Marks20-3030-4040-5050-6060-7070-80Number of students561053120.Find the missing frequency f for the following data if the mode for the data is 39 (f < 7).classes5-1515-2525-3535-4545-5555-6565-75frequency23f7422 SECTION D21.Find all the zeroes of 2x4 – 3x3 – 3x2 + 6x – 2, if you know that two of its zeroes are √2 and ? √2 . 22.2 women and 5 men can together finish an embroidery work in 4 days, while 3women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. What is the value of team work?23.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.24.Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.25.If secθ + tanθ =p, then prove that sinθ = p2- 1p2+ 1.26.If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium.27.Solve the following pair of linear equations. (a – b)x + (a + b)y = a2 – 2ab – b2 (a + b)(x + y) = a2 + b228.If anθ=78 , evaluate: (1+sinθ)(1-sinθ)(1+cosθ)(1-cosθ)29.The following table gives production yield per hectare of wheat of 100 farms of a village.Production(in kg/ha)50-5555-6060-6565-7070-7575-80No.of farms2812243816Change the distribution to a more than type distribution; draw its ogive and find the median.30.Prove that (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A31.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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