SUMMATIVE ASSESSMENT I, 2014

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1 SUMMATIVE ASSESSMENT I (0) SUMMATIVE ASSESSMENT I, 04 MATHEMATICS Lakdfyr ijh{kk CLASS &I - IX MATHEMATICS / f.kr Class IX / & IX 4600 Time allowed: 3 hours Maimum 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 0 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 ;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 0 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,, gsaa izr;sd iz u es a,d fodyi dk p;u djsaa (v) dsydqysvj dk iz;ks 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 page - 0

2 . The simplified form of is : (A) (B) 3 5 (C) 3 3 (D) (A) (B) 3 5 (C) 3 3 (D) 3 5. Which of the following is a polynomial in one variable : (A) 3 (B) (C) y 7 (D) (A) 3 (B) (C) y 7 (D) 3. Which of the following is a quadratic polynomial? (A) (B) (C) 3 (D) ( ) ( ) (A) (B) (C) 3 (D) ( ) ( ) 4. y If, (, y 0), then, the value of 3 y 3 is : y (A) (B) (C) 0 (D) y, (, y 0) 3 y 3 y Page of

3 (A) (B) (C) 0 (D) 5. Value of in the figure below is : (A) 80 (B) 40 (C) 60 (D) 0 (A) 80 (B) 40 (C) 60 (D) 0 6. In ABC, if AB AC, B 50, then A is equal to : (A) 40 (B) 50 (C) 80 (D) 30 ABC AB AC, B 50 A (A) 40 (B) 50 (C) 80 (D) A square and an equilateral triangle have equal perimeters. If the diagonal of the square is cm then area of the triangle is : (A) 4 cm (B) 4 3 cm (C) 48 3 cm (D) 64 3 cm (A) 4 (B) 4 3 (C) 48 3 (D) The side of an isosceles right triangle of hypotenuse 5 cm is : (A) 0 cm (B) 8 cm (C) 5 cm (D) 3 cm 5 (A) 0 (B) 8 (C) 5 (D) 3 Page 3 of

4 Section-B Question numbers 9 to 4 carry two marks each. 9. If 3, then find whether is rational or irrational Without actually calculating the cubes, find the values of If y 8 and y 5, find y. y 8 y 5, y. In the given figure, if POR and QOR form a linear pair and a b 80, then find the value of a and b. POR QOR a b 80 a b 3. In figure, B E, BD CE and. Show ABC AED. B E, BD CE ABC AED. Page 4 of

5 OR In the figure given below AC > AB and AD is the bisector of A. Show that ADC > ADB. AC > AB A AD ADC > ADB. 4. Find the co-ordinates of the point which lies on y ais at a distance of 4 units in negative direction of y ais. (A) ( 4, 0) (B) (4, 0) (C) (0, 4) (D) (0, 4) y 4 (A) ( 4, 0) (B) (4, 0) (C) (0, 4) (D) (0, 4) Section-C Question numbers 5 to 4 carry three marks each. 5. Represent on the number line. Epress 8.48 in the form of p q OR where p and q are integers, q p q p q q 0 6. If 5 6 then find the value of. Page 5 of

6 If 3 7, then find the value of Factorise : OR Using suitable identity evaluate (998) 3. (998) 3 9. In the given figure, lines AB and CD intersect at O. If AOC BOE 70 and BOD 40, find BOE and refle EOC. BOE AB CD O EOC AOC BOE 70 BOD 40 OR In the following figure, PQ ST, PQR 5 and RST 30. Find the value of. Page 6 of

7 PQ ST PQR 5 RST In the given figure, ABC is a triangle with BC produced to D. Also bisectors of and ACD meet at E. Show that BEC BAC. ABC E ABC BC D ABC ACD BEC BAC. In the given figure, sides AB and AC of ABC are etended to points P and Q respectively. Also PBC < QCB. Show that AC > AB. PBC < QCB. ABC AB AC P Q AC > AB. Page 7 of

8 . In the given figure, AC BC, DCA ECB and DBC EAC. DBC EAC and hence DC EC. Show that DC EC. AC BC, DCA ECB DBC EAC DBC EAC 3. The degree measure of three angles of a triangle are, y, and z. If then find the value of z. y, y, z z z y z 4. The perimeter of a triangular ground is 900 m and its sides are in the ratio 3 : 5 : 4. Using Heron s formula, find the area of the ground : 5 : 4 Question numbers 5 to 34 carry four marks each. Section-D y 5 5 If and then evaluate y. 5 5 y 5 5 y If a and b OR, find the value of a b 5 ab. Page 8 of

9 a b a b 5 ab 6. Rationalize the denominator of Factorize : (a) 4a 9b a 3b. (b) a b (ab ac bc) (a) 4a 9b a 3b. (b) a b (ab ac bc) 8. If ( 5) is a factor of 3 3 0, find the other factors ( 5) 9. Factorize a 7 ab 6. a 7 ab 6 OR If a 3 b 6 has as a factor and leaves remainder 4 when divided by, find the values of a and b. a 3 b 6 ( ) 4 a b 30. In the given figure, PQR is an equilateral triangle with coordinates of Q and R as (, 0) and (, 0) respectively. Find the coordinates of the verte P. Page 9 of

10 P PQR Q R (, 0) (, 0) 3. In the adjoining figure, the side QR of PQR is produced to a point S. If the bisectors of PQR and PRS meet at point T, then prove that QTR QPR. Page 0 of

11 T PQR QR S PQR PRS QTR QPR. 3. In the following figure, the sides AB and AC of ABC are produced to D and E respectively. If the bisectors of CBD and BCE meet at O, then show that A BOC 90. BCE ABC AB AC D E CBD A O BOC BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles. ABC BE CF RHS ABC 34. In a triangle ABC, AB AC, E is the mid point of AB and F is the mid point of AC. Show that BF CE. ABC AB AC E AB F AC BF CE. Page of

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