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-0 / 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. a b 00 a b (A) 0 (B) 1000 (C) 00 (D) 19 The HCF of two numbers a and b is and their LCM is 00. Then the product of a and b is : (A) 0 (B) 1000 (C) 00 (D) 19. x x4 (A) (B) (C) 0 (D) The number to be added to the polynomial x x4, so that is the zero of the polynomial is : (A) (B) (C) 0 (D). 4 : (A) 16 : 6 (B) : (C) : (D) 6 : 16 If the ratio of the perimeters of two similar triangles is 4 :, then the ratio of the areas of the similar triangles is : (A) 16 : 6 (B) : (C) : (D) 6 : 16 4. sin A 1 tan 4 A A (A) 60 (B) 4 (C) 0 (D) 1 If sin A 1 tan 4, where A is an acute angle, then the value of A is : (A) 60 (B) 4 (C) 0 (D) 1. (A) 6 (B) 4 (C) The rational number between and is : 6 (A) (B) (C) 4 (D) (D) 9 9 6. (A) (C) x4y7 9 1 x6y 0 (B) The pair of linear equations x4y7 and 9 1 x6y 0 has : (A) infinite number of solutions (B) no solution (C) a unique solution (D) two solutions (D) Page of 9
7. cosec cot p p (A) (B) 1 (C) 0 (D) If cosec and cot p, where is an acute angle, then the value of p is : (A) (B) 1 (C) 0 (D) 8. 101 10 0 0 0 0 7 1 (A) 4 (B) 0 (C) (D) 6 For the following distribution : Class 101 10 0 0 0 Frequency 0 7 1 The sum of the lower limit of the median class and the lower limit of the modal class is : (A) 4 (B) 0 (C) (D) 6 9 14 Question numbers 9 to 14 carry two marks each. / SECTION-B 9. 4q1 4q q Show that any positive odd integer is of the form 4q1 or 4q, where q is some integer. 10. p(x) g(x) p(x)4x 8x 8x7 g(x)x x1 Find the quotient and remainder on dividing p(x) by g(x) p(x)4x 8x 8x7 ; g(x)x x1 11. CBQR CAPR AQ1 AR0 PBCQ1 PC BR In the given figure, CBQR and CAPR. If AQ1 cm, AR0 cm, PBCQ1 cm, calculate PC and BR. Page 4 of 9
1. 6sin sec79 tan48 cosec11 cot4 6cos67 6sin sec79 tan48 Evaluate : cosec11 cot4 6cos67 1. p(x) x1 (x) p(x) On dividing a polynomial p(x) by x1, the quotient is x and the remainder is. Find p(x). 14. X 0 1010 10140 14010 10160 160170 8 1 0 8 0 The data regarding the heights of 0 girls of class X of a school is given below : Heights (in cm ) 1010 10140 14010 10160 160170 Total Number of girls 8 1 0 8 0 Change the above distribution to more than type distribution. 9.7 Write the relationship connecting three measures of central tendencies. Hence find the median of the given data if mode is 4. and mean is 9.7 4. 1 4 SECTION-C Question numbers 1 to 4 carry three marks each. 1. PQR PR QR S T P RTS RPQ RTS S and T are respectively the points on sides PR and QR of PQR such that P RTS. Show that RPQ RTS 16. p(x)x 11x 1 1 If and are zeroes of the polynomial p(x)x 11x, find the value of 1 1 17. 160 744 Find the HCF of 160 and 744 using Euclid s division algorithm. Prove that is irrational. 18. sinsin 1 cos cos 4 1 If sinsin 1, prove that cos cos 4 1 Page of 9
19. p(x)x 1x x g(x)x 11x10 What must be subtracted from the polynomial p(x)x 1x x so that the resulting polynomial is exactly divisible by g(x)x 11x10. 0. a b xy0, (ab)x (a7b) y00 Find the values of a and b for which the following pair of linear equations has infinitely many solutions. xy0, (ab)x(a7b)y00 x y 1x78y74 78x1y604 Solve for x and y : 1x78y74 78x1y604 1. 100 010 100 00 040 400 1 0 0 10 The following table shows the marks secured by 100 students in an examination : Marks 010 100 00 040 400 Number of students 1 0 0 10 Find the mean marks obtained by a student.. DEAC DFAE BF FE BE EC In the given figure, DEAC and DFAE. Prove that BF FE BE EC Page 6 of 9
ar (CED) : ar (AOB) CE DE, O AOB90 In the given figure CE and DE are equal chords of a circle with center O. If AOB90, find ar(ced) : ar (AOB). 1 sin (90 ) 4 4 sin (90 ) sin Prove that 1 sin (90 ) 4 4 sin (90 ) sin 4. 010 100 00 040 400 6 8 7 9 4 For the following distribution, find the median : Class 010 100 00 040 400 Frequency 6 8 7 9 4 4 4 / SECTION-D Question numbers to 4 carry four marks each.. n, n, n4 n Show that one and only one out of n, n, n4 is divisible by, where n is any positive integer. 6. xy1 ; xy8 y Solve the following pair of linear equations graphically : xy1 xy8 Also find the co-ordinates of the points where the lines, represented by the above equation, intersect y axis. Page 7 of 9
7. 1 sina sinb 1 cos A cosb 10 cos (AB)cosA. cosb sina. sinb AB4 1 1 If sina and sinb,, find the values of cosa and cosb. Hence using the formula 10 cos (AB)cosA. cosbsina. sinb, show that AB4 8. 8. x y 010 100 00 040 400 060 x 0 1 y 60 If the median of the distribution given below is 8., find the values of x and y : Classes 010 100 00 040 400 060 Total Frequency : x 0 1 y 60 9. x 4 6x x 10x obtain all other zeroes of the polynomial x 4 6x x 10x, if two of its zeroes are and 7 6 In a bag containing red and white balls, half the number of white balls is equal to one third the number of red balls. Thrice the total number of balls exceeds seven times the number of white balls by 6. How many balls of each colour does the bag contain? 0. 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. Prove that, in a right triangle, the square of the hypotenuse is equal to sum of the squares of the other two sides. 1. 1 tan A 1 tana tan A 1 cot A 1 cota 1 tan A 1 tana Prove that 1 cot A 1 cota tan A Page 8 of 9
. xy AC ABC AX AB In the given figure, the line segment xy is parallel to the side AC of ABC and it divides the triangle into two parts of equal area. Find the ratio AX AB.. sin tan70 sin sec cos 6 sin6cos 7 cos8 cot0 tan 7tan4tan 8 sin tan70 sinsec Evaluate : cos 6 sin6cos 7 cos8 cot0 tan 7tan4tan 8 4. 0 000 000 000 0400 40040 4000 10 11 8 6 10 The following distribution gives the daily income of 0 workers of a factory : Daily income (in Rs ) 000 000 000 0400 40040 4000 Number of workers 10 11 8 6 10 Convert the distribution to a less than type cumulative frequency distribution and draw its ogive. Hence obtain the median daily income. - o O o - Page 9 of 9