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1 â çüì ÂÚUèÿææ - I, SUMMATIVE ASSESSMENT I, »ç æì / MATHEMATICS ÿææ - IX / Class IX çùïæüçúuì â Ø : hours çï Ì Ñ 90 Time Allowed : hours Maimum Marks: 90 âæ æ Ø çùîðüàæ Ñ 1. âöè ÂýàÙ çùßæøü ãñ Ð. â ÂýàÙ Â æ ð 1 ÂýàÙ ãñ, çá ãð æúu ¹ ÇUæð, Õ, â ÌÍæ Î ð Õæ ÅUæ»Øæ ãñð ¹ ÇU- ð ÂýàÙ ãñ çáù ð ÂýˆØð 1 æ ãñ; ¹ ÇU-Õ ð 6 ÂýàÙ ãñ çáù ð ÂýˆØð ð ãñ ; ¹ ÇU-â ð 10 ÂýàÙ ãñ çáù ð ÂýˆØð ð ãñ ; ÌÍæ ¹ ÇU-Î ð 11 ÂýàÙ ãñ çáù ð ÂýˆØð ð ãñ Ð. â ÂýàÙ Â æ ð æð ü çß ËÂ Ùãè ãñð. ñ Ü é ÜðÅUÚU æ ÂýØæð» ßçÁüÌ ãñð General Instructions: 1. All questions are compulsory.. The question paper consists of 1 questions divided into four sections A, B, C and D. Section-A comprises of 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 11 questions of marks each.. There is no overall choice in this question paper.. Use of calculator is not permitted. ¹ ÇU- / SECTION-A ÂýàÙ â Øæ 1 âð ð ÂýˆØð æ 1 ãñð Question numbers 1 to carry one mark each æ æù ææð èçá Ð 1 Find the value of 6 5. âˆøæçâð èçá ç ÕãéÂÎ p() 1 æ àæê Ø ãñð 1 Verify whether is a zero of the polynomial p() 1. Îè ãé ü æ ë çì ð, ABD 66 æñúu ACB 60 ãñð ØçÎ A æ â çmöæá BC âð D ÂÚU ç ÜÌæ ãñ, Ìæð 1

2 ADB ææð èçá Ð In the given figure, ABD 66 and ACB 60. If bisector of A meets BC at D, then find ADB. ÌéÍü ÌéÍæZàæ ð çsíì æð ü Îæð çõ Îé çüç¹ Ð 1 Write any two points lying in the fourth quadrant. ¹ ÇU-Õ / SECTION-B ÂýàÙ â Øæ 5 âð 10 ð ÂýˆØð ð ãñ Ð Question numbers 5 to 10 carry two marks each ð ãúu æ ÂçÚU ðøè ÚU æ èçá Ð Rationalise the denominator of âúuü èçá Ñ ( y z) ( y z) Simplify : ( y z) ( y z). 7 Øæ Øêç ÜÇU è Âæ ßè çöïæúu ææ âð â æ ÐÚU ÚðU¹æ æð ð çsðˆß æ çù»ü ãæððæ ãñ? SÂcÅU èçá Ð Does Euclid s fifth postulate imply the eistence of parallel lines? Eplain. 8 ØçÎ P, Q æñú R U ç âè ÚUð¹æ ÂÚU ÌèÙ çõ Îé çsíì ã ñ ÌÍæ Q çõ Îé æð P æñúu R ð Õè ð çsíì ãñ, Ìæð çâh

3 èçá ç PQ QR PR ãñ (Îðç¹ æ ë çì)ð If P, Q and R are three points on a line and Q lies between P and R, then prove that PQ QR PR (see figure). 9 çùîðüàææ ÌÜ ÂÚU, çù Ù âæúu æè ð çî çõ Îé æð (, y) æð, ÿææð ÂÚU ÎêçÚUØæð è ÂØé Ì æ Øæð æ ØÙ ÚUÌð ãé, æüðç¹ì èçá Ñ y Plot the points (, y) given in the following table on the coordinate plane, choosing suitable units of distances on the aes : y â æð æ ç æöéá ð, æïæúu æñúu Ü Õ ý àæñ 10 m æñúu m ãñ Ð â ç æöéá æ ÿæð æè Ü ÐÍæ æü è Ü Õæ ü ææð èçá Ð In a right angled triangle, base and perpendicular are respectively 10 m and m. Find the area of the triangle and length of the hypotenuse. ¹ ÇU-â / SECTION-C ÂýàÙ â Øæ 11 âð 0 ð ÂýˆØð ð ãñ Ð Question numbers 11 to 0 carry three marks each. 11 ØçÎ ãñ, Ìæð 1 æ æù ææð èçá Ð If ; find the value of , 5, 66 æð ßÚUæðãè ý ð ÃØßçSÍÌ èçá Ð Arrange 9, 5, 66 in descending order.

4 1»é æù¹ ÇU èçá Ñ a b 9 16 Factorise : a b 'a' æ ßã æù ææð èçá çáâ ð çü ÕãéÂÎ a a a 1 æ»é æù¹ ÇU 1 ãñð Find the value of 'a' for which 1 is a factor of the polynomial a a a ABC ð BO æñúu CO ý àæñ ABC æñúu ACB ð â çmöæá â Âý æúu ãñ ç CBO BCO æñúu ABO ACO ãñð Îàææü ç ABC ACB ãñð In a triangle ABC, BO and CO are the bisector of ABC and ACB such that CBO BCO and ABO ACO. Show that ABC ACB. 16 çî» ç æ ð, ØçÎ ÚðU¹æ¹ ÇU AB, ÚðU¹æ¹ ÇU RS ð â æ ÐÚU ãñ ÐÍæ AS æ ŠØ-çÕ Îé O ãñ, Ìæð Îàææü ç Ñ (i) (ii) AOB SOR BR æ ŠØ-çÕ Îé Öè O ãñð In the given figure, if the line segment AB is parallel to another line segment RS and O is the mid-point of AS, then Show that : (i) (ii) AOB SOR O is also mid-point of BR 17 çâh èçá ç àæèáæüçö é¹ æð ææð ð Øé æð ð â çmöæá ãè ÚðU¹æ ð ãæðìð ãñ Ð Prove that the bisectors of pairs of vertically opposite angles are in the same straight line.

5 18 æ ë çì ð, ØçÎ AB æñúu CD â æ ÌÚU ãñ, Ìæð æ æù ææð èçá Ð In the figure, if AB and CD are parallel, find the value of. 19 çõ Îé A(, 6) æð æìèüø ÌÜ ð æüðç¹ì èçá Ð Õ, A ð ÎæðÙæð çùîðüàææ æð ð ç qæð æð ÕÎçÜ ÌÍæ âð çõ Îé B çã Ð B æð æüðç¹ì èçá Ð - ÿæ æñúu y- ÿæ ð A ð ÂÚUæßÌüÙæð æð æüðç¹ì èçá Ð Plot a point A(, 6) on the cartesian plane. Now, change the signs of both coordinates of point A and call it B. Plot B. Plot the reflections of A in -ais and y-ais. 0 ç âè ç æöéá è ÖéÁæ, 1 æñúu 1 ãñ Ð â æ ÿæð æè Ü 10 ãñð æ æù ææð èçá Ð The sides of a triangle are, 1 and 1. Its area is 10. Find the value of. ¹ ÇU-Î / SECTION-D ÂýàÙ â Øæ 1 âð 1 ð ÂýˆØð ð ã ñð Question numbers 1 to 1 carry four marks each. 1 ØçÎ a b a b a b a b ãñ, Ìæð Îàææü ç b a b 0 ãñð If a b a b, then show that b a b 0. a b a b

6 p q ð M Â ð ÃØ Ì èçá Ñ Epress in the form of p q : ÕãéÂÎ p() a a 7 æð ÁÕ ( 1) âð Öæ» çîøæ ÁæÌæ ãñ, Ìæð àæðáè Ü 19 æìæ ãñð a æ æù ææð èçá Ð çè ÚU àæðáè Ü ææð èçá ÁÕ p() æð âð Öæ» çîøæ ÁæÌæ ãñð The polynomial p() a a 7 when divided by ( 1) leaves the remainder 19. Find the value of a. Then, find the remainder when p() is divided by. ØçÎ y ãñ, Ìæð Îàææü ç 6y y 8 0 ãñð If y, then show that 6y y ßæSÐß ð ƒæùæð æ ÂçÚU ÜÙ ç çõùæ, (1) () () ( 5) ( 6) æ æù ææð èçá Ð çáâ âßüâç æ æ ÂýØæð» ãé æ ãñ ßã Öè çüç¹ Ð Without actually calculating the cubes, find the value of (1) () () ( 5) ( 6). Also write the identity used. 6»é æù¹ ÇU Âý ðø æ ÂýØæð» ÚUÐð ãé, a æ æù ææð èçá, ØçÎ 1 âð a çßöæ Ø ãñð Using factor theorem, find the value of a, if a is divisible by 1. 7 ÖßÙ çù æüìæ Ùð æòüæðùè æ Ù àææ â Âý æúu ÕÙæØæ ç ÜðÙ 'a', ÜðÙ 'b' ð â æ ÌÚU ãñ ÌÍæ Ù ð Õè ð Öæ» æð ãçúuì Öæ» ÚU¹Ùð è ØæðÁÙæ ÕÙæ ü, Áñâæ ç æ ë çì ð çî¹æøæ»øæ ãñð ðâæ ÚUÙð ÂÚU ßã ç â êëø æð Îàææü ÚUãæ ãñ? ØçÎ 1 10 ãñ, Ðæð àæðá âöè æð æ ææð èçá Ð Builder has made a layout of a colony so that lane 'a' is parallel to lane 'b'? In between lanes 'a' and 'b' he plans to leave green area as shown in the figure. What value is he showing by doing so? If measure of 1 is 10, find the measure of all other angles.

7 8 Îæð çß ýð Ðæ ÁêÙ ð æâ ð â æù ÚUæçàæ è çõ ý è ÚUÐð ãñ Ð ÁéÜæ ü æâ ð ÂýˆØð ÁêÙ æâ âð Îé»Ùè ÚUæçàæ è çõ ý Ø ÚUÌæ ãñ Ð ÁéÜæ ü æâ è çß ý Ø è ÌéÜÙæ èçá Ð â ÍÙ ð ÂýØé Ì Øéç ÜÇU SßØ Ð Ø æð çüç¹ Ð â ð çðçúu Ì Øéç ÜÇU ð Îæð SßØ Ð Ø çüç¹ Ð Two salesmen make equal sales during the month of June. In July, each salesmen doubles his sale of the month of June. Compare their sales in July. State which aiom you use here. Also give two more aioms other than the aiom used in the above situation. 9 ç æ ð, ØçÎ l m, 1 ( y), ( y) æñúu 6 (y 0) ãñ, Ìæð 7 ÌÍæ 8 ð æù ææð èçá Ð l In the figure, if l m, 1 ( y), ( y) and 6 (y 0), find 7 and 8. 0 çâh èçá ç ç æöéá ð ÐèÙæð æð ææð æ Øæð» Îæð â æð æ ãæððæ ãñð ØçÎ â æð æ ç æöéá ð ØêÙ æð æ ÎêâÚðU æ - æñíæ ü ãñ, Ðæð ØêÙ æð ææð æð ææð èçá Ð Prove that the sum of three angles of a triangle is two right angles. If in a right angled triangle an acute angle is one-fourth the other, find the acute angles.

8 1 ÌéÖéüÁ ABCD ð çß æü O ÂÚU ÂýçÐ ÀðUÎ ÚUÐð ãñ Ð çâh èçá ç AB BC CD AD<(AC BD) ãñð In a quadrilateral ABCD diagonals intersect at O. Prove that AB BC CD AD<(AC BD). -o0o0o0o-

10. SECTION - B Question numbers 11 to 18 carry 2 marks each C1 P.T.O.

10. SECTION - B Question numbers 11 to 18 carry 2 marks each C1 P.T.O. 940108 - C1 Class - IX MATHEMATICS Time : 3 to 3½ hours Maximum Marks : 80 â Ø : 3 âð 3½ ƒæ ÅUð çï Ì : 80 Total No. of Pages : 15 é Ü ÂëcÆUæð è â Øæ : 15 General Instructions : 1. All questions are compulsory.