SUMMATIVE ASSESSMENT I (0) Lakdfyr ijh{kk &I MATHEMATICS / xf.kr Class IX / & IX 46000 Time allowed: 3 hours Maximum Marks: 90 fu/kkzfjr le; % 3?k.Vs vf/kdre vad % 90 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 34 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 3 marks each and section D comprises 0 questions of 4 marks each. (iii) Question numbers to 8 in section-a are multiple choice questions where you are to select one correct option out of the given four. (iv) There is no overall choice. However, internal choice have been provided in question of two marks, 3 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. lkeku; funsz k % (i) lhkh iz u vfuok;z gsaa (ii) bl iz u i= esa 34 iz u gsa, ftugsa pkj [k.mksa v, c, l rfkk n esa ckavk x;k gsa [k.m & v esa 8 iz u gsa ftuesa izr;sd vad dk gs, [k.m & c esa 6 iz u gsa ftuesa izr;sd ds vad gsa, [k.m & l esa 0 iz u gsa ftuesa izr;sd ds 3 vad gs rfkk [k.m & n esa 0 iz u gsa ftuesa izr;sd ds 4 vad gsaa (iii) [k.m v esa iz u la[;k ls 8 rd cgqfodyih; iz u gsa tgka vkidks pkj fodyiks a esa ls,d lgh fodyi pquuk gsa (iv) bl iz u i= esa dksbz Hkh lokszifj fodyi ugha gs, ysfdu vkarfjd fodyi vadksa ds,d iz u esa, 3 vadksa ds 3 iz uksa esa vksj 4 vadks a ds iz uksa esa fn, x, gsaa izr;sd iz u es a,d fodyi dk p;u djsaa (v) dsydqysvj dk iz;ksx oftzr gsa 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. Page of 4

. Rationalisation of the denominator of : gives : 5 (A) (B) 5 (C) 5 (D) 0 5 (A) (B) 5 (C) 5 (D) 0 5 3 5 3. The coefficient of x in the expansion of (x3) 3 is : (A) (B) 9 (C) 8 (D) 7 (x3) 3 x (A) (B) 9 (C) 8 (D) 7 3. The value of the polynomial x x at x is : (A) 3 (B) (C) (D) 0 x x x (A) 3 (B) (C) (D) 0 4. Which of the following polynomials has 3 as a zero? (A) x3 (B) x 9 (C) x 3x (D) x 3 3 (A) x3 (B) x 9 (C) x 3x (D) x 3 5. The complement of (90a) is : (A) a (B) 90a (C) 90a (D) a (90a) (A) a (B) 90a (C) 90a (D) a Page of 4

6. In given fig., ADBC and BADABC, then ACB equals : (A) ABD (B) BAD (C) BDA (D) BAC ADBC BADABC, ACB 7. (A) ABD (B) BAD (C) BDA (D) BAC The perimeter of an equilateral triangle is 60m. Its area is : (A) 0 3 m (B) 00 3 m (C) 5 3 m (D) 0 3 m 60 (A) 0 (B) 00 3 3 (C) 5 3 (D) 0 3 8. The base and hypotenuse of a right triangle are respectively 6 cm and 0 cm long. Its area is : (A) 60 cm (B) 0 cm (C) 30 cm (D) 4 cm 6 0 (A) 60 (B) 0 (C) 30 (D) 4 Page 3 of 4

Section-B Question numbers 9 to 4 carry two marks each. 9. If a b then find value of a and b. a b a b 0. 3 Using remainder theorem, find the remainder when x 3 x 3 x is divided by x. 3 x 3 x 3 x x. Expand a b 3 c 4. a b 3 c 4. If a point C lies between two points A and B such that ACBC, prove that AC AB. Explain by drawing figure. C A B ACBC AC AB 3. In the figure below, the diagonal AC of quadrilateral ABCD bisects BAD and BCD. Prove that BCCD. BCCD ABCD AC, BAD BCD Page 4 of 4

If two lines are perpendicular to the same line, prove that they are parallel to each other. OR 4. From given figure write the following : (A) The coordinates of P (B) The abscissa of the point Q (C) The ordinate of the point R (D) The points whose abscissa is 0 Page 5 of 4

(A) P (B) Q 5. (C) R (D) 0 Section-C Question numbers 5 to 4 carry three marks each. Simplify : 486 486 7 7 l lm m mn n x x x nl m n l x x x Prove that. OR l lm m mn n x x x nl m n l x x x 6. Simplify : 3 3 3 8 4 5 5 6 9 Page 6 of 4

3 3 3 8 4 5 5 6 9 7. Find the value of a if (x) is a factor of the polynomial x 4 ax 3 4x x. a (x) x 4 ax 3 4x x Evaluate using suitable identity : (999) 3 OR (999) 3 8. Using suitable identity evaluate (8) 3 (9) 3 (9) 3. (8) 3 (9) 3 (9) 3 9. The sides BA and DC of a quadrilateral ABCD are produced as shown below. Show that xyab. ABCD BA DC xyab OR Page 7 of 4

In the given figure, if FDA85, ABC45 and ACB40, then prove that DFAE. FDA85, ABC45 ACB40 DFAE 0. In the figure below, if ABDE, then find the measure of ACD. ABDE ACD. In the following figure, inabc of the following figure, B 30, C 65 and the bisector of A meets BC in X. Arrange AX, BX and CX in ascending order of magnitude. Page 8 of 4

BX CX ABC B30, C65 A BC X AX,. In the following figure, AD is the bisector of A of ABC. PQ and PR are perpendiculars from any point lying on AD, P to sides AB and AC respectively. Show that PQA PRA and PQPR. AD ABC A PQ PR, AD P AB AC PQA PRA PQPR 3. In the figure below, l l and m m. Prove that 80. Page 9 of 4

l l m m 80 4. The length of the sides of a triangle are 0 cm, 4 cm and 6 cm respectively. Find the length of the perpendicular drawn from its opposite vertex to the side 5. whose length is 4 cm. Question numbers 5 to 34 carry four marks each. If x94 5, find the value of x x94 x 5 x 0 cm, 4 cm 6 cm 4 cm Section-D x Express. 36 0.3 OR as a fraction in simplest form.. 36 0.3 6. Simplify : 6 3 4 3 3 6 3 6 Page 0 of 4

6 3 4 3 3 6 3 6 7. Factorise : (x 3x) 8(x 3x)0. (x 3x) 8(x 3x)0 8. Using long division method show that the polynomial p(x)x 3 is divisible by q(x)x. Verify your result using Factor Theorem. p(x)x 3, q(x)x 9. If ab and ab7, find the value of a 3 b 3. ab ab7 a 3 b 3 OR The polynomial ax 3 3x 3 and x 3 5xa when divided by x4 leave the same remainder in each case. Find the value of a. ax 3 3x 3 x 3 5xa (x4) a 30. Find the co-ordinates of the vertices of a rectangle placed in III quadrant, in the cartesian plane with length p units on x-axis and breadth q units on y-axis. x- q, y- III p 3. Two sides AB and AC of a ABC (as shown in figure) are produced to P and Q respectively. The bisectors of PBC and QCB intersect each other at O. Prove that BOC 90 A. Page of 4

QCB ABC AB AC P Q PBC O BOC 90 A 3. In the given figure, AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD. Show that A > C and B > D. A > C AB CD ABCD B > D 33. In Fig. given below, AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD. Show that B > D. Page of 4

ABCD AB CD B > D. 34. In the given figure, PQRS is a square and SRT is an equilateral triangle. Prove that : (i) PST QRT (ii) PTQT (iii) QTR5 PQRS SRT (i) PST QRT (ii) (iii) PTQT QTR5 Page 3 of 4

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