Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for use in school based SA-I, September-01 only. This question paper is not to be used for any other purpose except mentioned above under any circumstances. ) The intellectual material contained in the question paper is the exclusive property of Central Board of Secondary Education and no one including the user school is allowed to publish, print or convey (by any means) to any person not authorised by the board in this regard. ) The School Principal is responsible for the safe custody of the question paper or any other material sent by the Central Board of Secondary Education in connection with school based SA-I, September-01, in any form including the print-outs, compact-disc or any other electronic form. 4) Any violation of the terms and conditions mentioned above may result in the action criminal or civil under the applicable laws/byelaws against the offenders/defaulters. Note: Please ensure that these instructions are not printed with the question paper being administered to the examinees. Page 1 of 9
I, 01 SUMMATIVE ASSESSMENT I, 01 MA-058 / MATHEMATICS X / Class X 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 4 8 1 6 10 10 4 (iii) 1 8 (iv) (v) 4 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 4 questions divided into four sections A, B, C and D. Section-A comprises of 8 questions of 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 10 questions of marks each and Section-D comprises of 10 questions of 4 marks each. (iii) Question numbers 1 to 8 in Section-A are multiple choice questions where you are required to select one correct option out of the given four. (iv) There is no overall choice. However, internal choices have been provided in 1 question of two marks, questions of three marks each and questions of four marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted. Page of 9
1 8 1 SECTION A Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1. 5 (A) (C) 5 Which of the following rational numbers has terminating decimal expansion? 5 (A) (C) 5. p(x) p(x) (A) x x 9 (C) x x 1 If and are the zeroes of a polynomial p(x), then p(x) is : (A) x x 9 (C) x x 1. ABC PQR ABC 81 AC. PR ar( PQR) 169 (A) 10.4 9 (C) 1 0.8 ABC PQR, if area of ABC 81 cm, ar( PQR) 169 cm and AC. cm, then PR is : (A) 10.4 cm 9 cm (C) 1 cm 0.8 cm 4. tan (A) 0 0 (C) 60 90 tan is not defined when is equal to : (A) 0 0 (C) 60 90 5. 5 (A) (C) 5 is : (A) a natural number an integer (C) a rational number an irrational number 6. x y 6x py 1 0 p (A) 1 1 (C) If the pair of equations x y and 6x py 1 0 has infinite number of solutions, then the value of p is : (A) 1 1 (C) Page of 9
. 5 tan 4 5 sin cos 5 sin cos (A) 0 1 (C) If 5 tan 4, then the value of 5 sin cos 5 sin cos (A) 0 1 (C) is : 1 1 8. 9. 154 0 10 10 0 0 0 0 40 40 50 50 60 8 10 1 0 18 (A) 10 0 0 0 (C) 0 40 40 50 The median class of the following frequency distribution is : Classes 0 10 10 0 0 0 0 40 40 50 50 60 Frequency 8 10 1 0 18 (A) 10 0 0 0 (C) 0 40 40 50 9 14 Question numbers 9 to 14 carry two marks each. Express 154 as the product of its prime factors. 10. p(x) x 5x 1 / SECTION-B Find the sum and product of the zeroes of the polynomial p(x) x 5x 1. 11. : If the altitudes of two similar triangles are in the ratio of : then find the ratio of their areas and also the ratio of their corresponding medians. 1. tan 45 sin 45 cos 45 tan 45 Evaluate : sin 45 cos 45 1. Find the polynomial whose zeroes are and. 14. 140 0 10 10 0 0 0 0 40 40 50 0 4 40 6 0 Page 4 of 9
The following frequency distribution shows marks secured by 140 students in an examination : Marks 0 10 10 0 0 0 0 40 40 50 Number of students 0 4 40 6 0 Calculate the mode of this distribution. 0 10 10 0 0 0 0 40 40 50 1 10 15 8 11 For the following frequency distribution, find the upper limit of the median class : Classes 0 10 10 0 0 0 0 40 40 50 Frequency 1 10 15 8 11 15 4 SECTION-C Question numbers 15 to 4 carry three marks each. 15. ABC PQR AD PM ABC PQR AB AD PQ PM If AD and PM are medians of triangles ABC and PQR, respectively, where ABC PQR, then prove that AB AD PQ PM. 16. x 5x 1 1 If and are the zeroes of the polynomial x 5x, then form a polynomial whose zeroes are 1 and 1. 1. 91 18 18. Find the HCF and LCM of the number 91 and 18 and verify : HCF LCM product of the two numbers. m m 1 m Show that the square of any positive integer is of the form m or m 1 for some integer m. (cos 5 cos 65 ) cosec. sec(90 ) cot. tan(90 ) Without using trigonometric tables evaluate the following : (cos 5 cos 65 ) cosec. sec(90 ) cot. tan(90 ) 19. (6x 19x x 11) (6x x ) Page 5 of 9
Divide the polynomial (6x 19x x 11) by (6x x ) and verify the result by division algorithm. 0. x y m y mx 1. 6 x 5 ; x 6 y y Solve the following pair of equations for x and y, also find the value of m such that y mx. 6 x 5 ; x 6 y y x y x y 14 x y 15 Solve for x and y : x y 14 and x y 15 0 10 10 0 0 0 0 40 40 50 50 60 60 0 6 8 10 15 5 4 Find the mean of the following data : Classes 0 10 10 0 0 0 0 40 40 50 50 60 60 0 Frequency 6 8 10 15 5 4. ABC CA CB D E C AE BD AB DE D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove AE BD AB DE ar(abc) ar(dbc) BC ABC DBC AD, BC O AO DO In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show ar(abc) AO ar(dbc) DO. tana tana seca 1 seca 1 coseca Page 6 of 9
Prove that : tana tana seca 1 seca 1 coseca 4. p 0 10 10 0 0 0 0 40 40 50 1 16 6 p 9 If the arithmetic mean of the following distribution is, then find the value of p : Classes 0 10 10 0 0 0 0 40 40 50 Frequency 1 16 6 p 9 5 4 4 / SECTION-D Question numbers 5 to 4 carry four marks each. 5. Prove that is an irrational number. Hence show that is also an irrational number. 6. x y 1 x y 1 y- Solve the following pair of linear equations graphically : x y 1 and x y 1 Find the area of the region bounded by the two lines representing the above equations and y-axis.. a cos b sin m a sin b cos n (m n ) (a b ). If a cos b sin m and a sin b cos n, prove that (m n ) (a b ). 8. 5 0 10 8 15 16 0 14 5 10 0 5 Find the median of the following data : Page of 9
Profit (in lakhs of rupees) Number of shops More than or equal to 5 0 More than or equal to 10 8 More than or equal to 15 16 More than or equal to 0 14 More than or equal to 5 10 More than or equal to 0 More that or equal to 5 9. 6x 4 x 0x x 6 Find the other zeroes of the polynomial 6x 4 x 0x x 6, if two of its zeroes are and. If is subtracted from the numerator and 1 is added to the denominator, a fraction becomes 1, but when 4 is added to the numerator and is subtracted from the denominator, it becomes. Find the fraction. 1 4 0. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Prove the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. 1. cosec 5 (i) cot cosec (ii) sin cos 1 If is an acute angle and cosec 5 (i) evaluate cot cosec (ii) verify the identity sin cos 1. ABC AB, BC, CA D, E F DEF CAB D, E, F are respectively the mid-points of the sides AB, BC, CA of ABC. Find ratio of areas DEF and CAB.. cosa sin A 1 tana sina cosa sina cosa Page 8 of 9
Prove that : cosa sin A 1 tana sina cosa sina cosa 4. 10 0 10 10 0 0 0 0 40 40 50 50 60 14 1 6 18 The following table gives the weight of 10 articles : Weight (in g) 0 10 10 0 0 0 0 40 40 50 50 60 Number of articles 14 1 6 18 Change the distribution to a more than type distribution and draw its ogive. - o O o - Page 9 of 9