SUMMATIVE ASSESSMENT II, 2016-17 / MATHEMATICS IX / Class IX - CBSE … · IX / Class – IX: 3...

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SUMMATIVE ASSESSMENT – II, 2016-17 / MATHEMATICS

IX / Class – IX : 3 hours 90

Time Allowed : 3 hours Maximum Marks: 90

1.

2. 31 4

1 6 2 10

3 11 4

3.

4.

General Instructions:

1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D.

Section-A comprises of 4 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 11 questions of 4 marks each.

3. There is no overall choice in this question paper. 4. Use of calculator is not permitted.

/ SECTION-A

1 4 1

Question numbers 1 to 4 carry one mark each.

1 2 6

7

xy x y

Express x in term of y : 2 6.7

xy

1

2 2x3y12, y

Find the coordinates of the point where the equation 2x3y12 cuts yaxis.

1

3 150

Construct an angle of measure 150 (using ruler and compasses only).

1

4 12 cm

The diagonal of a cube is 12 cm. Find its volume.

1

/ SECTION-B

5 10 2

Question numbers 5 to 10 carry two marks each.

5 ABCD AB E ar (EDC) 8 cm2 ABCD 2

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ABCD is a square. E is any point on side AB. If ar (EDC) 8 cm2, find the length of each side of ABCD.

6

If diagonals of a cyclic quadrilateral are diameters of the circle through the opposite vertices of the quadrilateral, prove that the quadrilateral is a rectangle.

2

7 O x

In the given figure, O is the centre of the circle. Find the value of x.

2

8 3.5 cm 12 cm

How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm?

2

9 1500

655 845

A coin is tossed 1500 times with the following frequencies: Head : 655, Tail : 845 Compute the probability for each event.

2

10 kg

7.97, 7.05, 7.08, 6.03, 7.00, 6.06, 6.08, 6.04, 6.00, 6.98, 7.15, 7.34, 7.23, 6.94, 7.12

7.1 kg

In a store, bags of coal powder each contained the following weights of powder (in kg): 7.97, 7.05, 7.08, 6.03, 7.00, 6.06, 6.08, 6.04, 6.00, 6.98, 7.15, 7.34, 7.23, 6.94, 7.12 kg. Find the probability that any one of these bags chosen at random contains more than 7.1 kg of coal powder.

2

/ SECTION-C

11 20 3

Question numbers 11 to 20 carry three marks each.

11 2xy7

(a) x- (b) y-

Represent 2xy7 by a graph. Write the coordinates of the point where it meets : (a) x-axis (b) y-axis

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12 x2, x2, y0 y4

Draw the graphs of x2, x2, y0 and y4 in the same cartesian plane. Identify the figure so formed.

3

13 6 cm PQ P l PQ

m lm

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 lm ?

3

14 AB CD O P

MPNP OM AB ON DC ABCD

In the figure, AB and CD are two chords of a circle with centre O, intersecting each other at P

when produced such that MPNP. If OM AB and ON DC, show that ABCD.

3

15 ABE AE D F D AB DC BE

C

ar (ACF)ar (BCFD)

In figure, D and F are points on side AE of ABE. Through point D a line DC is drawn which is parallel to AB and meets BE in C. Prove that

ar (ACF)ar (BCFD).

3

16 6 m, 8 m 10 m 3

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Metallic spheres of radii 6 m, 8 m and 10 m, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

17 20

375, 415, 525, 275, 815, 720,, 1085, 717, 807, 780, 315, 380, 417, 425, 375, 223, 245, 255, 615, 575.

100

The electricity bills of twenty households in a locality are as follows : 375, 415, 525, 275, 815, 720,, 1085, 717, 807, 780, 315, 380, 417, 425, 375, 223, 245, 255, 615, 575. Construct a frequency distribution table with class size 100.

3

18

1.3, 2.1, 1.8, 2.3, 2.2, 1.5. Find the median and mean of the given data : 1.3, 2.1, 1.8, 2.3, 2.2, 1.5.

3

/ SECTION-D

21 31 4

Question numbers 21 to 31 carry four marks each.

19

x5, x10, y2, y30.

Draw the graphs of the following equations on the same graph sheet : x5, x10, y2, y30. Also, find the area enclosed between these lines.

4

20 x y 70

(a) 30 (b) 20

In a certain test, Nikita scored marks x and y respectively in Mathematics and English. If her total score is 70, then form a linear equation in two variables for this. Also, draw its graph. Find graphically, her score in other subject if : (a) score in Mathematics is 30. (b) score in English is 20.

4

21 DEF EF7 cm, E40 DEEF13 cm

Construct a DEF in which EF7 cm, E40 and DEEF13 cm.

4

22 PQRS PQ E QE2 PE RS F 2

RFSF PERF ar(PERF) 1

3ar(PQRS)

PQRS is a parallelogram. E is a point on PQ such that QE2 PE and F is a point on RS such

that 2 RFSF. Show that PERF is a parallelogram and ar(PERF) 1

3ar(PQRS)

4

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23

Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

4

24 21 cm

98 cm 7 cm

On his birthday in the month of January, Harish distributed soup. He had it in a cylindrical bucket with base radius 21 cm and height 98 cm. He distributed the soup in a hemispherical bowl of radius 7 cm to the poor people and also gave a blanket to them. How many people were served the soup ? What value do you learn from Harish’s act ?

4

25 154 cm2

The curved surface area of a cylinder is 154 cm2. The total surface area of the cylinder is three times its curved surface area. Find the volume of the cylinder.

4

26 15.625 m3

1.2 m

A water storage tank is in the form of a cube. When it is full of water, the volume of water is

15.625 m3. If its present depth is 1.2 m, find the volume of water used from the tank and also find its ratio with the volume of remaining water in the tank.

4

27 IX 27-27 !

46, 31, 74, 68, 42, 54, 14, 61, 48, 37, 26, 8, 64, 57 93, 72, 53, 59, 38, 16, 88, 56, 46, 66, 45, 61, 54, 27 27, 44, 63, 58, 43, 81, 64, 36, 49, 50, 76, 38, 47 77, 62, 53, 40, 71, 60, 45, 42, 34, 46, 40, 59, 42

(i) 49

(ii) 39 100

Two sections of Class IX having 27 students each appeared for mathematics Olympiad. The marks obtained by them are shown below : 46, 31, 74, 68, 42, 54, 14, 61, 48, 37, 26, 8, 64, 57 93, 72, 53, 59, 38, 16, 88, 56, 46, 66, 45, 61, 54, 27 27, 44, 63, 58, 43, 81, 64, 36, 49, 50, 76, 38, 47 77, 62, 53, 40, 71, 60, 45, 42, 34, 46, 40, 59, 42 One student is selected at random. Find the probability that selected student is : (i) having marks more than 49. (ii) having marks between 39 and 100

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28

5-9 10-14 15-19 20-24 25-29 30-34 35-39

10 28 32 48 50 35 12

Draw a histogram to represent the following grouped frequency distribution :

Age (in yrs) 5-9 10-14 15-19 20-24 25-29 30-34 35-39

No. of persons 10 28 32 48 50 35 12

Also draw frequency polygon.

4

य/SECTION-E ( /Open Text)

(* Please ensure that open text of the given theme is supplied with this question paper.)

Theme : Quadrilateral in Architecture, WAH TAJ.

29

AB, BC CA D, E F

In the given figure of , let . If mid-point of side AB, BC and CA are D, E and F respectively then find .

3

30 PQRS C C’ SC’=

CQ SQ CC’

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Points C and C’ are taken on opposite sides of parallelogram PQRS (see figure) such that SC’= CQ. Show that SQ and CC’ bisect each other.

31

If D, E, F are the mid-points of side BC, CA and AB of an equilateral triangle ABC as shown in the figure, then prove that triangle DEF is also an equilateral triangle.

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SUMMATIVE ASSESSMENT II, 2016-17 / MATHEMATICS IX / Class IX - CBSE … · IX / Class – IX: 3...

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Transcript of SUMMATIVE ASSESSMENT II, 2016-17 / MATHEMATICS IX / Class IX - CBSE … · IX / Class – IX: 3...