MATHEMATICS CLASS - IX MATHEMATICS CLASS - IX

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1 I, 202 SUMMATIVE SUMMATIVE ASSESSMENT ASSESSMENT I, I, SUMMATIVE MATHEMATICS SUMMATIVE ASSESSMENT CLASS - I, IX 202 I, 20 MATHEMATICS CLASS - IX / MATHEMATICS MATHEMATICS CLASS - IX IX / Class IX MA Time allowed : hours Maximum Marks : 90 (i) (ii) (iii) 8 (iv) 2 (v) 2 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 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 2 marks each; Section-C comprises of 0 questions of marks each and Section-D comprises of 0 questions of 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 2 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 2 of 2 Page - 0

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.

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.. x (A) If (A) p x p (B) 2 (C) x and p then the value of p is : x (B) 2 (C) 2 2 (D) (D) 2. a ab 6 (A) a, (a 6 b 6 ) (B) b, (a 6 b 6 ) (C) a 6, (a b) (D) b 6, (a b) The factors of a ab 6 are : (A) a, (a 6 b 6 ) (B) b, (a 6 b 6 ) (C) a 6, (a b) (D) b 6, (a b). p(x) x x 2 x p ( ) (A) (B) (C) (D) If p(x) x x 2 x, then the value of p ( ) is : (A) (B) (C) (D). a b c 0 a b c (A) 0 (B) abc (C) 2abc (D) abc If a b c 0, then a b c is : (A) 0 (B) abc (C) 2abc (D) abc. PS l RQ l y (A) (B) 90 (C) 80 (D) Page of 2 Page - 02

In figure PS l and RQ l, the degree measure of y is :

ABC (A) C > B (B) B < A (C) C > A (D) B > A In ABC :

the x-axis, then the value of a is : (A) 0 (B) 2 (C)

3 In figure PS l and RQ l, the degree measure of y is : (A) (B) 90 (C) 80 (D) 6. ABC (A) C > B (B) B < A (C) C > A (D) B > A In ABC : (A) C > B (B) B < A (C) C > A (D) B > A. A(2, 0), B( 6, 0) C(, a ), x- a (A) 0 (B) 2 (C) (D) 6 If the points A(2, 0), B( 6, 0) and C(, a ) lie on the x-axis, then the value of a is : (A) 0 (B) 2 (C) (D) 6 8. Q (A) (,.) (B) (., ) (C) (,.) (D) (,.) Page of 2 Page - 0

The co-ordinates of point Q are : (A) (,.) (B) (.

) 9 2 / SECTION-B Question numbers 9 to carry two marks

4 The co-ordinates of point Q are : (A) (,.) (B) (., ) (C) (,.) (D) (,.) 9 2 / SECTION-B Question numbers 9 to carry two marks each. 9. x x If x then find the decimal expansion of x. 0. x 2 x Factorise : x 2 x 6. x 2 9 x 9 2 Find the value of the polynomial x 2 9 for x AB C AC D 2 AD AB. In figure C is the mid-point of AB and D is the midpoint of AC. Prove that AD AB.. AO OB AOC BOC 2 Page of 2 Page - 0

5 In figure AO OB. Find AOC and BOC. a b c d / OR AOC In figure a b c d. Prove that AOC is a straight line.. 2 Find the area of the triangle / SECTION-C Page 6 of 2 Page - 0

2 Question numbers to 2 carry three marks each.. 6 Find four rational numbers between and 6. / OR Evaluate : 2 2.

x / OR 2x x 2 26x Using remainder theorem, factorise : 2x x 2 26x 8. xy x y x y x y 2 xy x y x y x y Verify that : 2 9.

6 2 Question numbers to 2 carry three marks each.. 6 Find four rational numbers between and 6. / OR Evaluate : Simplify : 2 2. x x If x x, then find x x x. x / OR 2x x 2 26x Using remainder theorem, factorise : 2x x 2 26x 8. xy x y x y x y 2 xy x y x y x y Verify that : 2 9. PO AB x : y : z : : x, y z In the given figure PO AB. If x : y : z : : then find the degree measure of x, y and z. Page of 2 Page - 06

7 / OR If two lines intersect each other then prove that the vertically opposite angles are equal. 20. ABC AB AC ABC D CBD BCD ABC AD, BAC In figure ABC is an isosceles triangle with AB AC. D is a point in the interior of ABC such that CBD BCD. Prove that AD bisects BAC of ABC. 2. LMN MP NQ LN LM LMP LNQ LM LN LMN is a triangle in which altitudes MP and NQ to sides LN and LM respectively are equal. Show that LMP LNQ and LM LN. 22. ABC ABC > ACB AB AC P Q PBC < QCB In ABC, ABC > ACB. Sides AB and AC are extended to points P and Q respectively. Prove that PBC < QCB. 2. AB CD ABR ROD 0 ODC Page 8 of 2 Page - 0

In the figure AB CD. If ABR and ROD 0 then find ODC. 2. ABC AB AC 6 cm AB 0 cm ABC is an isosceles triangle with AB AC. The perimeter of the triangle is 6 cm and AB 0 cm.

26. x, y z 2 2 2 2 a ab b b bc c c2 ca a2 a b c

8 In the figure AB CD. If ABR and ROD 0 then find ODC. 2. ABC AB AC 6 cm AB 0 cm ABC is an isosceles triangle with AB AC. The perimeter of the triangle is 6 cm and AB 0 cm. What is the area of the triangle? 2 / SECTION-D Question numbers 2 to carry four marks each. 2. 0, Evaluate :, when it is given that x 6 x 8 x / OR If 2x 6 x 8, then find the value of x. 26. x, y z a ab b b bc c c2 ca a2 a b c x x x. b c. a x x x Assuming that x, y, z are positive real numbers and the exponents are all rational numbers, show that : a ab b b bc c c2 ca a2 a b c x x x. b c. a x x x Page - 08 Page 9 of 2

2. px 2 x r (x 2) x p r 2 If (x 2) and x are factors

p(x) kx 9x 2 x 8 (x ) 0( k) k The polynomial p(x) kx

positive real numbers such that 8x 2y 0 and 2x 2 y xy

P Q R S T U P x 0 6 6 y 0 2 Q Plot the following

2 What is the difference between the ordinate of

9 2. px 2 x r (x 2) x p r 2 If (x 2) and x are factors of px 2 x r then show that p r p(x) kx 9x 2 x 8 (x ) 0( k) k The polynomial p(x) kx 9x 2 x 8 when divided by (x ) leaves a remainder 0( k). Find the value of k. 29. x y 8x 2y 0 2x 2 y xy 2 2x y If x and y are two positive real numbers such that 8x 2y 0 and 2x 2 y xy 2 then evaluate : 2x y 0. P Q R S T U P x y 0 2 Q Plot the following points : Points P Q R S T U Co-ordination x y 0 2 What is the difference between the ordinate of points P and Q.. OA OD 2 OCB In figure OA OD and 2. Prove that OCB is an isosceles triangle. Page - 09 Page 0 of 2

10 2. AB AC, CH CB HK BC CAX CHK In figure AB AC, CH CB and HK BC. If CAX then find CHK. / OR ABC AC > AB B C O OC > OB In ABC, AC > AB. The bisectors of B and C intersect each other at O. Prove that OC > OB.. ABC AB AC P Q CBP BCQ BO CO O BOC 90 2 x of 2 Page - 0

11 The sides AB and AC of ABC are produced to point P and Q respectively. If bisectors BO and CO of CBP and BCQ respectively meet at point O then prove that BOC 90 2 x.. Prove that the angle opposite to equal sides of a triangle are equal. - o O o - Page - Page 2 of 2

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) ) This question paper is strictly meant for use in school based SA-I, September-202 only. This question paper