SUMMATIVE ASSESSMENT II, 2012 MATHEMATICS / Class IX /

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1 SUMMATIVE ASSESSMENT II, MATHEMATICS / II, 2012 Class IX / IX Time allowed : 3 hours Maximum Marks : 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 1 mark each, Section-B comprises of 6 questions of 2 marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 10 questions of 4 marks each. (iii) Question numbers 1 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 choices have been provided in 1 question of two marks, 3 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. (i) (ii) (iii) 1 8 (iv) 2 3 (v) Page 2 of 12

2 SECTION A / Question numbers 1 to 8 carry one mark each. For each questions, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1. Any point on the line y x is of the form : (A) (a, a) (B) (0, a) (C) (a, 0) (D) (a, a) y x (A) (a, a) (B) (0, a) (C) (a, 0) (D) (a, a) 2. A triangle and a parallelogram are on the same base and between the same parallels ; then the ratio of the area of the triangle to that of the parallelogram is (A) 1 : 1 (B) 2 : 1 (C) 1 : 2 (D) 1 : 4 एक त र ब ज तथ एक सभ तय चत ब ज एक ह आध य तथ एक ह सभ तय य ख ओ क फ च स थथत ह, त त र ब ज क पर क सभ तय चत ब ज क पर स अन ऩ त ह (A) 1 : 1 (B) 2 : 1 (C) 1 : 2 (D) 1 : 4 3. In the given figure, A, B, C and D are points on the circle such that ACB 40 and DAB 60, the measure of DBA is : (A) 70 (B) 80 (C) 60 (D) 100 DBA A, B, C, D ACB 40 DAB 60 (A) 70 (B) 80 (C) 60 (D) The equation x 7, in two variables can be written as : (A) 1.x 1.y 7 (B) 1.x 0.y 7 (C) 0.x 1.y 7 (D) 0.x 0.y 7 x 7 Page 3 of 12

3 (A) 1.x 1.y 7 (B) 1.x 0.y 7 (C) 0.x 1.y 7 (D) 0.x 0.y 7 5. Calculate the median of the following data : 4, 6, 9, 10, 13, 14 (A) 9 (B) 19 (C) 9.5 (D) 10 4, 6, 9, 10, 13, 14 (A) 9 (B) 19 (C) 9.5 (D) If the dimensions of a cuboid are a, b and c respectively, then the volume of the cuboid is. (A) abc (B) (ab bc ca) (C) a 3 (D) a 2 b 2 c 2 मदद एक घन ब क त र भ ऍ क रभश a, b, c ह, त घन ब क आमतन ह : (A) abc (B) (ab bc ca) (C) a 3 (D) a 2 b 2 c 2 7. When a coin is tossed 500 times, the following outcomes were recorded : Head : 270 times, Tail : 230 times If now a coin is tossed, the probability of getting a Head is : (A) (B) (C) 1 (D) (A) (B) (C) 1 (D) If the diameter of a sphere and the side of a cube are equal, then the ratio of volume of the cube to that of the sphere is. (A) 3 : 4 (B) 21 : 11 (C) 4 : 3 (D) 11 : 21 मदद एक ग र क व म स तथ एक घन क ब ज सभ न ह, त घन क आमतन क ग र क आमतन क अन ऩ त ह : (A) 3 : 4 (B) 21 : 11 (C) 4 : 3 (D) 11 : 21 SECTION-B / Page 4 of 12

4 Question numbers 9 to 14 carry two marks each. 9. ABCD is a quadrilateral and BD is one of its diagonals as shown in figure. Show that ABCD is a parallelogram and find its area. ABCD एक चत ब ज ह तथ BD उसक एक कर ह ज स आक तत भ दश म गम ह दश इए दक ABCD एक सभ तय चत ब ज ह तथ उसक पर ब त क स जए 10. The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes. द फ रन क त र ज म ओ भ 2 : 3 क अन ऩ त ह तथ उनक ऊ च ईम भ 5 : 3 क अन ऩ त ह, त उनक आमतन भ अन ऩ त त क स जए 11. The mean of 5 observations was calculated as 145, but it was later on detected that one observation was misread as 45 in place of 25. Find the correct mean of the observations A die is thrown 1000 times with the frequencies of outcomes 1, 2, 3, 4, 5 and 6 as given below : Outcome : Frequency : A die is thrown once again. Find the probability of outcome greater than , 2, 3, 4, Page 5 of 12

5 3 13. In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If DBC 55 and BAC 45, find BCD. BAC 45 BCD ABCD AC BD DBC 55 OR In the given figure, two chords AB and CD of a circle, with centre O, are such that OP and OQ, the perpendicular from the centre to the chords, are equal. Show that AB CD. AB CD. AB CD O OP OQ 14. Find the mode of the observations 17, 23, 25, 18, 17, 23, 19, 23, 17, 26, 23. If 4 is subtracted from each observation, what will be the mode of the new observations. 17, 23, 25, 18, 17, 23, 19, 23, 17, 26, 23 4 SECTION-C / Page 6 of 12

6 Question numbers 15 to 24 carry three marks each. 15. Express x in term of y, it is being given that 7x 3y 15. Check if the line represented by the equation intersects the y-axis at y 5. 7x 3y 15 x y y- y If a parallelogram and a triangle are on the same base and between the same parallels, then prove that area of the triangle is equal to half the area of the parallelogram. मदद एक सभ तय चत ब ज तथ एक त र ब ज एक ह आध य तथ एक ह सभ तय य ख ओ क फ च स थथत ह, त तसद ध क स जए दक त र ब ज क पर सभ तय चत ब ज क पर क आध ह 17. Construct a ABC in which BC 7 cm, B 75 and AB AC 12 cm. ABC BC 7 B 75 AB AC The length of a cinema hall is 20 m and its width is 16 m. The sum of the areas of its floor and flat roof is equal to the surface area of its four walls. Find the volume and height of the hall. एक तसन भ ह र क रम फ ई 20 भ तथ च ड़ ई 16 भ ह मदद इसक पश तथ सऩ ट छत क पर क म ग ह र क च य द य क ऩ ष म पर क फय फय ह, त ह र क ऊ च ई तथ घनपर त क स जए OR / अथ The length, breadth and height of a rectangular box are as 1 : 2 : 3. Find the volume of the box, when its surface area is 1078 sq m. एक आमत क य फक स क रम फ ई, च ड़ ई तथ ऊ च ई भ 1 : 2 : 3 क अन ऩ त ह मदद फक स क ऩ ष म पर 1078 ग भ ह, त फक स क आमतन त क स जए 19. A cricketer has a mean score of 58 runs in nine innings. Find out how many runs are to be scored in the tenth innings to raise his mean score to OR Find the Mean, Median, Mode of the following data 41, 39, 48, 52, 41, 48, 36, 41, 37, 35 41, 39, 48, 52, 41, 48, 36, 41, 37, 35 Page 7 of 12

7 20. Draw the graph of the equation 3x 4y 12. Also, find the coordinates of the point where the graphs cuts x-axis. 3x 4y 12 x- OR Draw the graphs of the equations 3x 4y 7 and 3x 2y 1 and find their point of intersection of lines representing the equations. 3x 4y 7 3x 2y The volumes of two spheres are in the ratio of 64 : 27. Find their radii if the sum of their radii is 21 cm. द ग र क आमतन भ 64 : 27 क अन ऩ त ह मदद उनक त र ज म ओ क म ग 21 स भ ह, त उनक त र ज म ए त क स जए 22. In the given figure, ABC is an isosceles triangle in which AB AC, AD bisects the exterior angle PAC and CD AB. Show that. (i) (ii) DAC BCA, and ABCD is a parallelogram. ABC AB AC AD, PAC CD AB (i) DAC BCA, (ii) ABCD 23. In the given figure, in a parallelogram ABCD, two points P and Q are taken on the diagonal BD such that DP BQ. Show that Page 8 of 12

8 (i) APD CQB (ii) AQB CPD (iii) APCQ is a parallelogram DP BQ ABCD BD P Q (i) APD CQB (ii) AQB CPD (iii) APCQ 24. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes : Outcomes 3 Heads 2 Heads 1 Head No Head Frequency Three coins are tossed once again together : Find the probability of getting. (i) 2 Heads (ii) at least 2 Heads (i) 2 (ii) SECTION-D / Question numbers 25 to 34 carry four marks each In the given figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O such that OB OD. If AB CD, then show that ar (DOC) ar (AOB). ABCD AC BD, O OB OD AB CD ar (DOC) ar (AOB). Page 9 of 12

9 26. Construct a triangle ABC, in which B 60, C 45 and AB BC CA 11 cm. ABC B 60, C 45 AB BC CA 11 OR Construct a right triangle whose base is 12 cm and sum of its hypotenuse and the other side is 18 cm Give the geometrical representation of the equation 3x 15 0 as an equation : (i) In one variable (ii) In two variables (i) 3x (ii) A solid cube of side 12 cm is cut into eight solid cubes of equal volumes. What will be the side of the new cube? Also, find the ratio between their surface areas. एक ठ स घन, स जसक ब ज 12 स भ ह, क आठ सभ न आमतन क ठ स घन भ क ट ज त ह नम घन क ब ज क म ह? उनक ऩ ष म पर भ अन ऩ त त क स जए 29. A circular park of radius 20 m is situated in a village. Three girls Rita, Sita and Gita are sitting at equal distance on its boundary each having a toy telephone in their hands to talk to each other. Find the length of the string of each phone. (There is no slack in the string) ABCD is a rhombus and P, Q, R and S are the mid-points of AB, BC, CD and DA respectively Prove that quadrilateral PQRS is a rectangle. ABCD P, Q, R S AB, BC, CD DA PQRS OR Page 10 of 12

10 ABCD is a trapezium in which AB CD and AD BC. Show that (i) A B (ii) C D (iii) ABC BAD ABCD AB CD AD BC (i) A B (ii) C D (iii) ABC BAD 31. Ramesh is driving his car with a uniform speed of 90 km per hour. Draw the time distance graph on the graph paper. From the graph, find the distance travelled by him in (i) 1 hour 2 (ii) 2 hours 90 / 1 (i) (ii) If two circles intersect at two points, prove that their centers lies on the perpendicular bisector of the common chord. 33. A hemispherical shaped container has curved surface area of 2772 cm 2. Find the capacity of container. एक अध ग र क य फत न क क र ऩ ष क पर 2772 स भ 2 ह फत न क ध रयत त क स जए 34. Draw a histogram and frequency polygon for the following data : Age (in years) No. of persons Page 11 of 12

11 o O o - Page 12 of 12

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