DELHIPUBLIC SCHOOL, JODHPUR

Summative Assessment - II (2013 – 14)

SUBJECT : Mathematics

CLASS : IX

Time: 3½ hours

/

Max. Marks 100

General Instructions:

  1. Please check that this question paper contains 03 printed pages and 32 questions.
  2. All questions are compulsory.
  3. The question paper consists of 32 questions divided into 4 Sections A, B, C, D and OTBA. Section A comprises of 4questions of 1 mark each, Section B comprises of6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each, Section D comprises of 11 questions of 4 marks each and OTBA of 10 marks.
  4. All questions in Section A are to be answered in one word, one sentence or as per exact requirement of the question.
  5. There is no overall choice in this question paper.
  6. Use of calculators is not permitted.

Section : A (1 Mark)

1.
/ Find the mean of prime numbers between 20 and 30.
2.
/ The radius of sphere is then find its volume in terms of .
3.
/ In ABC, E is mid-point of median AD. If ar(ABC) = 16 cm2, find the ar(BED).
4.
/ Express in the form of then write the value of a, b and c.

Section : B (2 Marks)

5.
/ In parallelogram ABCD, AB = 8 cm. The altitudes corresponding to the side AB and AD are respectively 4 cm and 5 cm. Find the measure of AD.
6.
/ If the surface area of a sphere is 154 cm2, find its diameter.
7.
/ In the figure 1, O is the centre of the circle and find

Fig. 1
8.
/ Check whether point (3, 2) lies on the graph of the equation or not ?
9.
/ Find p, if (– 3, p) is a solution of the equation
10.
/ In figure 2, ABCD is a quadrilateral. If AO and BO are the bisectors of and respectively. Find the value of x.

Fig. 2

Section : C (3 Marks)

11.
/ The cost of 7 apples is Rs. 3 more than the cost of 4 oranges. Write the information as a linear equation in two variable and also find two solutions.

P.T.O.

12.
/ It costs Rs. 2,200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting its inner curved surface is at the rate of Rs. 20 per m2 then find its radius.
13.
/ P and Q are any two points on the sides DC and AD respectively of a parallelogram ABCD, show that .
14.
/ Using ruler and compass construct a PQR with cm, then construct angle bisector of
15.
/ If the observations 6, 7, x – 2, x, 17 & 20 are written in ascending order and their median is 16, find the value of ‘x’. Using the value of x, find the mean of given ovservations.

16.

/ A die is thrown once. Find the probability of getting
(a)an even number (b)a prime number(c)a number greater than 4.

17.

/ The scorers (out of 100) obtained by 33 students in a mathematics test are as follows :
69, 48, 84, 58, 48, 73, 83, 48, 66, 58, 84, 66, 64, 71, 64, 66, 69, 66, 83, 66, 69, 71, 81, 71, 73, 69, 66, 66, 64, 58, 64, 69, 69.
Represent this data in the form of a frequency distribution table taking one of the class 50 – 60.

18.

/ Show that the diagonals of a square are equal and bisect each other at right angles.

19.

/ In the given figure 3, O is the centre of circle, and , then find Further if AB = BC, then find /
Fig. 3

20.

/ Diagonal AC of a parallelogram ABCD bisects . Show that (i) it bisects also (ii) ABCD is a rhombus.

Section : D (4 Marks)

21.

/ Solve the equation, and represent the solution (a) on the number line, (b) on the Cartesian plane.

22.

/ Draw the graph of the linear equation Find the coordinates of the point where the line meets the two axes.

23.

/ Find the values of x, y, z and w from the figure 4, where O is the centre of the circle such that and . /
Fig. 4

24.

/ In the given figure 5, PQRS is a parallelogram. B and D are mid points of the sides PS and QR respectively. Show that ABCD is a parallelogram. /
Fig. 5

25.

/ Prove that the angle subtended by an arc at the centre is double the angle subtended by it at the remaining part of the circle.

26.

/ Construct a ABC in which BC = 6 cm, B = 75º and AB + AC = 14 cm using ruler and compass.

27.

/ The height of a right circular cone is 16 cm and its base radius is 12 cm. Find the total surface area and volume in terms of

28.

/ The sum of the radius of the base and height of a cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2. Find the volume of the cylinder.

29.

/ The daily earning of 30 workers are given below :
Daily earning (in Rs.) / 0 – 50 / 50 – 100 / 100 – 150 / 150 – 200 / 200 – 250
Number of Workers / 5 / 9 / 7 / 5 / 4
Draw a histogram and frequency polygon for the above data on the same graph.

30.

/ Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as follows :
Sum / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12
Frequency / 14 / 30 / 42 / 55 / 72 / 75 / 70 / 53 / 46 / 28 / 15
If the dice are thrown once more, what is the probability of getting the sum of
(a)3(b)more than 10
(c)less than or equal to 5 (d)between 8 and 12

31.

/ A person has constructed some rooms in a village for the free education of females. One of the classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three widows each measuring 2 m x 1 m. Find the cost of white-washing the interior walls and the ceiling of class room at the rate of Rs. 7.50 per m2. Which values of the person are depicted here ?

32.

/ Questions for OTBA (10 Marks)

Theme 1 : Planning a Garden.

(i)

/ (a)Determine the area of four foot path. / [ 2 ]
(b)How many tiles are required to cover the foot path ? / [ 3 ]

(ii)

/ (a)Find the volume of used fertilizer. / [ 3 ]
(b)Find the cost of fertilizer required for the Garden. / [ 2 ]

OR

Theme 2 : Adventure Camp

(i)

/ (a)What is the difference in volume proposed by Swati and the actual volume of the conical tent ? / [ 3 ]
(b)What is the total accommodation capacity of the 4 buses hired for the tour and how many seats remained vacant after all members were accommodated ? / [ 2 ]

(ii)

/ (a)Find the probability of successful people in first attempt. / [1½]
(b)What will be the chance of success who attempt more than 2 times ? / [1½]
(c)Find the chance of success of those people who tries at least one time. / [ 2 ]

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