SUMMATIVE ASSESSMENT I (2011) Lakdfyr ijh{kk &I. MATHEMATICS / xf.kr Class IX / & IX

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1 SUMMATIVE ASSESSMENT I (0) Lakdfyr ijh{kk &I 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

2 . p q form of the number 03. is : 3 3 (A) (B) (C) (D) p q 3 3 (A) (B) (C) (D) Which of the following is a cubic polynomial? (A) (B) 47 (C) 3 4 (D) 3( ) (A) (B) 47 (C) 3 4 (D) 3( ) 3. If a polynomial f () is divided by a, then remainder is (A) f (0) (B) f (a) (C) f (a) (D) f (a) f (0) f () a (A) f (0) (B) f (a) (C) f (a) (D) f (a) f (0) 4. What is the remainder when 3 is divided by ()? (A) 0 (B) (C) (D) 3 () (A) 0 (B) (C) (D) 5. In the figure below if ABAC, the value of is : Page of

3 (A) 55 (B) 0 (C) 50 (D) 70 ABAC (A) 55 (B) 0 (C) 50 (D) If ABC is congruent to DEF by SSS congruence rule, then : (A) C < F (B) B < E (C) A < D (D) A D, B E, C F SSS ABCDEF (A) C < F (B) B < E (C) A < D (D)A D, BE,CF 7. The area of an equilateral triangle is 6 3 m. Its perimeter (in metres) is : (A) (B) 48 (C) 4 (D) m (A) (B) 48 (C) 4 (D) The base of a right triangle is 5 cm and its hypotenuse is 5 cm. Then its area is : (A) 87.5 cm (B) 375 cm (C) 50 cm (D) 300 cm 5 5 (A) 87.5 (B) 375 (C) 50 (D) 300 Page 3 of

4 Section-B Question numbers 9 to 4 carry two marks each. 9. Simplify If () is a factor of the polynomial p() a then find the value of a? () p() a a. Simplify : In the given figure, find the value of. 3. In the figure, OAOB and ODOC. Show that (i) AOD BOC (ii) ADBC OAOB ODOC (i) AOD BOC (ii) ADBC Page 4 of

5 An eterior angle of a triangle is 0 and one of the interior opposite angles is 40. Find the other two angles of a triangle A point lies on ais at a distance of 9 units from y ais. What are its coordinates? What will be the coordinates of a point if it lies on y ais at a distance of 9 units from ais? y - 9 y (9) Section-C Question numbers 5 to 4 carry three marks each. 5. Find the value of Represent 3 on number line. 3 Page 5 of

6 6. Prove that Factorise : What are the possible epressions for the dimensions of a cuboid whose volume is given below? Volume ky 8ky0k. ky 8ky0k 8. If y6 then find the value of 3 8y 3 36y6. y6 3 8y 3 36y6 9. In ABC, B45, C55 and bisector of A meets BC at a point D. Find ADB and ADC. ABC B45, C55 A BC D ADB ADC In the figure below, l l and a a. Find the value of. Page 6 of

7 l l a a 0. In the figure below, l l and m m. Prove that 80. l l m m 80. In the given figure, ABAC, D is the point in the interior of ABC such that DBC DCB. Prove that AD bisects BAC of ABC. ABAC ABC D DBC DCB AD ABC BAC Page 7 of

8 . In the given figure, ABBC and ADEC. Prove that ABE CBD. ABBC ADEC ABE CBD 3. In the given figure, if ABCD, APQ50 and PRD7, find and y. AB CD, APQ50 PRD7, y 4. The perimeter of a triangular field is 300 cm and its sides are in the ratio 5 : : 3. Find the length of the perpendicular from the opposite verte to the side whose length is 30 cm : : 3 30 Page 8 of

9 Question numbers 5 to 34 carry four marks each. Section-D 5. Find the values of a and b if a 5b a 5b a b Evaluate after rationalizing the denominator of that 5.36 and It is being given Simplify : Prove that : (a b ) 3 (b c ) 3 (c a ) 3 3 (ab) (bc) (ca) (ab) (bc) (ca) (a b ) 3 (b c ) 3 (c a ) 3 3 (ab) (bc) (ca) (ab) (bc) (ca) 8. If remainder is same when polynomial p() 3 8 7a is divided by () and (), find the value of a. p() 3 8 7a () () a Page 9 of

10 9. Find and, if () and () are factors of () () Factorize : Plot the points A (4, 0) and B (0, 4). Join AB to the origin O. Find the area of AOB. A (4, 0) B (0, 4) O,A, B AOB 3. In the given figure, if PQST, PQR0 and RST30find QRS. PQST, PQR0 RST30 QRS 3. In the given 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. T PQR QR S PQR PRS QTR QPR. Page 0 of

11 33. ABCD is a parallelogram. If the two diagonals are equal. Find the measure of ABC. ABCD ABC 34. In figure, ABC is an isosceles triangle in which ABAC. Side BA is produced to D such that ADAB. Show that BCD is a right angle. ABC ABAC BA D ADAB BCD Page of

12 SUMMATIVE ASSESSMENT I (0) Lakdfyr ijh{kk &I 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

13 . 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

14 (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 ABAC, B50, then A is equal to : (A) 40 (B) 50 (C) 80 (D) 30 ABC ABAC, B50 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

15 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 y8 and y5, find y. y8 y5, y. In the given figure, if P and Q form a linear pair and ab80, then find the value of a and b. P Q ab80 a b 3. In figure, BE, BDCE and. Show ABC AED. BE, BDCE ABC AED. Page 4 of

16 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 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

17 If 3 7, then find the value of Factorise : 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 In the following figure, PQST, PQR 5 and RST 30. Find the value of. Page 6 of

18 PQST 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

19 . In the given figure, ACBC, DCA ECB and DBC EAC. DBCEAC and hence DCEC. Show that DCEC. ACBC, DCA ECB DBC EAC DBCEAC 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 3 3 and b 3 3, find the value of a b 5 ab. Page 8 of

20 a 3 3 b 3 3 a b 5 ab 6. Rationalize the denominator of Factorize : (a) 4a 9b a3b. (b) a b (abacbc) (a) 4a 9b a3b. (b) a b (abacbc) 8. If (5) is a factor of 3 30, find the other factors (5) 9. Factorize a 7 ab 6. a 7 ab 6 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

21 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

22 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, ABAC, E is the mid point of AB and F is the mid point of AC. Show that BFCE. ABC ABAC E AB F AC BFCE. Page of

23 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 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

24 . The value of is : (A) (B) 0 (C) 9 5 (D) (A) (B) 0 (C) 9 5 (D) 5. Which of the following epressions is a polynomial? (A) (B) (C) 3 3 (D) (A) (B) (C) 3 3 (D) 3. What is the coefficient of in the polynomial 3 4? 6 (A) 3 (B) 4 (C) (D) (A) 3 (B) 4 (C) 6 (D) 0 4. The maimum number of terms in a polynomial of degree 0 is : (A) 9 (B) 0 (C) (D) 0 (A) 9 (B) 0 (C) (D) 5. In the figure below, if, y and z are eterior angles of ABC, then yz is : Page of

25 (A) 80 (B) 360 (C) 70 (D) 90, y z ABC yz (A) 80 (B) 360 (C) 70 (D) In ABC and DEF, ABFD, A D. The two triangles will be congruent by SAS aiom if : (A) BCDE (B) ACEF (C) BCEF (D) ACDE ABC DEF ABFD, A D SAS (A) BCDE (B) ACEF (C) BCEF (D) ACDE 7. The perimeter of a triangle is 36 cm and its sides are in the ratio a : b : c 3 : 4 : 5 then a, b, c are respectively : (A) 9 cm, 5 cm, cm (B) 5 cm, cm, 9 cm (C) cm, 9 cm, 5 cm (D) 9 cm, cm, 5 cm 36 a : b : c 3 : 4 : 5 a, b, c (A) 9, 5, (B) 5,, 9 (C), 9, 5 (D) 9,, 5 8. The area of ABC in which ABBC4cm and B 90 is : (A) 6 cm (B) 8cm (C) 4cm (D) cm ABBC4 B 90 Page 3 of

26 (A) 6 (B) 8 (C) 4 (D) Section-B Question numbers 9 to 4 carry two marks each. 9. Simplify : Find the remainder when 4 3 is divided by Using suitable identity prove that : In the given figure, if AOB is a line then find the measure of BOC, COD and DOA. AOB BOC, COD DOA Page 4 of

27 3. In the given figure, AB > AC and BO and CO are the bisectors of B and C respectively. Show that OB > OC. AB > AC BO CO B C OB > OC In the figure below, ray OC stands on the line AB. Ray OP bisects AOC and ray OQ bisects BOC. Prove that POQ90. OC AB OP, AOC OQ BOC POQ90 4. Plot the point P (, 6) on a graph paper and from it draw PM and PN perpendiculars to -ais and y-ais, respectively. Write the coordinates of the points M and N. P(, 6) P PM PN - y - Page 5 of

28 M N Section-C Question numbers 5 to 4 carry three marks each. 5. Simplify : Simplify : Simplify the following : If , then find the value of Factorise : y 6y8 y 6y8 8. Factorize : 8 a 3 b 3 a b6ab 8a 3 b 3 a b6ab 9. The eterior angles obtained on producing the base of a triangle both ways are Page 6 of

29 00 and 0. Find all the angles In the following figure, PQRS, MXQ 35 and MYR 35. Find XMY PQRS, MXQ 35 MYR 35 XMY 0. In the given figure, PQR PRQ, then prove that PQS PRT. PQR PRQ PQS PRT.. In the figure, AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD. Show that A > C Page 7 of

30 ABCD CD AB A > C. ABC is an isosceles triangle in which ABAC. Side BA is produced to D such that ADAB. Show that BCD is a right angle. ABC ABAC BA D ADAB. BCD 3. In the given figure, if BE is bisector of ABC and CE is bisector of ACD, then show that BEC BAC. BE CE ABC ACD BEC BAC. 4. Manisha has a garden in the shape of a rhombus. The perimeter of the garden is 40 m and its diagonal is 6 m. She wants to divide it into two equal parts and use these parts in rotation. Find the area of each part of the garden Question numbers 5 to 34 carry four marks each. Section-D Page 8 of

31 5. Rationalise the denominator of Epress with rational denominator If a 3 3 and b 3 3, find the value of a b 5 ab. a 3 3 b 3 3 a b 5 ab 7. If (yz)0, then prove that ( 3 y 3 z 3 )3yz. (yz)0 ( 3 y 3 z 3 )3yz 8. The lateral surface area of a cube is 4 times the square of its edge, find the edge of a cube whose lateral surface area is given by : If is the root of the equation (p)0 and is also the zero of the polynomial p k then find the value of k. k (p)0 p k Without actual division prove that is eactly divisible by Page 9 of

32 30. Plot the points A (3, 3), B (3, 3), C (3, 3), D (3, 3) in the cartesian plane. Also, find the length of line segment AB. AB A (3, 3), B (3, 3), C (3, 3) D (3, 3) 3. Prove that if two lines intersect, then the vertically opposite angles are equal. 3. Q is a point on side SR of PSR as shown in the figure below such that PQPR. Show that PS > PQ. PSR SR Q PQPR PS > PQ 33. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of PQR. Show that ABCPQR. ABC PQR ABPQ, BCQR AM PN ABCPQR. Page 0 of

33 34. In the figure given below, y and PQQR. Prove that PERS. y PQQR PERS. Page of

34 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 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 fodyiksa esa ls,d lgh fodyi pquuk gsa (iv) bl iz u i= esa dksbz Hkh loks Zifj 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.. Every rational number is : Page of

35 (A) a natural number (C) a real number (B) an integer (D) a whole number (A) (C) (B) (D). If p() 3, then value of p( ) p() is : (A) 4 (B) 4 (C) 0 (D) p() 3, p( ) p() (A) 4 (B) 4 (C) 0 (D) 3. If p() 3 3 4, then p() is : (A) (B) (C) 0 (D) p() p() (A) (B) (C) 0 (D) 4. If AB3, BCand AC45, then for what value of, B lies on AC? (A) 8 (B) 5 (C) (D) 3 AB3, BC AC45 B AC (A) 8 (B) 5 (C) (D) 3 5. Find the measure of the angle which is complement of itself : (A) 30 (B) 90 (C) 45 (D) 80 (A) 30 (B) 90 (C) 45 (D) In ABC and PQR, ABPR and AP. The two triangles will be congruent by SAS aiom if : Page of

36 (A) BCQR (B) ACPQ (C) ACQR (D) BCPQ ABC PQR ABPR AP SAS (A) BCQR (B) ACPQ (C) ACQR (D) BCPQ 7. The area of an equilateral triangle is 6 3 m. Its perimeter (in metres) is : (A) (B) 48 (C) 4 (D) m (A) (B) 48 (C) 4 (D) The area of a triangle whose sides are 3 cm, 4 cm and 5 cm is : (A) 4 cm (B) 86 cm (C) 84 cm (D) 00 cm (A) 4 (B) 86 (C) 84 (D) 00 Section-B Question numbers 9 to 4 carry two marks each. 9. Simplify : Factorize : Write the epansion of (3yz). (3yz) Page 3 of

37 . In the adjoining figure, ACXD, C is midpoint of AB and D is midpoint of XY. Using an Euclid s aiom, show that ABXY. ACXD C, AB D, XY (aiom) ABXY. 3. In the figure below, O is the mid point of AB and CD, prove that ACBD. O AB CD ACBD. In the figure below, AOC and BOC form a linear pair. If b80, find the Page 4 of

38 value of a. AOC BOC b80, a 4. Plot the point P (, 6) on a graph paper and from it draw PM and PN perpendiculars to -ais and y-ais, respectively. Write the coordinates of the points M and N. P(, 6) P PM PN - y - M N Section-C Question numbers 5 to 4 carry three marks each. 5. Prove that If a, b3 then find the values of the following : (i) (a b b a ) (ii) (a a b b ) a, b3 Page 5 of

39 (i) (a b b a ) (ii) (a a b b ) 6. If 3, then find the value of Divide the polynomial by and find its quotient and remainder If both () and are factors of p 5r, show that pr. () p 5r pr 8. Using suitable identity evaluate (4) 3 (8) 3 (4) 3. (4) 3 (8) 3 (4) 3 9. Prove that the sum of three angles of a triangle is In the following figure, lm and TR is a transversal. If OP and RS are respectively bisectors of corresponding angles TOB and D, prove that OPRS. lm TR OP RS TOB D OPRS Page 6 of

40 0. In the given figure, X7, XZY46. If YO and ZO are bisectors of XYZ and XZY respectively of XYZ, find OYZ and YOZ. X7, XZY46 YO ZO XYZ XYZ XZY OYZ YOZ. In Fig. given below, AD is the median of ABC. BEAD, CFAD. Prove that BECF. ABC AD BEAD CFAD BECF.. Prove that angles opposite to equal sides of an isosceles triangle are equal. Page 7 of

41 3. In the given figure, if FDA85, ABC45 and ACB40, then prove that DFAE. DFAE FDA85, ABC45 ACB40, 4. A triangular park has sides 0 m, 80 m and 50 m. A gardener has to put a fence all around it and also plant grass inside. How much area does he need to plant? Find the cost of fencing it with barbed wire at the rate of Rs. 0 per meter leaving a space 3 m wide for a gate on one side Page 8 of

42 Question numbers 5 to 34 carry four marks each. Section-D 5. Rationalize the denominator of If a74 3, find the value of a a a74 3 a a 6. Epress as a fraction in simplest form The polynomials a and 3 5a when divided by () leave the remainders p and q respectively. If pq4, find the value of a. () a a p q pq4 a 8. If 4 is a zero of the polynomial p() 3 44, find the other zeroes. p() (i) Epand a b 4 (ii) (i) Evaluate (0) 3, using suitable identity. a b 4 (ii) (0) 3 Factorise : a 3 b 3 3ab. Page 9 of

43 a 3 b 3 3ab 30. Plot the points given in the table below in the Cartesian plane. 3. In the figure below, if PQST, PQR0 and RST30, find QRS. PQST PQR0 RST30 QRS 3. Prove that the sum of any two sides of a triangle is greater than twice the length of median drawn to the third side. 33. In the given figure, if AD is the bisector of BAC then prove that : (i) AB > BD (ii) AC > CD AD BAC (i) AB > BD (ii) AC > CD Page 0 of

44 34. In figure below, ABAD, ACAE and BAD CAE. Prove that BCDE. ABAD, ACAE BAD CAE BCDE. Page of

45 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 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 fodyiksa esa ls,d lgh fodyi pquuk gsa (iv) bl iz u i= esa dksbz Hkh loks Zifj 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 Questions number 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

46 . Value of is : 3 (A) (B) 9 (C) 3 (D) (A) (B) 9 (C) 3 (D) 9 3. is a polynomial of degree : (A) (B) 0 (C) (D) (A) (B) 0 (C) (D) 3. Degree of the polynomial ( 3 )( ) is : (A) 0 (B) 5 (C) 3 (D) ( 3 ) ( ) (A) 0 (B) 5 (C) 3 (D) 4. Degree of which of the following polynomials is zero : (A) (B) 5 (C) y (D) (A) (B) 5 (C) y (D) 5. Two angles measure (30a) and (5a). If each one is the supplement of the other, then the value of a is : (A) 45 (B) 35 (C) 5 (D) 65 (30a) (5a) a (A) 45 (B) 35 (C) 5 (D) 65 Page of

47 6. In ABC, if BCAB and B80, then A is equal to : (A) 80 (B) 40 (C) 50 (D) 00 ABC BCAB B80 A (A) 80 (B) 40 (C) 50 (D) The area of a triangle whose sides are 3 cm, 4 cm and 5 cm is : (A) 4 cm (B) 86 cm (C) 84 cm (D) 00 cm (A) 4 (B) 86 (C) 84 (D) The area of an equilateral triangle is 6 3 m. Its perimeter (in metres) is : (A) (B) 48 (C) 4 (D) m (A) (B) 48 (C) 4 (D) 306 Section-B Question numbers 9 to 4 carry two marks each. 9. Evaluate, Find the value of a if () is a factor of a. () a a. 4 4 Find the product of,, and. 4,, and 4. In figure, AEDF, E is the mid point of AB and F is the mid point of DC. Using an Page 3 of

48 Euclid aiom, show that ABDC. AEDF E AB F DC ABDC 3. ABC is an isosceles triangle with ABAC. Draw AP BC. Show that B C. ABC ABAC AB BC B C. In the given figure, line segments PQ and RS intersect each other at a point T such that PRT40, RPT95 and TSQ75. Find SQT. PQ RS T PRT40, RPT95 TSQ75 SQT Page 4 of

49 4. Which of the following points lies on -ais? Which on y ais? A(0, ), B(5, 6), C(3, 0), D(0, 3), E(0, 4), F(6, 0), G(3, 0) y A(0, ), B(5, 6), C(3, 0), D(0, 3), E(0, 4), F(6, 0), G(3, 0) Section-C Question numbers 5 to 4 carry three marks each. 5. Find the value of : Represent 3. on the number line Simplify the following into a fraction with rational denominator If pa, prove that a 3 6app Page 5 of

50 pa a 3 6app Factorize Using suitable identity evaluate (3) 3 (8) 3 (4) 3. (3) 3 (8) 3 (4) 3 9. Prove that if two lines intersect, the vertically opposite angles are equal. If the bisector of a pair of interior alternate angles formed by a transversal with two given lines are parallel, prove that the given lines are parallel. 0. ABC is a right angled triangle in which A90 and ABAC, find the values of B and C. ABC A90 ABAC B C. In given figure below, ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that (i) ABE ACF Page 6 of

51 (ii) ABAC ABC BE CF AC AB (i) ABE ACF (ii) ABAC. In given figure below, C is the mid point of AB. ACEBCD and CADCBE. Show that (i) DAC EBC (ii) ADBE AB C ACEBCD CADCBE (i) DAC EBC (ii) ADBE 3. In figure, prove that l m. Page 7 of

52 l m. 4. Find the height of the trapezium in which parallel sides are 5 cm and 0 cm and non parallel sides are 4 cm and 3 cm Question numbers 5 to 34 carry four marks each. Section-D Simplify : If and y, find the value of yy. 3 3 Page 8 of

53 y 3 3 If 94 5, find the value of, yy (i) Epand a b 4 (ii) (i) Evaluate (0) 3, using suitable identity. a b 4 8. (ii) (0) 3 If 3ab5c5 and 6ab0bc5ac4, find the value of 7a 3 5c 3 90abc8b 3. 3ab5c5 6ab0bc5ac4 7a 3 5c 3 90abc8b 3 9. State Factor theorem. Using this theorem factorise Find the value of a if the polynomias a and 3 5a when divided by (4), leave the same remainder. a a (4) a 30. Plot the points A (0, 3), B (5, 3), C (4, 0), and D (, 0) on the graph paper Identify the figure ABCD and find whether the point (, ) lies inside the figure or not? A (0, 3), B (5, 3), C (4, 0), D (, 0) ABCD (, ) Page 9 of

54 3. In figure given below, if ABCD, EF CD and GED6, find AGE, GEF and FGE. ABCD, EF CD GED6 AGE, GEF FGE 3. In figure below, D is a point on side BC of ABC such that ADAC. Show that AB > AD. AB > AD ABC BC D ADAC 33. In the given figure, if ABFE, BCED, AB BD and FE EC, then prove that ADFC. Page 0 of

55 ABFE, BCED, AB BD FE EC ADFC. 34. ABC is an isoceles triangle in which ABAC. Side BA is produced to D such that ADAB. Show that BCD is a right angle. ABC ABAC BA D ADAB BCD Page of