II, ( ) SUMMATIVE ASSESSMENT II MATHEMATICS / Class IX /

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1 II, (01-015) SUMMATIVE ASSESSMENT II MATHEMATICS / Class IX / IX OGCGUZ 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 1 (iii) (iv) General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 1 questions divided into five sections A, B, C,D and E. Section-A comprises of questions of 1 mark each, Section-B comprises of 6 questions of marks each, Section-C comprises of 8 questions of marks each and Section-D comprises of 10 questions of marks each. Section E comprises of two questions of marks each and 1 question of marks from Open Text theme. (iii) There is no overall choice. (iv) Use of calculator is not permitted. / SECTION-A 1 1 Question numbers 1 to carry one mark each. 1 y 5, x- x- 1 Is line parallel to x-axis at a distance of 5 units below x-axis is given by the linear equation y = Page 1 of 1

2 5? x 5x 0y 500 y 0 1 Find the value of x for which y = 0 is a solution of the equation 5x 0y Name the special type of parallelogram whose diagonals are equal and they bisect each other at right angles. Also, state its one more property. r h 1 A cylinder of base radius r and height h is dipped vertically to half the height in a bucket full of purple paint. Find the area of the surface which gets painted. / SECTION-B 5 10 Question numbers 5 to 10 carry two marks each. 5 XYZ XZ YZ A B YA YB O AB XY ar ( AOX) ar ( BOY) In XYZ, A and B are points on sides XZ and YZ respectively. YA and YB intersect at O. If Page of 1

3 AB XY, than show that ar ( AOX) ar ( BOY) 6 DOE 15 DOE MOE 7 1 Draw DOE 15, using protractor. Now, using DOE, construct MOE 7 1, with the help of compass and ruler. 7 : : 1 80 In a quadrilateral, three angles are in the ratio of : : 1 and the fourth angle is 80. Find the measure of equal angles m 110 m Curved surface area and circumference at the base of a solid right circular cylinder are 00 m and 110 m respectively. Find its height and radius. 9 A B AB O The blood group of students are selected of class X and recorded as below : Blood group A B AB O Number of Students If a student is chosen at random find the probability that it has A blood group. A Page of 1

4 (a) (b) Teachers and students are selected at random to make two teams of 0 members each on sports day to participate in the event of ''Tug of War''. The numbers of volunteers are as follows : TEACHERS STUDENTS Male Female Male Female Find the probability that the person chosen at random (a) (b) is a male is a female student. / SECTION-C Question numbers 11 to 18 carry three marks each. 11 x- x- Page of 1

5 Write the equation of a line which is parallel to x-axis and at a distance of units above x-axis. Also draw the graph. 1 ( 1, 10), x by 7 b x 7 Determine the value of b if ( 1, 10) is a solution of the equation x by 7 Also find the coordinates of the point on its graph for which x 7. 1 ABCD O ar( AOD) cm ar (ABCD) ABCD is a parallelogram and O is the point of intersection of its diagonals. If ar( AOD) cm, find area (ABCD). 1 ABCD B 5 D C A ABCD is a cyclic quadrilateral such that B 5 D and C A, find the measure of the each angle of the quadrilateral Construct an angle of measure P, Q R ABC AB, BC CA BA CS PR S QRSC Page 5 of 1

6 In the figure; P, Q and R are the mid-points of sides AB, BC and AC of ABC respectively. CS is drawn parallel to BA to meet PR produced in S. Prove that QRSC is a parallelogram. 17 O ABC OD BC BOD A In the figure, if O is the circumcentre of a ABC and OD BC, prove that BOD A. 18 Page 6 of 1

7 10 cm 1 cm.1 Find the volume of metal used to construct a hollow metallic sphere of internal and external diameters as 10 cm and 1 cm respectively. (use.1) / SECTION-D 19 8 Question numbers 19 to 8 carry four marks each. 19 ` x ` y ` 9 Let cost of a pencil and an eraser be ` x and ` y respectively. A girls pays ` 9 for pencils and erasers. Write the given data in the form of a linear equation in two variables. Also, represent it graphically. 0 Write the equation of the lines drawn in following graph. Also, find the area enclosed between them. Page 7 of 1

8 1 ABCD AD AB P Q APOQ ar(apoq) : ar(abcd) BR 1 BC DS 1 CD ABCD is a rectangle. P and Q are points on sides AD and AB respectively. Show that APOQ is a rectangle and find ar(apoq) : ar(abcd), when it is given that BR 1 BC and DS 1 CD. Page 8 of 1

9 Prove that the quadrilateral formed by bisectors of the interior angles of a cyclic quadrilateral is also cyclic. PQR QR cm, Q 155 and PQ PR 5.7 cm Construct PQR, QR cm, Q 155 and PQ PR 5.7 cm. PQRS A, B, C D PQ, QR, RS PS AC BD In the figure, PQRS is a quadrilateral in which A, B, C and D are mid points of the sides PQ, QR, RS and PS respectively. Show that AC and BD bisect each other. 5 7 m ` Page 9 of 1

10 The dome of a building where people live is in the shape of a hemisphere of radius 7 m. Eleven children decided to help the old aged people by collecting money for white washing the dome. If white washing costs ` per square meter, how much would each children would pay? Also find volume of air inside the dome? Which value is depicted by the children? 6 7. m.5 m 5 cm 9 cm 0 0 A rectangular water reservoir is 7. m by.5 m at the base. Water flows into it throught a pipe whose cross section is 5 cm 9 cm at the rate of 0 m per second. Find the height to which the water will rise in the reservoir in 0 minutes? 7 1 cm 18.5 cm 1 cm 17.5 cm A fruit tin has a square base with side 1 cm and height 18.5 cm. Another cylindrical tin has a diameter of the base 1 cm and height 17.5 cm. Which tin has more capacity and by how much? 8 80 ( ) Page 10 of 1

11 (a) 900 (b) There are 80 bulbs in a box and their life time (in hours) is recorded as follows : Life time (in hours) Frequency One bulb is selected at random. Find the probability (a) (b) that the bulb selected has at most the life of 900 hours. the bulb selected has at least the life of 700 hours. Verify that the probability of the bulb selected at random having the life of 900 hours is 10. य/SECTION-E ( /Open Text) (* Please ensure that open text of the given theme is supplied with this question paper.) Theme : Atithidevo Bhavah 9 (i) (ii) Page 11 of 1

12 Refer to Table- and answer the following questions : (i) The percentage of people travelling by land is less. What do you think are the factors responsible for it? (ii) FTA by land route is mostly from which countries? 0 (i) (ii) Consider month-wise percentage share of FTA and answer the following questions : (i) (ii) Find the mean percentage of foreign visitors in the summer (April july) Find the mean percentage of foreign visitors in the winter (November February) 1 The division on the basis of gender of foreign tourist arrival in the year 01 is 60% (male) and 0%(female). Calculate age wise distribution of females on the basis of table and prepare a histogram. -o0o0o0o- Page 1 of 1