SUMMATIVE ASSESSMENT I, 2012 / MATHEMATICS. X / Class X

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Evangeline Potter
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hours Maximum Marks : 90 (i) (ii) 4 8 6 0 0 4

questions divided into four sections A, B, C

Section-A comprises of 8 questions of mark

marks each, Section-C comprises of 0 questions

However, internal choices have been provided

1 I, 0 SUMMATIVE ASSESSMENT I, 0 MA-0 / MATHEMATICS X / Class X 90 Time allowed : hours Maximum Marks : 90 (i) (ii) (iii) 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 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 0 questions of 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, 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

8 SECTION A Question numbers to 8 carry one mark each.

You have to select the correct choice.. 8 (A) 0.5 (B) 0.05 (C) 0.075 (D) 0.75 in decimal form is : 8 (A) 0.

2 8 SECTION A Question numbers 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.. 8 (A) 0.5 (B) 0.05 (C) (D) 0.75 in decimal form is : 8 (A) 0.5 (B) 0.05 (C) (D) p(x)4x x9 (A), (B), (C), 4 (D), 4 The zeroes of the polynomial p(x)4x x9 are : (A), (B), (C), 4 (D), 4. ABC PQR x (A).5 (B).5 (C).75 (D) In the given figure if ABC PQR The value of x is : (A).5 cm (B).5 cm (C).75 cm (D) cm 4. xa cos, yb sin b x a y a b (A) (B) (C) 0 (D) ab If xa cos, yb sin, then b x a y a b is equal to : (A) (B) (C) 0 (D) ab Page of 9

5. 5 7 8 9 (A) (B) (C) (D) 5 A rational number which has non

of the pair of equation xy and xy4, then the respective values of a

sin 60sin 0 (A) 4 (B) (C) 4 (D) The value of sin 60sin 0 is : (A)

5 (D) 5 The class mark of the class 0 5 is : (A) 7 (B) 8 (C) 7.

3 (A) (B) (C) (D) 5 A rational number which has non terminating decimal representation is : 7 9 (A) (B) (C) (D) xa, yb xy xy4 a b (A), 5 (B) 5, (C), (D), If xa, yb is the solution of the pair of equation xy and xy4, then the respective values of a and b are : (A), 5 (B) 5, (C), (D), 7. sin 60sin 0 (A) 4 (B) (C) 4 (D) The value of sin 60sin 0 is : (A) (B) 4 (C) 4 (D) (A) 7 (B) 8 (C) 7.5 (D) 5 The class mark of the class 0 5 is : (A) 7 (B) 8 (C) 7.5 (D) Question numbers 9 to 4 carry two marks each / SECTION-B Find the HCF of 55 and 867 by Euclid division algorithm. 0. f(x)x 7x p, q p q If p, q are zeroes of polynomial f(x)x 7x, find the value of p q.. 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

following frequency distributions : Class : 0 6 6 8 8 4 4 0 Frequency : 7 5

4 PKR90 and KR8 cm find PK.. sina cot A If sina, find the value of cot A.. 4. Find the quadratic polynomial whose zeroes are and Find the mean of the following frequency distribution : Class : Frequency : /OR Find the mode of the following frequency distributions : Class : Frequency : SECTION-C Question numbers 5 to 4 carry three marks each. 5. Prove that the sum of squares on the sides of a rhombus is equal to sum of squares on its diagonals. 6. 4x 4x Show that and are the zeroes of the polynomial 4x 4x and verify the relationship between zeroes and co-efficients of polynomial. Page 5 of 9

7. 4 Prove that 4 0. 78 is an irrational number.

78 in the form of rational number a b. 8.

sin90 sin40 tan 45 Find the value of the following without

b (x) x 9x xb Find the value of b for which (x) is a

x5y0, 6x0y400 Using graph, find whether the pair of linear

5 7. 4 Prove that is an irrational number. a b /OR Express the number in the form of rational number a b. 8. cos50 4 cosec 59 tan tan tan78.sin90 sin40 tan 45 Find the value of the following without using trigonometric tables : cos50 4 cosec 59 tan tan tan78.sin90 sin40 tan b (x) x 9x xb Find the value of b for which (x) is a factor of x 9x xb 0. x5y0, 6x0y400 Using graph, find whether the pair of linear equations x5y0, 6x0y400 is consistence or inconsistent. Write its solution. /OR x y 6 x y 5, x, y x y Solve for x and y : 6 x y 5, where x, y x y. 7 p p 0 If the mean of the following distribution is 7, find the value of p : Class : Frequency : 8 p 0. If the areas of two similar triangles are equal, then prove that they are congruent. /OR Page 6 of 9

QRAD. ABC DBC BC PQBA PRBD In the given figure, two

that PQBA and PRBD. Prove that QRAD.. sincos(6), 6 4.

median for the following data : Class : 0 0 0 0 0 0

n n By Euclid division algorithm, show that square

6 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.. sincos(6), 6 4. If sincos(6), where 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 4 carry four marks each. 5. n n By Euclid division algorithm, show that square of any positive integer is of the form n or n. 6. k xy (k)x(k)yk For what value of k will the pair of equations have no solution? xy (k)x(k)yk Page 7 of 9

7. (secatana) (sina)sina Prove that (secatana) (sina)sina 8.

the following distribution : Scores : 0 0 0 40 40 50 50 60 60 70 70 80 Frequency :

p(x)8x 4 4x x 8x 4x x p(x) What must be subtracted or added to p(x)8x 4 4x x 8x so

/OR x y x87y5 87xy07 Solve for x and y x87y5 and 87xy07 0.

AC respectively such that PQ is parallel to BC.

In an equilateral ABC, ADBC. Prove that AB 4AD.

7 7. (secatana) (sina)sina Prove that (secatana) (sina)sina 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 4x x 8x 4x x p(x) What must be subtracted or added to p(x)8x 4 4x x 8x so that 4x x is a factor of p(x)? /OR x y x87y5 87xy07 Solve for x and y x87y5 and 87xy07 0. 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. /OR ABC ADBC AB 4AD. In an equilateral ABC, ADBC. Prove that AB 4AD.. sincosm seccosecn, n(m )m If sincosm and seccosecn, then prove that n(m )m. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.. tan sin sec tan sin sec tan sin sec Prove that : tan sin sec Page 8 of 9

4. f 65 0 0 0 40 40 60 60 80 80 00 00 0 6

8 4. f f 6 5 6, 8, f Find the value of f from the following data if its mode is 65 : Class Frequency 6 8 f 6 5 where frequency 6, 8, f and are in ascending order. - o O o - Page 9 of 9

9 SUMMATIVE ASSESSMENT I, 0 MA-0 Class X MARKING SCHEME MATHEMATICS SECTION A. (D) (A),. (D) cm 4. (C) (D) (C), 7. (B) 8. (C) 7.5 SECTION-B HCF Page of 9

10 0.. pq 7, pq p q (pq) pq QPR90 PR cm PKR90 PK cm sina BC AC AB cota cot A. Zeroes are, quadratic polynomialx ( )x ( ) x x4 4. x f fx fx60, f40 Mean OR Page of 9

11 f Mode m f l f f f m f SECTION-C 5. AOOC, BOOD AC (OAOC) OA OC OAOC OA OC OA BD OB OD OB AB BC CD AD (OA OB OC OD ) OA OB OA OB OA OC OA OB OD OD (OAOC) (OBOD) AC BD (OAOC, OBOD) 6. f(x)4x 4x f f , are zeroes of polynomial 4x 4x 4 Sum of zeroes 4 Product of zeroes as per formula 4 4 Relation between zero and coeff. of polynomial is verified. 7. Prove that is irrational is irrational being product of rational and an irrational Again 4 is irrational as rational minus irrational 4 is irrational. OR Page of 9

12 Let x x x Subtracting 9990 x x cos50cos(9040)sin40 cosec 59cosec (90)sec tan78tan(90)cot The given expression becomes sin40 4(sec tan ) tan cot. sin If (x) is a factor then is a zero of the poly nomial 9 b b Correct graph of st equation Correct graph of nd equation Lines are parallel No solution. Equations are inconsistant Let p and x 6pq q y 6pq 5pq 5pq6 p7 OR p Putting in (i) 6 q q q x x4 y y5 Page 4 of 9

13 . x f 8 p 0 fx 40 5p fx455p, f4p 45 5p 7 4 p 67p455p p84 p7. ABC PQR arabc AB AC BC arpqr PQ PR QR It is given that arabcarpqr AB AC BC PQ PR QR ABPQ, ACPR, BCQR ABC PQR OR In ABC. PQAB BP AQ (i) PC QC Again in BCD PRBD BP DR (ii) PC RC From (i) and (ii) AQ DR QC RC QRAD. sincos(6) sincos(90)cos(6) Page 5 of 9

14 4. x f f(x) fx640, f00 Mean Class : Cumulative frequency : Median SECTION-D 5. Let x be a positive integer Diving x by we get xq or q or q x 9q (q ) or (q) or (q) n 9q 6q 9q q4 (q q) n where q n where q qn Square of any positive integer is of the form n or n (q 4q) n 6. a For no solution b c a b c (i) (ii) (iii) k k k From (i) and (ii) kk k k Again from (ii) and (iii) k k k 7. LHS(secAtanA) (sina) sina sina cosa cosa sina. sina cos A sina. sina sina sina LHSRHS Page 6 of 9

15 8. Less than series More than series Score Frequency Score Frequency Less than 0 8 More than 0 50 Less than 40 8 More than 0 4 Less than 50 More than 40 Less than More than 50 8 Less than More than 60 6 Less than More than 70 Correct graph of less than Correct graph of more than Median Verification : x x 8x 4 8x x x 4 x x 8 x 6 x 4 x 8x 8x x 8x 6 x 4 x 4 x x 4 x x 5 x 4 Subtract 5x4 or add 5x4 for exact division OR x87y (i) 87xy (ii) (i)(ii) 0 (xy)660 xy (A) (i)(ii) 46(xy)46 xy (B) From (A) and (B) x, y PQBC APRB And ARPADB APR ABD Page 7 of 9

16 AP AR PR (i) AB AD BD AQ AR RQ Similarly (ii) AC AD DC From (i) and (ii) PR RQ BD DC But BDDC (D is mid point) PRRQ AD bisects PQ OR ABC is equilateral ADBC BDDC BC AD AB BD AB BC 4 AB AB 4 ( ABBC) AD 4 AB 4AD AB. sincosm m sincos n(m )sincos(seccosec) (sincos) m. Correct figure, given, to prove, construction Correct proof x4=. tan sin LHS tan sin sin cos sin cos cos cos sec cos RHS sec cos LHSRHS Page 8 of 9

17 4. f Mode f 6 f f f 8 f 4 484f8f f0 - o O o - Page 9 of 9

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

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