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1 SUMMATIVE ASSESSMENT I (0) Lakdfyr ijh{kk &I MATHEMATICS / f.kr Class IX / & IX 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 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 ;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,, 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.. Two rational numbers between and 5 are : 3 3 Page of

(A) and 6 6 (B) and 5 7 6 6 (C) and (D) and 4 5 3 3 3 3 (A) 6 6 (B) (C) 5 7 (D)

2 (A) and 6 6 (B) and (C) and (D) and (A) 6 6 (B) (C) 5 7 (D) Which of the following is a trinomial in? (A) 3 (B) 3 (C) (A) 3 (C) (D) 3 (B) 3 (D) 3 3. A cubic polynomial is a polynomial with degree : (A) (B) 3 (C) 0 (D) : (A) (B) 3 (C) 0 (D) 4. The zeroes of the polynomial p()(6) (5) are : (A) 6, 5 (B) 6, 5 (C) 6, 5 (D) 6, 5 p()(6) (5) (A) 6, 5 (B) 6, 5 (C) 6, 5 (D) 6, 5 5. In the figure, AOB is a straight line. The measure of COD is equal to : Page of

3 (A) 60 (B) 80 (C) 0 (D) 60 AOB COD (A) 60 (B) 80 (C) 0 (D) The eterior angle of a triangle is equal to the sum of two (A) Eterior angles (C) Interior opposite angles (B) Interior angles (D) Alternate angles 7. (A) (B) (C) (D) The sides of a are 7 cm, 4 cm and 5 cm. Its area is : (A) 68 cm (B) 84 cm (C) 87.5 cm (D) 300 cm (A) (B) 84 (C) 87.5 (D) The sides of a triangular plot are in the ratio 4 : 5 : 6 and its perimeter is 50 cm. Then the sides are (A) 4 cm, 5 cm, 6 cm (B) 40 cm, 50 cm, 60 cm (C) 8 cm, 0 cm, cm (D) 0 cm, 50 cm, 80 cm 4 : 5 : 6 50 (A) 4, 5, 6 (B) 40, 50, 60 Page 3 of

In figure, OP bisects BOC and OQ bisects

4 (C) 8, 0, (D) 0, 50, 80 Section-B Question numbers 9 to 4 carry two marks each. 9. Evaluate : Using factor theorem, prove that g () 4 is a factor of p() g () 4, p() Evaluate using a suitable identity ; (999) 3. (999) 3. In figure, OP bisects BOC and OQ bisects AOC. Show that POQ90 OP, BOC OQ, AOC POQ90 3. In the given figure, D is the mid point of base BC, DE and DF are Page 4 of

5 perpendiculars to AB and AC respectively such that DEDF. B C. Prove that BC D DE DF AB AC DEDF. B C. OR An angle is equal to five times its complement. Find the measure of the angle. 4. Write the co-ordinates of A, B, C and D from the following figure : A, B, C D Page 5 of

6 Section-C Question numbers 5 to 4 carry three marks each. 5. Find the value of : Simplify : OR 6. Epress 3 3 with rational denominator. 7. Without finding the cubes, find the value of : Page 6 of

7 Factorize : 37 (ab). OR 37 (ab) 8. If 9 then find the value of In the figure below, ABAC, DBDC. Prove that ABDACD. ABAC, DBDC ABDACD OR In the figure given below, if PQRS and PXM50 and MYS0, find the value of. PQRS PXM50 MYS0 Page 7 of

8 0. In the given figure, POQ is a line. Ray OR PQ, OS is another ray lying between rays OP and OR. Prove that ROS QOS POS. POQ OR PQ, OS OP OR ROS QOS POS.. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that BADABE and EPADPB. Show that DAPEBP. AB P D E AB BADABE EPADPB. DAPEBP.. ABC is an isosceles triangle with ABAC. P and Q are points on AB and AC respectively such that APAQ. Prove that CPBQ. Page 8 of

9 ABC ABAC AB AC P Q APAQ CPBQ. 3. In figure, prove that ABEF. ABEF. 4. The sides of a triangular ground are 5m, 7m and 8m respectively. Find the cost of levelling the ground at the rate of Rs. 0 per m. (use 3. 73). ( 3. 73) Question numbers 5 to 34 carry four marks each. Section-D Page 9 of

10 5. Rationalize the denominator of If a74 3, find the value of a a OR a74 3 a a 6. Epress as a fraction in simplest form Simplify : (5a3b) 3 (5a3b) 3 (5a3b) 3 (5a3b) 3 3 If 34, find 9. 3 considering only ve values of Factorise a 7 ab 6. a 7 ab 6. Factorise : 3u 3 4u u6 OR 3u 3 4u u6 30. (i) Plot the points A (0, 4), B (3, 0), C (0,4), D (3, 0) Page 0 of

11 (ii) Name the figure obtained by joining the points A, B, C, D. (iii) Also, name the quadrants in which sides AB and AD lie. (i) A (0, 4), B (3, 0), C (0,4) D (3, 0) (ii) A, B, C D ABCD (iii) AB AD 3. The sides AB and AC of ABC are produced to points P and Q respectively. If bisectors of PBC and QCB intersect at O. Prove that BOC90 A. ABC AB AC P Q PBC QCB O BOC90 A. 3. ABCD is quadrilateral in which ABBC and ADCD. Show that BD bisects both the angles ABC and ADC. ABCD ABBC ADCD. BD ABC ADC 33. ABC is an isosceles triangle with ABAC. Side BA is produced to D such that ABAD. Prove that BCD is a right angle. ABAD ABC ABAC BA D BCD 34. ABC is a triangle, in which altitudes BE and CF to sides AC and AB respectively are equal. Show that ABEACF. Also, show that ABC is an isosceles triangle. Page of

12 ABC BE CF, AC AB ABCACF. ABC Page of

SUMMATIVE ASSESSMENT I, 2014

SUMMATIVE ASSESSMENT I, 2014 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