Important Instructions for the School Principal (Not to be printed with the question paper) ) This question paper is strictly meant for use in school based SA-I, September-202 only. This question paper is not to be used for any other purpose except mentioned above under any circumstances. 2) 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. 3) 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-202, 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 of 0
I, 202 SUMMATIVE ASSESSMENT I, 202 MA2-040 / MATHEMATICS X / Class X 3 90 Time allowed : 3 hours Maximum Marks : 90 (i) (ii) 34 8 6 2 0 3 0 4 (iii) 8 (iv) 2 3 (v) 3 4 2 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section-A comprises of 8 questions of mark each, Section-B comprises of 6 questions of 2 marks each, Section-C comprises of 0 questions of 3 marks each and Section-D comprises of 0 questions of 4 marks each. (iii) Question numbers 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 question of two marks, 3 questions of three marks each and 2 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 2 of 0
8 SECTION A Question numbers to 8 carry one mark each. For each question, four answer choices have been provided of which only one is correct. You have to select the correct answer.. 6243 3 4 2 5 (A) 4 (B) 3 (C) 2 (D) 6243 The decimal expansion of the rational number 3 4 2 5 will terminate after : (A) 4 places of decimal (B) 3 place of decimal (C) 2 places of decimal (D) one place of decimal 2. f (x) x 2 7x8 (A) 6 (B) 8 (C) 8 (D) If is a zero of the polynomial f (x) x 2 7x8, then the other zero is : (A) 6 (B) 8 (C) 8 (D) 3. ABC DEF 2ABDE BC8 EF (A) 2 (B) 4 (C) 6 (D) 8 If triangle ABC is similar to triangle DEF such that 2ABDE and BC8 cm, then EF is equal to : (A) 2 cm (B) 4 cm (C) 6 cm (D) 8 cm 4. 2 2 cot cos (A) (B) 0 (C) The value of 2 2 is : cot cos (A) (B) 0 (C) (D) (D) 5. (HCF) (A) (B) 3 (C) 2 (D) 4 The HCF of the smallest composite number and the smallest prime number is : (A) (B) 3 (C) 2 (D) 4 6. ad bc axbyp cxdyq (A) (B) (C) (D) 2 If ad bc, then the pair of linear equations axbyp and cxdyq has : (A) no solution (B) infinitely many solutions (C) unique solution (D) exactly 2 solutions Page 3 of 0
7. coseccot 4 coseccot (A) 4 (B) If coseccot, then the value of coseccotis : 4 4 (C) (D) (A) 4 (B) 4 (C) (D) 8. (A) (C) (B) (d) The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curve of a grouped data is : (A) mean (B) median (C) mode (d) half of the total frequency 9 4 2 Question numbers 9 to 4 carry 2 marks each. / SECTION-B 9. 4 n, n n (0) Show that the number 4 n, when n is a natural number cannot end with the digit zero for any natural number, n. 0. f(x)abx 2 (b 2 ac)xbc Find the zeroes of the quadratic polynomial f(x)abx 2 (b 2 ac)xbc.. ABC A BC AD AD 2 3BD 2. In an equilateral triangle ABC, AD is drawn perpendicular to BC meeting BC in A. Prove that AD 2 3BD 2. 2. 2cosec 2 303sin 2 60 3 4 tan2 30. Evaluate : 2cosec 2 303sin 2 60 3 4 tan2 30. 3. m n 3x 2 m n x4 n m If m and n are the zeroes of the polynomial 3x 2 x4, find the value of m n n m Page 4 of 0
4. p q (f) (cf) 00-200 200 300 2 p 300 400 0 33 400 500 q 46 500 600 20 66 600 700 4 80 In the following data, find the values of p and q. Also find the median class and modal class. Class Frequency (f) 00-200 200 300 2 p 300 400 0 33 400 500 q 46 500 600 20 66 600 700 4 80 Cumulative frequency (cf) /OR 0020 2 2040 4 4060 8 6080 6 80200 0 Find the mode of the following data : Class frequency 0020 2 2040 4 4060 8 6080 6 80200 0 5 24 3 Question numbers 5 to 24 carry 3 marks each. SECTION-C 5. ABC AB AC P Q AP3.5 PB7 AQ3 QC6 PQ4.5 BC Page 5 of 0
In the given figure, P and Q are points on the sides AB and AC respectively of ABC, such that AP3.5 cm ; PB7 cm ; AQ3 cm and QC6 cm. If PQ4.5 cm, find BC. 6. 3x 2 8x2k k If one zero of a polynomial 3x 2 8x2k is seven times the other, find the value of k. 7. 65 7 (HCF) 65m 7 m 65 7 (LCM) The HCF of 65 and 7 is expressible in the form 65 m 7. Find the value of m. Also find the LCM of 65 and 7 using prime factorization method. /OR n n n2 or n4 3 Show that one and only one out of n, n2 or n4 is divisible by 3, where n is any positive integer. 8. 2 2 cos 45 cos 45 tan60 tan30 2 2 cos 45 cos 45 Evaluate : tan60 tan30 cosec 75 sec 5 cosec 75 sec 5 9. 3x 3 4x 2 5x3 g(x) 3x0 6x43 g(x) On dividing a polynomial 3x 3 4x 2 5x3 by a polynomial g(x), the quotient and the remainder were (3x0) and (6x43) respectively. Find g(x). 20. x, y 4x93y89 ; 93x4y45 Solve the following pair of linear equations for x and y : 4x93y89 ; 93x4y45 /OR Page 6 of 0
a b 2x3y7 ; (ab)x (ab3)y4ab For what values of a and b will the following system of linear equations has infinitely many solutions? 2x3y7 ; (ab)x (ab3)y4ab 2. 4.7 p q 0 6 6 2 2 8 8 24 24 30 30 36 36 42 0 p 4 7 q 4 40 If the mean of the following data is 4.7, find the values of p and q. Class 0 6 6 2 2 8 8 24 24 30 30 36 36 42 Total Frequency 0 p 4 7 q 4 40 22. ABC DBC BC AD BC O ABC AO DBC DO In the given figure, ABC and DBC are on the same base BC. AD and BC intersect at O. Prove that ar ABC AO ar DBC DO DBBC ; DEAB ACBC / OR BE AC DE BC In the given figure, DBBC ; DEAB and ACBC. Prove that BE AC DE BC Page 7 of 0
23. 3 3 3 3 Prove that cos sin cos sin 2 cos sin cos sin 3 3 3 3 cos sin cos sin 2 cos sin cos sin 24. 00 50 60 8 60 70 0 70 80 2 80 90 6 90 00 8 00 0 4 0 20 2 20 30 0 The following table shows the weights (in gms) of a sample of 00 apples, taken from a large consignment. Weight (in gms) No. of apples 50 60 8 60 70 0 70 80 2 80 90 6 90 00 8 00 0 4 0 20 2 20 30 0 Find the median weight of apples. 25 34 4 Question numbers 25 to 34 carry 4 marks each. / SECTION-D 25. 4q 4q2 4q 4q3 q Show that any positive even integer is of the form 4q or 4q2 and any positive odd integer is of the form 4q or 4q3 where q is any integer. Page 8 of 0
26. 2xy4 2xy4 y - Solve the following pair of linear equations graphically : 2xy4 2xy4 Also find the co-ordinates of the vertices of the triangle formed by the lines with y-axis. 27. xr sinacosc ; yr sinasinc zr cosa r 2 x 2 y 2 z 2 If xr sina cosc ; yrsinasinc and zr cosa, prove that r 2 x 2 y 2 z 2 28. 39 f 5 5 5 25 25 35 35 45 45 55 55 65 65 75 2 3 f 7 4 2 2 Find the missing frequency f for the following data if the mode for the following data is 39. Class 5 5 5 25 25 35 35 45 45 55 55 65 65 75 Frequency 2 3 f 7 4 2 2 29.A. 3x 4 5x 3 7x 2 5x6 3 3 Find all the zeros of the polynomial 3x 4 5x 3 7x 2 5x6 if two of its zeros are and 3. /OR 3 B 6 3 8 5 A two digit number is obtained by either multiplying the sum of digits by 8 and then subtracting 5 or by multiplying the difference of digits by 6 and adding 3. Find the number. 30. Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides. /OR Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Page 9 of 0
3. sin sin 2sec sin sin Prove that sin sin 2sec sin sin 32. ABC B D BC AC 2 4AD 2 3AB 2 Triangle ABC is right angled at B and D is the mid-point of BC. Prove that : AC 2 4AD 2 3AB 2 33. 34. 4sin3 If 4 sin 3, find the value of x if x 2 2 cosec cot 7 2cot cos 2 sec x 2 2 cosec cot 7 2cot cos 2 sec x 50 55 55 60 60 65 65 70 70 75 75 80 2 8 2 24 38 6 Change the following distribution to a more than type distribution and then draw its ogive. Class : 50 55 55 60 60 65 65 70 70 75 75 80 Frequency : 2 8 2 24 38 6 Also, find the median from the ogive. - o O o - Page 0 of 0