SAMPLE PAPER-SA II MATHEMATICS Class IX Time allowed : hours Maximum Marks : 90 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 Question numbers 1 to carry one mark each. 1 The graph of linear equation x 5y 7, passes through ( 1, ) or not? 1 Find whether (, ) is a solution of y x = 0. 1 In the given figure, ABCD is a parallelogram. If AL=cm and AB=6 cm, find ar( ADC). 1 If the diameter of the base of a closed right circular cylinder be equal to its height h, find total surface area of cylinder. 1 SECTION-B Page 1 of 6
Question numbers 5 to 10 carry two marks each. 5 In PQR, A and B are points on side QR such that QA = AB = BR. Prove that ar ( PQB) = ar ( PQA) + ar ( PBR) 6 Using compass and ruler construct the angle of the measurement 10 0. Name the angle. 7 The angles of a quadrilateral are (x) 0, (7x) 0, (15x) 0 and (10x) 0. Find the smallest and largest angles of the quadrilateral. 8 The radius of spherical balloon increases from 7 cm to 1 cm as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases. 9 A batsman's runs in 80 one-day matches are as follows : Runs 0-9 0-9 0-9 50-59 60-69 70-79 80-89 90-99 No of 1 1 8 1 0 1 Matches What is the probability that in the next match the batsman will score : (a) atleast 70 runs, (b) atmost 59 runs. 10 Following table shows the birth month of the students of class XII. Jan Feb Mar Apr May June 5 6 7 10 July Aug Sept Oct Nov Dec 5 10 6 8 8 8 Find the probability that a student was born in August. Page of 6 SECTION-C
Question numbers 11 to 18 carry three marks each. 11 Draw the graph of linear equation 7x + 5y = 5. Find the point where this graph meets the line parallel to x - axis and units above it. 1 Verify that which of the followings are solution of equation x y : (0, ), (0, ), (, 0), (, 1), (, ½) and (5, 0). 1 PQRS is a parallelogram. X and Y are mid points of sides PQ and SR respectively and PS XY QR. If ar (PQRS) is cm, find ar (SYQX). 1 In the figure, if O is the centre of the circle, PQR is an isosceles triangle with PQ = PR and PQR = 0 0, find the measures of QSR, QTR and QOR. 15 Draw a line segment AB=5.6 cm. At point A, construct an angle of 10 0, using compass. Now construct its supplement at the point A. 16 In a ABC, median AD is produced to a point P such that AD = DP. Prove that ABPC is a parallelogram. 17 Draw a line segment PQ of length 6 cm. Construct perpendicular at point P. Name it as l. Also construct perpendicular bisector of PQ. Name it as m. Is l m? 18 60 circular plates, each of radius 7 cm and thickness one-third of a cm, are placed one above another to form a solid circular cylinder. Find the total surface area and the volume of the cylinder so formed. Page of 6 SECTION-D
Question numbers 19 to 8 carry four marks each. 19 Let cost of a pen and a pencil be Rs x and Rs y respectively. Anuj pays Rs for pens and pencils. Write the given data in the form of a linear equation in two variables. Also, represent it graphically. 0 Write the equations of the lines p and r in following graph : A student answered equation of line q as x + y = 1. Did he answer correctly? Also, find the area enclosed between lines p, q and r. 1 In a quadrilateral PQRS, diagonals PR and QS intersect each other at O such that ar( POS) = ar( QOR). If distance between sides PQ and SR is cm, PQ = cm and SR = 7 cm, find ar(pqrs). Two chords of lengths 5 cm and 11 cm of a circle are parallel and lie on the same side of the centre. If the distance between them is cm, find the radius of the circle. Construct EFG in which EF = 5. cm, GE + GF = 8 cm and E = 17 0. ABCD is a quadrilateral in which the bisectors of A and C meet DC produced at Y and BA produced at X respectively. Prove that : X + Y = 1 ( A + C). 5 The "Caring old people organisation" needs money to build the old age home which requires Page of 6
16000 bricks. Bricks measure 10 cm 8 cm cm and cost of brick depends on its volume at the rate of Rs 1 per 100 cm. It requires cylindrical cans of paint of radius 1 cm and height 0 cm. The cost of paint is Rs 1 per 0 cm. How much money is required by organisation? If A company gives the money to organization then, what common value is depicted by A company and organisation. 6 The cost of papering the walls of the room 1 m long at the rate of Rs. 1.5 per m is Rs. 0.0 and the cost of matting the floor at the rate of 85 paisa per m is Rs. 91.80. Find the height of the room. 7 A hemispherical bowl is made of 0.50cm thick brass. The inner radius of the bowl is 6cm. Find the outer and inner curved surface area and volume of the bowl. 8 A company selected 000 families at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information so obtained is listed in the following table : Monthly Income No. of television in a family (In Rupees) 0 1 Above < 10000 0 80 10 0 10000-1999 10 0 60 0 15000-19999 0 80 10 0 0000-999 0 50 70 80 5000 and above 0 1110 760 0 Suppose a family is chosen at random. Find the probability that the selected family : (i) has earning Rs 10000 Rs 1999 per month and has exactly one television. (ii) has earning Rs 5000 and more per month and owns televisions. (iii) is not having any television. (iv) has and more than televison Page 5 of 6
SECTION-E (Open Text) (* Please ensure that open text of the given theme is supplied with this question paper.) Theme :Atithidevo Bhavah 9 Refer to Table- and answer the following questions : (i) What is the difference in FTAs from Europe and America for the year 01? (ii) What is the difference in FTAs from Asia and Africa for the year 01? (iii) What was the FTA from Australia in the year 01? 0 Refer to Table and answer the following questions : (i) What was the percentage of children (age group 0-15) in FTAs in India during 1996-01? (ii) What was the percentage of senior citizens (age group 65 and above) in FTAs in India during 1996 01? (iii) What was the percentage of elderly (age group 55 and above) in FTAs in India during 1996 01? 1 Refer to figure-1 : Arrival of foreign tourist in percentage in 01. (a) Draw a bar graph for arrival of foreign tourist (in percentage) month wise in 01 taking months on vertical axes and percentage arrival on horizontal axes. (b) Calculate the average of percentage arrival of foreign tourists in April, May and June 01. Page 6 of 6