SUMMATIVE ASSESSMENT I, IX / Class IX


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1 I, 0 SUMMATIVE ASSESSMENT I, 0 0 MATHEMATICS / MATHEMATICS MATHEMATICS CLASS CLASS  IX  IX IX / Class IX MA0 90 Time allowed : hours Maximum Marks : 90 (i) (ii) (iii) 8 (iv) (v) General Instructions: (i) All questions are compulsory. (ii) The question paper consists of questions divided into four sections A, B, C and D. SectionA comprises of 8 questions of mark each; SectionB comprises of 6 questions of marks each; SectionC comprises of 0 questions of marks each and SectionD comprises of 0 questions of marks each. (iii) Question numbers to 8 in SectionA 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 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 (a) (b) The value of 8 7 is : 8 (a) (b) 6 6 (c) (c) (d) (d) 8 8. p(x) x x k k (a) 0 (b) 8 (c) 8 (d) 5 If is the zero of the polynomial p(x) x x k, then value of k is : (a) 0 (b) 8 (c) 8 (d) 5. (a) 0 (b) (c) (d) Maximum number of zeroes in a cubic polynomial are : (a) 0 (b) (c) (d). x 8x 5 x x 0 (a) x (b) x 5 (c) x 5 (d) x Common factor in quadratic polynomials x 8x 5 and x x 0 is : (a) x (b) x 5 (c) x 5 (d) x 5. ABC A B 05, B C 0 B (a) 65 (b) 80 (c) 5 (d) 5 If in a triangle ABC, A B 05, B C 0 then B is : (a) 65 (b) 80 (c) 5 (d) 5 6. ABC A B (a) 5 (b) 60 (c) 0 (d) 90 A rt. angled isosceles triangle ABC is right angled at A. Then B is : (a) 5 (b) 60 (c) 0 (d) (, 5) (a) I (b) II (c) III (d) IV Point (, 5) lies in the quadrant : (a) I (b) II (c) III (d) IV Page of 0
3 8. x y, (x, y) (y, x), x y (a) (x, y) (y, x) (b) (x, y) ( y, x) (c) (x, y ) ( x, y) (d) (x, y) ( x, y) If x y, then (x, y) (y, x), But if x y, then (a) (x, y) (y, x) (b) (x, y) ( y, x) (c) (x, y ) ( x, y) (d) (x, y) ( x, y) 9 / SECTIONB Question numbers 9 to carry two marks each Find the two irrational numbers between 0.5 and y y y Factorize : y y y. (0) Using suitable identity evaluate (0). AC BD AB CD In figure, if AC BD, then prove that AB CD. AB CD, APQ 0 PRD 8 x, y In figure, if AB CD, APQ 0 and PRD 8, find x and y. AB CD EF x : y : z Page of 0
4 In figure if AB CD EF and x : y :, find z.. 6 cm cm 0 cm Find the area of a triangle when two sides are cm and 0 cm and the perimeter of the triangle is 6 cm. 5 / SECTIONC Question numbers 5 to carry three marks each. 5. (79) 6 Find the value of 6 (79) 0.5 p q p, q q 0 Show that 0.5 can be expressed in the form p, where p and q are integers and q q a b 5 a b 5 5 Find the value of a and b, when a b p p p 6 9 Factorize 7 p p p 6 Page 5 of 0
5 a 6 b 6 Factorize : a 6 b 6 8. x x 0 x 5x px b p b 9. If x and x 0 are zeroes of the polynomial x 5x px b, then find the value of p and b If the bisectors of a pair of alternate angles formed by a transversal with two given lines are parallel, prove that the given lines are parallel. Prove that if two lines intersect, then the vertically opposite angles are equal. 0. AC BC, DCA ECB DBC EAC DC EC In the given figure AC BC, DCA ECB and DBC EAC Prove that DC EC. Prove that Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.. ABC B C AC AB BE CF BE CF (i) ABE ACF (ii) AB AC Page 6 of 0
6 ABC is triangle in which altitudes BE and CF are equal. Then show that : (i) ABE ACF and (ii) AB AC. PQ RS AB, PQ B BC RS C CD AB CD In figure PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB CD.. 5 m 0 m m m A field is in the shape of a trapezium whose parallel sides are 5 m and 0 m, The non parallel sides are m and m. Find the area of the field. 5 / SECTIOND Question numbers 5 to carry four marks each. 5. x, y x y xy If x, y, then find the value of x y xy. Page 7 of 0
7 x, If x, find x x x x Prove that : (a b c) (a b c) b c Simplify and factorise (a b c) (a b c) b c 8. a b c 6 ab bc ca a b c abc If a b c 6 and ab bc ca, find the value of a b c abc 9. bx x x 5x b x R R R R 0 b The polynomial bx x and x 5x b when divided by x leave the remainders R and R respectively. Find the value of b if R R 0 0. A(, ), B(6, 0) C(0, ) D (, ) ABCD A D Plot the points A(, ), B(6, 0), C(0, ) and D (, ) on the graph paper. Draw figure ABCD and write in which quadrant A and D lie.. If two parallel lines are intersected by a transversal, then prove that bisectors of the interior angles from a rectangle.. ABC AB AC BA D BA AD BCD Page 8 of 0
8 ABC is an isosceles triangle in which AB AC. Side BA is produced to D such that BA AD. Show that BCD is a right angle. AC AE AB AD BAD EAC BC DE In the given figure AC AE, AB AD and BAD EAC Show that BC DE. ABC BC D E BD EC AD AE AB AC In ABC points D and E are on BC such that BD EC and AD AE, Prove that AB AC Page 9 of 0
9 . Show that the sum of the three altitudes of a triangle is less than the sum of the three sides of a triangle.  o O o  Page 0 of 0
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