Important Instructions for the School Principal. (Not to be printed with the question paper)

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1 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. 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-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

2 I, 01 SUMMATIVE ASSESSMENT I, 01 MA-01 / MATHEMATICS X / Class X 3 90 Time allowed : 3 hours Maximum Marks : 90 (i) (ii) (iii) 1 8 (iv) 3 (v) 3 4 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 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 10 questions of 3 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, 3 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

3 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 (A) 0.15 (B) (C) (D) in decimal form is : 8 (A) 0.15 (B) (C) (D) p(x)4x 1x9 (A) 3, 3 (B) 3, 3 (C) 3, 4 (D) 3, 4 The zeroes of the polynomial p(x)4x 1x9 are : 3 (A), 3 (B) 3, 3 (C) 3, 4 (D) 3, 4 3. ABC PQR x (A).5 (B) 3.5 (C).75 (D) 3 In the given figure if ABC PQR The value of x is : (A).5 cm (B) 3.5 cm (C).75 cm (D) 3 cm 4. xa cos, yb sin b x a y a b (A) 1 (B) 1 (C) 0 (D) ab If xa cos, yb sin, then b x a y a b is equal to : (A) 1 (B) 1 (C) 0 (D) ab Page 3 of 9

4 (A) (B) (C) (D) 5 A rational number which has non terminating decimal representation is : (A) (B) (C) (D) xa, yb xy xy4 a b (A) 3, 5 (B) 5, 3 (C) 3, 1 (D) 1, 3 If xa, yb is the solution of the pair of equation xy and xy4, then the respective values of a and b are : (A) 3, 5 (B) 5, 3 (C) 3, 1 (D) 1, 3 7. sin 60sin 30 (A) 1 4 (B) 1 (C) 3 4 (D) 1 The value of sin 60sin 30 is : 1 1 (A) (B) 4 (C) 3 4 (D) (A) 17 (B) 18 (C) 17.5 (D) 15 The class mark of the class 10 5 is : (A) 17 (B) 18 (C) 17.5 (D) Question numbers 9 to 14 carry two marks each / SECTION-B Find the HCF of 55 and 867 by Euclid division algorithm. 10. f(x)x 7x3 p, q p q If p, q are zeroes of polynomial f(x)x 7x3, find the value of p q. 11. PQR QPR90, PQ4 QR6 PKR PKR90, KR8 PK In the given triangle PQR, QPR90, PQ4 cm and QR6 cm and in PKR, Page 4 of 9

5 PKR90 and KR8 cm find PK. 1. sina 3 cot A1 If sina 3, find the value of cot A Find the quadratic polynomial whose zeroes are and Find the mean of the following frequency distribution : Class : Frequency : Find the mode of the following frequency distributions : Class : Frequency : SECTION-C Question numbers 15 to 4 carry three marks each. 15. Prove that the sum of squares on the sides of a rhombus is equal to sum of squares on its diagonals x 4x3 1 Show that and 3 are the zeroes of the polynomial 4x 4x3 and verify the relationship between zeroes and co-efficients of polynomial. Page 5 of 9

6 Prove that is an irrational number. a b Express the number in the form of rational number a b. 18. cos50 4 cosec 59 tan 31 tan1 tan78.sin90 sin40 3tan 45 3 Find the value of the following without using trigonometric tables : cos50 4 cosec 59 tan 31 tan1 tan78.sin90 sin40 3tan b (x3) x 3 9x xb Find the value of b for which (x3) is a factor of x 3 9x xb 0. 3x5y0, 6x10y400 Using graph, find whether the pair of linear equations 3x5y0, 6x10y400 is consistence or inconsistent. Write its solution. x y x1 y 5 1, x 1, y x1 y Solve for x and y : x1 y 5 1, where x 1, y x1 y 1. 7 p p If the mean of the following distribution is 7, find the value of p : Class : Frequency : 8 p If the areas of two similar triangles are equal, then prove that they are congruent. Page 6 of 9

7 QRAD. ABC DBC BC PQBA PRBD In the given figure, two triangles ABC and DBC lie on same side of BC such that PQBA and PRBD. Prove that QRAD. 3. sin3cos(6), If sin3cos(6), where 3 and 6 are both acute angles, find the value of Find mean, and median for the following data : Class : Frequency : / SECTION-D Question numbers 5 to 34 carry four marks each. 5. 3n 3n1 By Euclid division algorithm, show that square of any positive integer is of the form 3n or 3n1. 6. k 3xy1 (k1)x(k1)yk1 For what value of k will the pair of equations have no solution? 3xy1 (k1)x(k1)yk1 Page 7 of 9

8 7. (secatana) (1sinA)1sinA Prove that (secatana) (1sinA)1sinA Draw less than and more than ogives for the following distribution : Scores : Frequency : Hence find they median. Verify the result through calculations. 9. p(x)8x 4 14x 3 x 8x1 4x 3x p(x) What must be subtracted or added to p(x)8x 4 14x 3 x 8x1 so that 4x 3x is a factor of p(x)? x y 133x87y353 87x133y307 Solve for x and y 133x87y353 and 87x133y ABC AB AC P Q PQ BC A BC AD PQ In ABC, P and Q are the points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that median AD drawn from A to BC bisects PQ also. ABC ADBC 3AB 4AD. In an equilateral ABC, ADBC. Prove that 3AB 4AD. 31. sincosm seccosecn, n(m 1)m If sincosm and seccosecn, then prove that n(m 1)m 3. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides. 33. tan sin sec 1 tan sin sec 1 tan sin sec 1 Prove that : tan sin sec 1 Page 8 of 9

9 34. f f , 8, f 1 1 Find the value of f 1 from the following data if its mode is 65 : Class Frequency 6 8 f where frequency 6, 8, f 1 and 1 are in ascending order. - o O o - Page 9 of 9

10 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. 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-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

11 I, 01 SUMMATIVE ASSESSMENT I, 01 MA-05 / MATHEMATICS X / Class X 3 90 Time allowed : 3 hours Maximum Marks : 90 (i) (ii) (iii) 1 8 (iv) 3 (v) 3 4 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 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 10 questions of 3 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, 3 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

12 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 (A) 1 (B). 3 (C) 3 (D) 4 The decimal expansion of 189 will terminate after : 15 (A) 1 place of decimal (B) places of decimal (C) 3 places of decimal (D) 4 places of decimal (A) (B) (C) (D) The maximum number of zeroes that a polynomial of degree 3 can have is : (A) One (B) Two (C) Three (D) None 3. ABC PQR PQ9 AB 4. sin (A) 6 (B) 10 (C) 15 (D) 4 The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ9 cm, then AB equals : (A) 6 cm (B) 10 cm (C) 15 cm (D) 4 cm 1 3 (A) (B) The maximum value of sinis : (A) 1 (B) 3 (C) 1 (D) (C) 1 (D) (A) 40 (B) 480 (C) 10 (D) 960 The least positive integer divisible by 0 and 4 is : (A) 40 (B) 480 (C) 10 (D) xy6 y- (A) (, 0) (B) (0, 3) (C) (, 0) (D) (0, 3) The point of intersection of the lines represented by 3xy6 and the y-axis is : (A) (, 0) (B) (0, 3) (C) (, 0) (D) (0, 3) Page 3 of 9

13 7. 8. A, B C ABC tan A B (A) sin C (B) cos C C (C) cot (D) tan C If A, B and C are interior angles of a ABC, then tan A B equals : (A) sin C (B) cos C (C) cot C (D) tan C (0.5, 15.5) (A) 36.0 (B) 0.5 (C) 15.5 (D) 5.5 If the less than type ogive and more than type ogive intersect each other at (0.5, 15.5), then the median of the given data is : (A) 36.0 (B) 0.5 (C) 15.5 (D) 5.5 / SECTION-B 9 14 Question numbers 9 to 14 carry two marks each. 9. (867, 55) Find the HCF (867, 55) using Euclid s division lemma Write the quadratic polynomial whose zeroes are 4 5 and ABCD ABCDEF, AE BF ED FC In the given figure, if ABCD is a trapezium in which ABCDEF, then prove that AE BF. ED FC 1. sin 3 cos Find the value of cos if sin 3. Page 4 of 9

14 13. 4t 5 Find the zeroes of the polynomial 4t Find the sum of lower limit of mediun class and the upper limit of model class : Classes : Frequency : Convert the following data into more than type distribution : Class : Frequency : SECTION-C Question numbers 15 to 4 carry three marks each. 15. ADBC AB CD BD AC In the given figure, if ADBC, prove that AB CD BD AC 16. x 6xa a If and are zeroes of the polynomial x 6xa, find a if. Page 5 of 9

15 17. x, y z y z 'x' Find the value of x, y, and z in the following factor tree. Can the value of 'x' be found without finding the value of y and z, if yes, explain : Prove that is irrational. 18. cosec 13 sin 3 cos 1 4 sin 9 cos If cosec 13 sin 3 cos, then evaluate 1 4 sin 9 cos. 19. ax 5xc 10 a c If the sum and product of the zeroes of the polynomial ax 5xc is equal to 10 each, find the value of a and c. 0. x5y6 ; x10y1 Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair : x5y6 ; x10y1 x3y7 ; x()y8 Find the value of and for which the following pair of linear equations has infinite number of solutions : x3y7 ; x()y8 Page 6 of 9

16 Compute the mode of the following data : Class : Frequency : ABC AB AC D E BC AD AE. AB AC If a line segment intersects sides AB and AC of a ABC at D and E respectively and is parallel to BC, prove that AD AE. AB AC AOB ABCD ABDC O ABCD COD The diagonals of a trapezium ABCD, in which ABDC intersect at O. If ABCD, then find the ratio of areas of triangles AOB and COD. 3. sina, tana coseca seca 4. Express sina, tana and coseca in terms of seca Draw the less than type ogive for the following data and hence find the median from it. Classes : Frequency : / SECTION-D Question numbers 5 to 34 carry four marks each. 5. n n n Prove that n n is divisible by for every positive integer n. 6. x y : (3xy)5xy ; (x3y)5xy Solve for x and y : (3xy)5xy ; (x3y)5xy 7. sec41.sin49cos49.cosec41 3 tan0tan60tan703(cos 45sin 90) Evaluate : sec41.sin49cos49.cosec41 3 tan0tan60tan703(cos 45sin 90) Page 7 of 9

17 p q p 0 15 q 5 The median of the following frequency distribution is 8.5 and the sum of all the frequencies is 60. Find the values of p and q : Classes : Frequency : 5 p 0 15 q 5 9. x 3 x 13x Show that 3 is a zero of the polynomial x 3 x 13x6. Hence find all the zeroes of this polynomial The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and the breadth is increased by 3 units. The area is increased by 67 square units if length is increased by 3 units and breadth is increased by units. Find the perimeter of the rectangle. Prove that The ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding sides. Prove that In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 31. (sinaseca) (cosacoseca) (1secAcosecA) 3. Prove that (sinaseca) (cosacoseca) (1secAcosecA) If two sides and a median bisecting one of these sides of a triangle are respectively proportional to the two sides and the corresponding median of another triangle, then prove that the two triangles are similar. 33. tana tana coseca seca 1 seca 1 tana tana Prove that : coseca seca 1 seca 1 Page 8 of 9

18 34. ` ` < 100 < 00 < 300 < 400 < Calculate the average daily income (in `) of the following data about men working in a company : Daily income (in `) < 100 < 00 < 300 < 400 < 500 Number of men o O o - Page 9 of 9

19 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. 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-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

20 I, 01 SUMMATIVE ASSESSMENT I, 01 MA-035 / MATHEMATICS X / Class X 3 90 Time allowed : 3 hours Maximum Marks : 90 (i) (ii) (iii) 1 8 (iv) 3 (v) 3 4 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 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 10 questions of 3 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, 3 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

21 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 (A) (C) Decimal expansion of will be : (A) terminating (B) non-terminating (C) non-terminating and repeating (D) non-terminating and non-repeating (B) (D). 5 4 (A) x 5x4 (B) x 5x4 (C) x x0 (D) x 9x0 The polynomial whose zeroes are 5 and 4 is : (A) x 5x4 (B) x 5x4 (C) x x0 (D) x 9x0 3. DEF ABC DE : AB : 3 DEF 44 ABC 176 (A) 99 (B) 10 (C) (D) 66 9 DEF ABC ; If DE : AB : 3 and ar(def) is equal to 44 square units, then area (ABC) in square units is : 176 (A) 99 (B) 10 (C) (D) sin 0tan 453sin 70 (A) 0 (B) 1 (C) (D) 1 3sin 0tan 453sin 70 is equal to : (A) 0 (B) 1 (C) (D) (LCM) (A) 3 (B) 3 3 (C) (D) 3 L.C.M. of 3 3 and 3 3 is : (A) 3 (B) 3 3 (C) (D) 3 6. x, y3 (A) x3y130 (B) 3xy310 (C) x3y130 (D) x3y130 x, y3 is a solution of the linear equation : (A) x3y130 (B) 3xy310 (C) x3y130 (D) x3y130 Page 3 of 9

22 7. sin a b tan (A) a b b (B) b b a (C) a a b (D) a b a, then tan is equal to : (A) Given that sin a b b a b (B) b b a (C) a a b (D) a b a 8. (A) 3 (B) 3 (C) 3 (D) 3 Relationship among mean, median and mode is : (A) 3 MedianMode Mean (B) 3 MeanMedian Mode (C) 3 ModeMean Median (D) Mode3 Mean Median / SECTION-B 9 14 Question numbers 9 to 14 carry two marks each (HCF) Using Euclid s algorithm, find the HCF of 40 and Find a quadratic polynomial whose zeroes are 3 and ABDC x In the given figure, if ABDC, find the value of x. Page 4 of 9

23 1. 3 sincos0 0 < < 90 If 3 sincos0 and 0 < < 90, find the value of Find the quadratic polynomial whose sum and product of the zeroes are respectively and Convert the following distribution to a more than type cumulative frequency distribution : Class : Frequency : Find the mode of the following frequency distribution : Class : Frequency : Question numbers 15 to 4 carry three marks each. SECTION-C 15. D, E F ABC AB, BC CA DEF ABC D, E, F are respectively the mid-point of the sides AB, BC and CA of ABC. Find the ratios of the area of DEF and ABC. 16. x 35x Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the co-efficients x 35x (LCM) (HCF) Find the LCM and HCF of 336 and 54 and verify that LCMHCFProduct of the two numbers. Page 5 of 9

24 847, 160 Using Euclids division algorithm, find whether the pair of numbers 847, 160 are coprimes or not seca sin A seca 1 cosa 1 seca sin A Prove that : seca 1 cosa 19. x 3 11x 3x Find all the zeroes of x 3 11x 3x35, if two of its zeros are 1 and k 3xy1; (k1)x(k1)yk1 For which value of k will the following pair of linear equations have no solution? 3xy1, (k1)x(k1)yk The sum of digits of a two-digit numbers is 7. If the digits are reversed, the new number decreased by equals twice the original number. Find the number Calculate the median for the following distribution : Marks obtained Number of students Below 10 6 Below 0 15 Below 30 9 Below Below Below ABCD, ABDC O ABCD AOB COD Diagonals of a trapezium ABCD with ABDC intersect each other at the point O. ABCD, find the ratio of the area of triangles AOB and COD. If Page 6 of 9

25 Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals tan A cota tana cosec A 1 tan A cota Prove that : tana cosec A Compute the arithmetic mean for the following data : Marks obtained No. of students Less than Less than 0 Less than Less than Less than Less than / SECTION-D Question numbers 5 to 34 carry four marks each. 5. 3m 3m1 m Use Euclids Division Lemma to show that the square of any positive integer is either of the form 3m or 3m1 for some integer m. 6. x3y6 ; x3y1 Check graphically, whether the pair of equations x3y6 ; x3y1 is consistent. If so, than solve them graphically. 7. sec tan 1 cos tan sec 1 1 sin sec tan 1 cos Prove that : tan sec 1 1 sin Page 7 of 9

26 8. N100 3 f 1 f f f Find the missing frequencies f 1 and f in the following frequency distribution table, if N100 and median is 3. Class : Total Frequency : 10 f f x 4 6x 3 16x 5x10 (x xk) xa k a If the polynomial x 4 6x 3 16x 5x10 is divided by (x xk) the remainder comes out to be xa, find k and a. x y Sovle for x and y : 5 1 ; x1 y 5 1 ; x1 y x1 y x1 y 30. ABC DBC BC AD BC O ( ABC) AO. ( DBC) DO In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC ar( ABC) at O, show that AO. ar( DBC) DO If the area of two similar triangles are equal, prove that they are congruent. 31. cot(90 ) sin(90 ) cot 40 cos 0 cos 70 sin tan 50 cot(90 ) sin(90 ) cot 40 cos 0 cos 70 sin tan 50 Evaluate : Page 8 of 9

27 3. Prove that the ratio of the area of two similar triangles is equal to the ratio of the squares of their corresponding sides. 33. cos sin (cos sin ) 1 tan 1 cot cos sin Prove that : (cos sin ) 1 tan 1 cot For the following frequency distribution, draw a cumulative frequency curve of less than type Class : Frequency: o O o - Page 9 of 9

28 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. 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-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

29 I, 01 SUMMATIVE ASSESSMENT I, 01 MA-038 / MATHEMATICS X / Class X 3 90 Time allowed : 3 hours Maximum Marks : 90 (i) (ii) (iii) 1 8 (iv) 3 (v) 3 4 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 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 10 questions of 3 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, 3 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

30 SECTION A Question numbers 1 to 8 carry 1 mark each. In each question, select one correct option out of the given four. 1. (HCF) (a, b)1 ab1800 (LCM )(a, b) (A) 1800 (B) 900 (C) 150 (D) 90 If HCF (a, b)1 and ab1800, then LCM (a, b) is : (A) 1800 (B) 900 (C) 150 (D) 90. x 5x1 (A) (B) 1 (C) 1 (D) 3 If and are the zeroes of the polynomial x 5x1, then the value of is : (A) (B) 1 (C) 1 (D) 3 3. ABC BDE D BC ABC BDE (A) : 1 (B) 1 : (C) 4 : 1 (D) 1 : 4 ABC and BDE are two equilateral triangles such that D is the mid point of BC. Ratio of the areas of triangle ABC and BDE is : (A) : 1 (B) 1 : (C) 4 : 1 (D) 1 : , 0< < 90 sec (A) 1 (B) (C) Maximum value of 1 sec, 0< < 90 is : (A) 1 (B) (C) 1 1 (D) (D) (A), 3 5 (B) 3 (C) 3 5 (D) 5 A rational number can be expressed as a terminating decimal if the denominator has factors : (A), 3 (or) 5 only (B) (or) 3 only (C) 3 (or) 5 only (D) (or) 5 only 6. (A) (B) Page 3 of 9

31 (C) (D) If a pair of linear equations is consistent, then the lines represented by these equations will be : (A) parallel (b) coincident always (C) intersecting (or) coincident (D) intersecting always 7. tan 30 1 tan 30 (A) sin60 (B) cos60 (C) tan60 (D) sin30 tan 30 The value of 1 tan 30 (A) sin60 (B) cos60 (C) tan60 (D) sin (A) 0-40 (B) (C) (D) The median class for the following data is : Class Frequency (A) 0-40 (B) (C) (D) / SECTION-B 9 14 Question numbers 9 to 14 carry marks each (HCF) Find the HCF of 918 and 16 using Euclid s Division Algorithm Form a quadratic polynomial whose one zero is 8 and the product of the zeroes is X Page 4 of 9

32 In the given figures, find the measure of X. 1. ABCD AP AQ APBAQD30 (APAQ) In the given figure, ABCD is a rectangle in which segment AP and AQ are drawn such that APBAQD30. Find the length of (APAQ). 13. p(x)(a 9) x 45x6a a If one zero of the polynomial p(x)(a 9) x 45x6a is reciprocal of the other, find the value of a Find the mode of the following data. Marks obtained : No. of students Write the following frequency distribution as more than type and less than type cumulative frequency distribution. Class : Frequency : Page 5 of 9

33 SECTION-C Question numbers 15 to 4 carry 3 marks each. 15. DEBC DE : BC3 : 5 ADE BCED In the given figure, DEBC. If DE : BC3 : 5, find ar ADE ar trap.bced 16. p(x)(a1)x (a3)x(3a4) 1 If the sum of the zeroes of the polynomial p(x)(a1)x (a3)x(3a4) is 1, then find the product of its zeroes Prove that 3 5 is irrational (HCF) (LCM) Find the HCF and LCM of 404 and 96 and verify HCFLCMProduct of two given numbers. 18. Find the value of : 3 cos 55 4 cos 70. cosec 0. cos 30 7 sin 35 7 tan 5. tan 5. tan 60. tan 65. tan 85 3 cos 55 4 cos 70. cosec 0. cos 30 7 sin 35 7 tan 5. tan 5. tan 60. tan 65. tan 85 Page 6 of 9

34 19. x 3 4x 5x7 g(x) x 75x g(x) On dividing the polynomial x 3 4x 5x7 by a polynomial g(x), the quotient and the remainder were x and 75x respectively. Find g(x). 0. x y 3xy9xy ; 9x4y1xy ; x, y 0. Solve the following pair of equations for x and y : 3xy9xy ; 9x4y1xy ; x, y 0. p q 4x5y ; (p7q)x(p8q)yqp1 For what values of p and q will the following pair of linear equations has infinitely many solutions? 4x5y ; (p7q)x(p8q)yqp Find the median for the following table which shows the daily wages drawn by 00 workers in a factory. Daily wages (in Rs.) Less than 100 Less than 00 Less than 300 Less than 400 Less than 500 No. of workers Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. 3. cot cosec1 sec cosec1 cot cot cosec1 Prove that : sec cosec1 cot f 1 f f 1 30 f The mean of the data in the following table is 50. Find the missing frequencies f 1 and f. Class : Total Frequency : 90 f 1 30 f Page 7 of 9

35 Question numbers 5 to 34 carry 4 marks each. / SECTION-D 5. 1, 7 10 (LCM) (HCF) Find the LCM and HCF of 1, 7 and 10 using prime factorisation. Also show that HCFLCM Product of three given numbers. 6. x3y40 ; x3y80 x Solve the following pair of equations graphically : x3y40 ; x3y80 Also shade the region formed by the lines with the xaxis. 7. cossinp seccosecq q(p 1)p If cossinp and seccosecq, prove that q(p 1)p 8. a, b, c, d, e f b 10 d e 50 a 5 c f Find the unknown entries a, b, c, d, e and f in the following distribution and hence find their mode. Height (in cm) : Total Frequency : 1 b 10 d e 50 Cumulative frequency : a 5 c f 9.A x 4 5x 3 x 10x8 Find the other zeroes of the polynomial x 4 5x 3 x 10x8 if it is given that two of its zeroes are and. 9.B 11 : 7 9 : The ratio of incomes of two persons is 11 : 7 and the ratio of their expenditures is 9 : 5. If each of them manages to save Rs. 400 per month, find their monthly incomes. Page 8 of 9

36 30. 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 triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle. 31. sec A sin A 3 tan A 8 4 cos A tan A If sec A 17 8, verify that : 3 4 sin A 3 tan A 4 cos A tan A 3. ABC XYAC ABC AX AB In the given figure, XYAC in triangle ABC and it divides the triangle into two parts of equal area. Find AX AB tan 4 sec 3 (seccosec) sin 34. If 15 tan 4 sec 3, then find the value of (seccosec) sin Convert the following distribution into a less than type cumulative frequency distribution and draw its ogive. Also find the median from the ogive. Class : Frequency : o 0 o - Page 9 of 9

37 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. 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-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

38 I, 01 SUMMATIVE ASSESSMENT I, 01 MA-039 / MATHEMATICS X / Class X 3 90 Time allowed : 3 hours Maximum Marks : 90 (i) (ii) (iii) 1 8 (iv) 3 (v) 3 4 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 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 10 questions of 3 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, 3 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

39 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 3 q r a 3q r, r (a) 0 r < 3 (b) 1 < r < 3 (c) 0 < r < 3 (d) 0 < r 3 For any positive integer a and 3, there exist unique integers q and r such that a 3q r, where r must satisfy. (a) 0 r < 3 (b) 1 < r < 3 (c) 0 < r < 3 (d) 0 < r 3. 3x kx 6 3 k (a) 9 (b) 3 (c) 3 (d) 6 If the sum of the zeroes of the quadratic polynomial 3x kx 6 is 3, then the value of k is : (a) 9 (b) 3 (c) 3 (d) 6 3. ABC PQR ABC 3 PQR 48 PR 6 AC (a) 9 (b) 4 (c) 8 (d) 18 If ABC PQR, perimeter of ABC 3 cm, perimeter of PQR 48 cm PR 6 cm, then the length of AC is equal to : (a) 9 cm (b) 4 cm (c) 8 cm (d) 18 cm 4. tancot 5 tan cot (a) 3 (b) 5 (c) 7 (d) 15 If tancot 5, then the value of tan cot is : (a) 3 (b) 5 (c) 7 (d) (a) (c) is : 7 (a) a rational number (b) an irrational number (c) a prime number (d) an even number (b) (d) and 6. 4x3y 14 (a) 3x4y 14 (b) 8x6y 8 (c) 1x9y 4 (d) 1x9y Page 3 of 9

40 Two lines are given to be parallel. The equation of one of the lines is 4x3y 14. The equation of the second line can be : (a) 3x4y 14 (b) 8x6y 8 (c) 1x9y 4 (d) 1x9y 7. seca cosec(a 7) A A (a) 35 (b) 37 (c) 39 (d) 1 If seca cosec(a 7) where A is an acute angle, then the measure of A is : (a) 35 (b) 37 (c) 39 (d) 1 8. (a) (c) Mode is the value of the variable which has : (a) maximum frequency (b) minimum frequency (c) mean frequency (d) middle most frequency (b) (d) 9 14 / SECTION-B Question numbers 9 to 14 carry two marks each. 9. HCF) (LCM) HCF and LCM of two numbers is 9 and 459 respectively. If one of the number is 7, find the other number Form a quadratic polynomial whose zeroes are 3 and ABC AB AC P 1 DEF DE DF P ( ABC ) ( DEF ) The sides AB and AC and the perimeter P 1 of ABC are respectively three times the corresponding sides DE and DF and the perimeter P of DEF. Are the two triangles ar ( ABC ) similar? If yes, find ar ( DEF ) 1. cos (AB)0 sin ( AB) 1 A, B A B If cos (AB)0 and sin ( AB) 1, then find the value of A and B where A and B are acute angles. 13. x px q x 5x 3 p q Page 4 of 9

41 If the zeroes of the polynomial x px q are double in value to the zeroes of x 5x 3, find the value of p and q Convert the following frequency distribution to a more than type cumulative frequency distribution. Marks obtained No. of Students Find the mode of the following data. Height (in cms) No. of students SECTION-C Question numbers 15 to 4 carry three marks each. 15. CDLA DEAC BE 4 EC CL In the given figure, CDLA and DEAC. Find the length of CL if BE 4 cm and EC cm y 1 1 7y If and are the zeros of the polynomial 6y 7y, find a quadratic polynomial whose Page 5 of 9

42 zeros are 1 and Prove that 5 is irrational and hence show that 3 5 is also irrational (HCF) (LCM) Find the HCF and LCM of 510 and 9. And verify that HCF LCM Product of two given numbers. 18. Sec 41.sin49cos9.cosec61 (tan0.tan60.tan70 3 3(sin 31 sin 59 ) Sec 41.sin49cos9.cosec61 (tan0.tan60.tan70 Evaluate 3 3(sin 31 sin 59 ) 19. x x 4 x 3 x x3 Check by division whether x is a factor of x 4 x 3 x x3. 0. x y a b a b b a 0 ; a b, x 0; y 0 x y x y Solve the following pair of equations for x and y a b a b b a 0 ; a b, x 0; y 0 x y x y 1. 7x 4y 49 ; 5x 6y 57 Find whether the following pair of linear equations has a If unique solution yes, find the solution. 7x 4y 49 ; 5x 6y Find the mean of the following data. Class less than 0 less than 40 less than 60 less than 80 less than 100 Frequency Page 6 of 9

43 . AD BC BD 1 3 CD AC AB BC In the given figure, AD BC and BD 1 3 CD. Prove that AC AB BC If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium. 3. sin cos sin cos sin cos sin cos sin 1 Prove that : sin cos sin cos sin cos sin cos sin Weekly income of 600 families is given below. Income in Rs No. of families Find the median / SECTION-D Question numbers 5 to 34 carry four marks each m 4 m 1 m Show that square of any positive integer is of the form 4 m (or) 4 m 1, where m is any integer. Page 7 of 9

44 6. x 3y 6; x3y 1 y Solve the following pair of linear equations graphically. x 3y 6 ; x3y 1 Also find the area of the triangle formed by the lines representing the given equations with y axis. 7. cosec cot p If cosec cot p, then prove that cos cos p 1 p 1 p 1 p x y x 6 y Find the values of x and y if the median for the following data is 31. Class Total Frequency 5 x 6 y ( x 5 ) 3 x x x , Given that x 5 is a factor of the polynomial zeroes of the polynomial. 3 x x x , find, all the 0 The age of the father is twice the sum of the ages of his children. After 0 years, his age will be equal to the sum of the ages of his children. Find the age of the father. 30. Prove that if in a triangle, the square on one side is equal to the sum of the squares on the other two sides, then the angle opposite to the first side is a right angle. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. 31. sec 1 sec 1 cosec sec 1 sec 1 Page 8 of 9

45 sec 1 sec 1 Prove that : cosec sec 1 sec 1 3. BL CM ABC A 4(BL CM ) 5BC In the given figure, BL and CM are medians of a triangle ABC right angled at A Prove that 4(BL CM ) 5BC C 1 1 ABC sin (ABC ) cos (BCA) A, B In an acute angled triangle ABC, if sin (A B C ) find A, B and C 1 and cos (B C A ) Draw less than ogive and more than ogive for the following distribution and hence find its median. Class Frequency o O o - Page 9 of 9