BLUE PRINT SA I, SET-III. Subject Mathematics. Units VSA(1) SA-I(2) SA-II(3) LA(4) Total Number 1(1) 1(2) 2(6) 2(8) 6(17)
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1 BLUE PRINT SA I, SET-III Class IX Subject Mathematics Units VSA() SA-I(2) SA-II(3) LA(4) Total Number () (2) 2(6) 2(8) 6(7) system Algebra () (2) 2(6) 4(6) 8(25) Geometry () 2(4) 4(2) 5(20) 2(37) Co-ordinates () (2) (3) - 3(6) Geometry Mensuration - (2) (3) - 2(5) Total 4(4) 6(2) 0(30) (44) 3(90) *Marks inside the bracket.
2 KENDRIYA VIDYALAYA SANGATHAN PATNA REGION Summative Assessment I, स कल त म ल य कन I SET III Class IX क ९ Time Allowed 3 Hours नरॐर रर त सर र ३ घ ट Subject Mathematics Max. Marks 90 व षर गण त अधर कतर अ क ९० General Instruction:-. All questions are compulsory. 2. The question paper consists of 3 questions divided into four sections A, B, C and D. 3. Section A contains 4 questions of mark each. Section B contains 6 questions of 2 marks each. Section C contains 0 questions of 3 marks each and Section D contains questions of 4 marks each. 4. Use of Calculator is prohibited. 5. An additional 5 minutes has been allotted to read the question paper. During this period students will read the question paper only and will not write any answer on the answer book. स र न र नरॐर श :- १.सर प रश रॐ अनरॐ र ह! २.इस प रश रॐ र त र र ३१ प रश रॐ ह ज च र ख ड अ, र, स और र र व र जजत ह ३.ख ड अ र ४ प रश रॐ ह जजरॐर स प रत र क १ अ क क ह! ख ड र र ६ प रश रॐ ह जजरॐर स प रत र क २ अ क क ह! ख ड स र १० प रश रॐ ह जजरॐर स प रत र क ३ अ क क ह! ख ड र र ११ प रश रॐ ह जजरॐर स प रत र क ४ अ क क ह ४.क रक़क रक़ टर क प रर ग जज त ह! ५.इस प रश रॐ र त र क र ढ़रॐ क लरक़ए १५ लर रॐट क अनतरर क त सर र दर र गर ह! इस अ धर क र र रॐ व द र र क रक़ प रश रॐ र त र क र ढ़ ग और उत तर र जततक र र क ई उत तर रॐह लरक़ख ग!. Write a rational number between and. SECTION A ख ड अ और क र च एक र रर र र स ख र लरक़ख! 2. Evaluate (-6) 3 + (-3) (-6) 3 + (-3) 3 क र रॐ र त ए! 3. In a ABC, AB = AC, BAC = 80 0, then find ABC.
3 ककस त रत रर ज ABC र, AB = AC तर BAC = 80 0 ह त ABC क र र र त ए! 4. What will be the general form of co-ordinates of any point on the y-axis? y-अ र र जतर त ककस त रर र क नरॐर र क क स र न र र र क र ह ग? SECTION B ख ड ब 5. Express 3 in the decimal form and state the kind of decimal expansion. 3 क र शर रक़ क र र र व र क त कर और र ह र त ए क इसक र शर रक़ र र ककस प रक र क ह? 6. Evaluate the product without multiplying directly. त रर रॐ ग ककर ह ए ग रॐर रक़ र त ए 04 x In the given figure, if AB =BC and BX = BY show that AX =CY. दर ए गए धचत र र अगर AB =BC और BX = BY त र श र कक AX =CY. 8. In the given figure, AD is the perpendicular bisector of side BC of ABC. Show that ABD रॐ च दर ए गए धचत र र, AD ABCक र ज BC क रक़म र त सम द व र जक र ख ह! र श र कक ABD 9. On which axes do the given points lie? दर ए गए त रर र ककरॐ अ र र जतर त ह?
4 (0, 4), (-2, 0), (3, 0) and (0, -) 0. Find the area of triangle of sides 2 cm, 6cm, and 20 cm. उस त रत रर ज क त रर रक़ नरॐक रक़, जजसक र ज ए 2 स.र., 6 स.र. और 20 स.र. ह! SECTION C ख ड स. Find the values of a and b if = a + b. a और b क र रॐ नरॐक रक़ र दर = a + b 2. Represent 5 on the number line. Write the steps of construction. 5 क स ख र र ख र र नरॐर वर त कर! र रॐ ट क त रर लर न रॐ र र क लरक़ख! 3. Write (x + 2y 3z) 2 in expanded form. (x + 2y 3z) 2 क व तत त र र र लरक़ख! 4. If 2x + 3y = 2 and xy = 6 find the value of 8x y 3 र दर 2x + 3y = 2 और xy = 6 ह त 8x y 3 क र रॐ नरॐक रक़! 5. In the figure, AB CD, APQ = 50 0 and PRD = 25 0 find y x. दर ए गए धचत र र, AB CD, APQ = 50 0 और PRD = 25 0 ह त y x क र रॐ नरॐक रक़! 6. In ABC, B = 35 0, C = 65 0 and bisector of A meets BC at point D. Find ADB and ADC. ABC र B = 35 0, C = 65 0 और क A क सर द व र जक र ख BC स D त रर र र र लर रक़त ह! ADB और ADC क र रॐ नरॐक रक़!
5 7. In the figure, if l m, = (x ) and 2 = (2x ).Find 3 and 4. धचत र र र दर l और m सर रॐ तर = (x ) और 2 = (2x ).ह त 3 और 4 क र रॐ नरॐक रक़!. 8. In the given figure, B < A and C < D. Show that AD < BC. दर ए गए धचत र र B, A स छ ट ह और C, D स छ ट ह, र श र कक AD, BC स छ ट ह! 9. Plot the points A(-3,2), B(-5,-4), C(-2,-4) and D(0,2). What figures do you get on joining the points in order. त रर न र र A(-3,2), B(-5,-), C(-2,-4) तर D(0,2) क ग र र र र र र र र श र! इरॐ त रर न र र क क रर स लर रक़ रॐ र र क रॐ स आक नत लर रक़त ह?. 20. In the four sided field, the length of longer diagonal is 28m. The lengths of perpendiculars from the opposite vertices upon this diagonal are 22.7 m and 7.3 m. find the area of the field.
6 एक चत र ज क र ख त क व क क रक़म र ई 28 र. ह! व क क सम र ख श ष स व क र र ड रक़ गए रक़म र क रक़म र ईर 22.7 र. और 7.3 र. ह! ख त क त रर रक़ नरॐक रक़! SECTION D ख ड द 2. If x = and y = find x 2 + xy + y 2. अगर x = और y = ह त x 2 + xy + y 2. क र रॐ नरॐक रक़! 22. Prove that (स त रर त कर कक): = 23. Factorise (ग रॐख ड कर ): 2x 3 9x 2 + x If x + y + z = 0 show that x 3 + y 3 + z 3 = 3xyz र दर x + y + z = 0 त र श र कक x 3 + y 3 + z 3 = 3xyz 25. If the polynomials ax 3 + 4x 2 + 3x 4 and x 3 4x + a leave the same remainder when divided by (x-3), find the value of a. अगर र ह र र ax 3 + 4x 2 + 3x 4 और x 3 4x + a क (x-3) स व र जजत ककर ज र त सर रॐ श ष र लश प र प त ह त ह त a क र रॐ नरॐक रक़! 26. If a + b + c = 5 and a 2 + b 2 + c 2 = 83, find the value of a 3 + b 3 + c 3-3abc अगर a + b + c = 5 और a 2 + b 2 + c 2 = 83 ह त a 3 + b 3 + c 3-3abc क र रॐ र त ए! 27. Prove that the sum of three angles of a triangle is two right angles.. स त रर त कर कक ककस त रत रर ज क त रॐ क क र ग र सर क क र र र र ह त ह! 28. In the given figure, AC = AE, AB = AD and BAD = EAC. Show that BC = DE. दर ए गए धचत र र, AC = AE, AB = AD और BAD = EAC ह त र श र कक BC = DE 29. ABC is a right angled triangle in which A = 90 0 and AB = AC. Find B and C. ABC एक सर क त रत रर ज ह, जजसक क A सर क ह और AB = AC ह त क B तर क C क र रॐ नरॐक रक़! 30. BE and CF are two equal attitudes of a triangle ABC. Using RHS congruence rule, Prove that triangle ABC is isosceles.
7 त रत रर ज ABC क ऊ च ईर BE और CF र र र र ह! आर एच एस स गसर नरॐर र क उर र ग कर त ह ए स त रर त कर कक ABC एक सर द व र ह त रत रर ज ह! 3. Anwar Ali has a farm in the shape of a square ABCD. Its diagonals AC and BD intersect at O. Show that AOB BOC COD DOA. He makes a will in which he gives two triangular parts to his son and daughter and other two parts for opening a dispensary and a library. Which values are shown by decision of Anwar Ali in making provisions for library and dispensary. अरॐ र अरक़ क र स ABCD ग क आकर क एक ख त ह! इसक व क AC और BD एक र सर क O त रर र र र क टत ह! र श र कक - AOB BOC COD DOA ह! ह अर रॐ स र त र र त रत रर ज क र र ग अर रॐ र ट और र ट क र रॐ च हत ह और श ष र त रत रर ज क र र ग र अतर त रक़ और र ततक रक़र ख रक़रॐ च हत ह! र ततक रक़र और अतर त रक़ क स व र प रर रॐ कर रॐ र अरॐ र अरक़ ककरॐ र ल र क प रर लश त कर त ह?
8 ERROR ANALYSIS Summative Assessment I, Name of Student Class IX Sec Roll No. Subject : Mathematics Units Number System Algebra Geometry Co-ordinate Geometry Q.No To T t t o o 9 t t Marks Allotted Marks Awarded to t Mensuratio n 2 t 0 0 o t Grand Total Examiner
9 Marking scheme Class IX Mathematics SA-, Set -III ABC = 50 o 4. (0,y) 5. 3 = 3.8, terminating decimal 2 6. ( ) (00-4) = = AB-BX= BC-BY AX = CY 8. BD = CD, BDA = CDA = 90, AD = AD 9. Y-axis, X- axis, X-axis, Y-axis 2 0. S=24cm. area = 96cm Representation of number line 2 For writing steps of construction. 3. =x 2 + 4y 2 + 9z 2 + 4xy - 2yz 6zx 4. (2x + 3y) 3 8xy( 2x + 3y) = (2) 3 8 x 6 x BAC = 80 o BAD = CAD = 40 ADB = = 05 ADC = = =80 so, =45 o 3= =75 4= 2=05 8. AO < OB OD < OC so, AD < BC 9. For proper plotting of points on graph paper for reporting the figure formed on joining the points in order. 3
10 20. area of field = x 28 x ( ) = 64 x 40 = 2560 m = 22. = 2 = 23. ( ) is a factor of on dividing by( +) the quotient is 2 so the factor of = ( ) ( -4) (2-3) 24. = = = = 83 +2(ab + bc + ca) ab + bc + ca = 7 a 3 + b 3 + c 3 3abc = (a + b + c) (a 2 + b 2 + c 2 ab bc - ca) = 5 x (83 7) = For given, to prove correct fig. 2 For correct proof In the given fig. BAC= DAE AB=AD, BAC = DAE, AC = AE BC=DE (cpct) 29. In A= 90 0 B + C=90 0 AB=AC & B = C So, 2 B = 90 0 B = 45 0 B = C, C= 45 A= B= C= 60
11 30. BE=CF, BEC = CFB = 90 2 CB = BC 2 BCE = CBF BCA = CBA AB=AC 3. Diagonals of a square bisect each other AO = CO, OB = OB, AB = BC AOB BOC(SSS) similarly, BOC COD, COD DOA SO, AOB BOC COD DOA values Highlighting equal shares for son and daughter, showing interest for improvement in health and education facilities.
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