2x x 1 ADB. ∠ and BOC 2x ∠ =

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SUMMATIVE ASSESSMENT –I 2015-16 Class – IX

MATHEMATICS ST0XLIF Time allowed: 3 hours Maximum Marks: 90

General Instructions: 1. All question 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 question of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted.

Section-A

Question number 1 to 4 carry one mark each.

Q.1 Which is the greatest among 3 42, 4 3 and ?

Q.2 If 2x+1 is one factor of the polynomial 22x x 1 , then find the other factor.

Q.3 In the given figure, oABD 66 and oACD 60 . If bisector of A meets BC at D, then find

ADB.

Q. 4 What do you mean by ordinate of point?

Section-B

Question number 5 to 10 carry two marks each.

Q.5 Is zero (0) a rational number? Justify your answer.

Q.6 Factories’ : 3 23y y 3y 1

Q.7 In the figure, if oAOB 60 and BOC 2x , then find the value of x so that AOC is a straight

line.


Q.8 In the give figure ; if 1 3, 2 4 and 3 4, write a relation between 1 and 2 by

using an Euclid’s axiom. Write the axiom also.

Q.9 A point is a distance of 4 units from z-axis and 5 units from the y-axis. Represent the position of

the point in the Cartesian plane and also write its co-ordinates.

Q.10 Compute the area of the trapezium shown in the figure :

Section C

Question number 11 to 20 carry three marks each.

Q.11 Simplify : 8 4 164 81x y z

Q.12 If x 2 3 ; find the value of 33

1x

x

Q.13 Using a suitable identity, evaluate 3 3 3(43) (18) (24) .

Q.14 Let 1R and 2R are the remainders when the polynomials 3 2f (x) 4x 3x 12ax 5 and

3 2g(x) 2x ax 6x 2 are divided by (x-1) and (x-2) respectively. 1 2If 3x R 28 0 , find the

value of ‘a’.

Q.15 Write any three Euclid’s Postulate.

Q.16 In the give figure, if the line segment AB is parallel to another line segment RS and O is the

mid-point of As, then Show that :

(a) AOB SOR

(ii) O is also mid-point of BR


Q.17 In the figure, oPQ PR,PQ || RL, RQT 38 and oQTL 75 . Find x and y.

Q.18 Prove that if two lines intersect, vertically opposite angles are equal.

Q.19 On the graph paper, plot a point A(-2,-2). Reflect point A in x-axis and y-axis. Let these points be B and C respectively. Guess the measure of BAC .

Q.20 The Perimeter of a triangular garden is 900 cm and its sides are in the ratio 3 : 5 : 4. Using

Heron’s formula, find the area of the garden.

Section D

Question number 21 to 31 carry four marks each.

Q.21 Express in the form of p

q: 0.38 1.27

Q.22 Rationalise the denominator of the following: 3

3 5 2

Q.23 If ab + bc + ca = 0 find value of 2 2 2

1 1 1

a bc b ca c ab

Q.24 Verify if -3 and 4 are zeroes of the polynomial 3 22x 3x 23x 12. If yes, then factorise the

polynomial.

Q.25 Using long division method, show that the polynomial p(x)= 3x 1 is divisible by q(x) = x+1.

Verify your result using factor theorem.

Q.26 Show that 2 2 23 3 3 1a b c 3abc a b c a b b c c a

2

Q. 27 For spreading the message “Save environment Save future” a rally was organized by some

students of a school. They were given triangular cardboard piece ABC which they divided in to two


parts by drawing the angle bisectors BO and CO of base angles B and C. Prove that

1BOC 90 A.

2 what is the benefit of these types of rallies?

Q.28 Solve the equation a-35=75 and state which axiom you use here. Also give two more axioms

other than the axiom used in the above situation.

Q.29 In the figure, two straight lines PQ and RS intersect each other at O. If oPOT 75 , find the

values of a, b and c.

Q.30 In the given figure, prove that oA B C D E F 360 .

Q.31 The angles of a triangle are o

o o xx 40 , x 20 and 10

2

. Find the value of x and then the

angles of the triangle.


Class – IX Sub: Mathematics

Time allowed: 3 hours Maximum Marks: 90

Question numbers 1 to 4 carry 1 mark each:-

Q. 1 If xx

25125

5= find x.

Q. 2 Find the value of P 2

3

for p(y) = 3 22y y 13y 6.

Q. 3 Do the points lie in the same quadrant? (6,-6) and (-6, 6).

Q. 4 Find complementary angle of o35

Section B

Question numbers 5 to 10 carry 2 marks each:

Q. 5 Without actually calculating the cubes, Find the value of 3 3 345 25 20 .

Q. 6 If the area of an equilateral triangle is 216 3cm The Find perimeter.

Q.7 Angles of a triangle are in the ration 3:4:5. Find largest angle of the triangle.

Q.8 AB=BC and BP-BQ Show that AP=CQ

Q. 9 Plot the points (2,-2), (-4,4) and join them does the line pass through origin.

Q.10 Find a rational and irrational no. between 2 and 3 .

Section C

Question numbers 11 to 20 carry 3 marks each.


Q.11 Express 0.123 in the form of p

q

Q.12 Find the area of triangular park whose sides are of length 120m, 80m and 50m.

Q.13 If (3x-2) is a factor of 3 23x x 20x 12. Find other factors.

Q.14 If AB||CD. Determine x.

Q.15 If two lines intersect each other then prove that vertically opposite angles are equal.

Q.16 If a line 1 is the bisector of A , then find OQ.

Q.17 Mr. Saxena has a rectangular plot of land ABCD which he decided to donate to his society for

the organization of fitness campaign like yoga, mediation etc. the co-ordinates of three vertices of

plot are A(-2,-5), B(6,-5) and (6,-1). Plot these points find co-ordinates of fourth vertex.

Which value does Mr. Saxena possess?

Q.18 find product using suitable identity 2 42 4

1 1 1 1x x x x2 2 x x

Q.19 If AB||CD, CD||EF and x:y=3:2 find Z.

Q20. ABC is an isosceles has points D and E on BC such that BE=CD Show that AD=AE.


Section D

Questions numbers 21 to 31 carry 4 marks each:

Q. 21 Simplify : 6 82 6 2 3

2 3 6 3 6 2

Q. 22 The volume of cuboid is polynomial. P(x) = 3 24x 20x 33x 18 find possible expression for dimension of

the cuboid.

Q.23 Factorise : 12x 1

Q.24 Prove that angles opposite to equal sides of a triangle are equal

Q.25 Find (a=b)

Q.26 AC=AE, AB=AD and BAD EAC Show that BC=DE

Q.27 If 3 2x ax bx 6 has (x-2) has factor and leaves remainder 3 when divided by (x-3). Find the values of a

and b.

Q.28 T is a point on side QR of PQR and S is a exterior point such that RT=ST. Prove that PQ+PR>QS

Q.29 <1=<3, <2=<4, <3=4 Write the relation between <1 and <2 Using a Euclid’s axiom

Q.30 Locate 3 on a number line.

Q.31 If x+y+z =10 and 2 2 2x y z 40 Find xy+yz+zx.


SUMMATIVE ASSESSMENT-I, 2015-16 CLASS: IX, MATHEMATICS M Time allowed: 3 hours Maximum Marks: 90

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 question 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’

Question numbers 1 to 4 carry one mark each.

Q.1 Find the value of 0.16 0.0981 81 .

Q.2 Using suitable identity, find (2+3x)(2-3x).

Q.3 In the figure, If oA 40 and oA 70 , then fine BCE.

Q.4 In which quadrants the points P(2,-3) and Q(-3,2) lie?

Section ‘B’

Question numbers 5 to 10 carry two mark each.

Q.5 Find the value of 2 3

, 3 1.732 3

if

Q.6 Using remainder theorem, find the remainder when 4 3 2x 3x 2x 4 is divided by x+2.

Q.7 In given figure PR = QS, then show that PQ = RS. Name the mathematician whose postulate/axiom is used

for the same.

Q.8 In the give figure, B A and C< D , show that AD<BC.


Q.9 Find the perimeter of an isosceles right angled triangle having an area of 5000 2m .

Use 2 1.41

Q.10 On which axes the following points lie?

0,4 , 5,0 , 5,0 and 0, 3

Section ‘C’

Question numbers 11 to 20 carry three mark each.

Q.11 Find the values of a and b. if 3 2

a b 23 2

Q.12 Represent 1 9.5 on the number line.

Q.13 Expand

21 1

x y z2 3

Q.14 Factorise 2 2 24x y 25z 4xy 10yz 20zx and hence find its value when x = -1, y = 2 and z = -3.

Q.15 In the figure, o o oPDQ 45 , PQD 35 and BOP 80 . Prove that p||m.

Q.16 In the given figure, show that XY||EF.


Q.17 In the given figure, AB=AC. D is a point on AC and E on AB such that AD=ED=EC=BC. Prove that A : B 1: 3 .

Q.18 In figure, if l||m, o3 (x 30) and o6 (2x 15) , find 1 and 8.

Q.19 Find the area of a triangle whose perimeter is 180 cm and two of its sides are 80 cm and 18

cm. Calculate the altitude of triangle corresponding to its shortest side.

Q.20 Plot two points P(0,-4) and Q(0,4) on the graph paper. Now, plot R and S such that PQR and PQS are isosceles triangles.

Section ‘D’

Question numbers 21 to 31 carry four mark each.

Q.21 If 2 1 2 1

x2 1 2 1

and y=

, find the value of 2 2x y xy.

Q.22 Prove that : 1 1 1 1 1

5.3 8 8 7 7 6 6 5 5 2

Q.23 Find the value of ‘a’, if x + a is a factor of the polynomial 3 2p(x) x ax 2x a 4.

Q.24 If (x+1) and (x+2) are the factors of 3 2x ax 2x a 4.

Q.25 Divide the polynomial 3 2x 3x 3ax , then find a and .

Q.26 If x + y + z = 1, xy + yz + zx = -1 and xyz = -1, find the value of 3 3 3x y z .

Q.27 A farmer has two adjacent farms PQS and PSR as shown in the figure. He decides to give on e farm for

hospital. What value is he exhibiting by doing so? If PQ>PR and PS is bisector of P, show that PSQ PSR.


Q.28 In an isosceles triangle ABC with AB=AC, D and E are two points on BC such that BE =CD.

Show that AD = AE.

Q.29 In figure, OA = OD and 1 2. Prove that OCB is and isosceles triangle.

Q.30 Prove that the angles opposite to equal sides of a triangle are equal.

Q.31 In the figure, X and Y are the points on equal sides AB and AC of a ABC such that AX = AY.

Prove that XC = YB.

Material downloaded from

Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks

Time: 3 Hours

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of

Section-A comprises of 4 question of

marks each, Section-C comprises of

10 question of 4 marks each.

1 question of 4 marks from Open Text theme.

(iii) There is no overall choice.

(iv) Use of calculator is not permitted.


1. In the figure PQRS and AQBC are parallelogram. If

2. If the number of square centimeter on the surface area of sphere is equal to the number of cubic

centimeters in its volume, what is the diameter of the

3. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,

18, 10, 24. Find the mean.

4. In a frequency distribution, the mid

Find the lower limit of the class

Question number 5 to 10 carry two



Mathematics

Class -IX

Summative Assessment – II

Max. Marks: 90

All questions are compulsory.

The question paper consists of 31 question divided into five section A, B, C, D and E

question of 1 mark each, Section-B comprises of

comprises of 8 question of 3 marks each and Section

each. Section E comprises of two questions of 3 marks each and

1 question of 4 marks from Open Text theme.

Use of calculator is not permitted.

SECTION-A

mark each.

. In the figure PQRS and AQBC are parallelogram. If ∠S =70o, find ∠ACB.

. If the number of square centimeter on the surface area of sphere is equal to the number of cubic

centimeters in its volume, what is the diameter of the sphere?

. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,

frequency distribution, the mid-point of a class – interval is 20 and the width of the class 8.

lower limit of the class – interval.

SECTION-B

two marks each.

http://onlineteachers.co.in

ax. Marks: 90

section A, B, C, D and E.

comprises of 6 question of 2

Section-D comprises of

of 3 marks each and

. If the number of square centimeter on the surface area of sphere is equal to the number of cubic

. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,

interval is 20 and the width of the class 8.



5. WXYZ is a parallelogram with XP

6. Why we cannot construct a triangle ABC if

∆ABC is ∠A=60o, AB =6 cm and AC

7.

In the figure PQRS is a parallelogram. Find the value of x and y.

8. The outer and the inner radii of a hollow

9. A die is thrown 100 times and the outcomes are recorded as follows:

Outcome 1 2 3

Frequency 25 20 12

If the die is thrown once again, what is the probability of getting:

(a) even number.

(b) prime number.

10. A coin is tossed 1200 times with the following outcomes:

probability for each event.

Question numbers 11 to 18 carry

11. (a) Find the mean of the square of the first five natural numbers.

(b) Find the mean of the cubes of

12. Convert the following frequency distribution into a continuous grouped frequency table:



. WXYZ is a parallelogram with XP��WZ and ZQ�WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm,

. Why we cannot construct a triangle ABC if ∠A=60o, AB=6 cm, AC+BC=5 cm but construction of

, AB =6 cm and AC-BC=5 cm.

In the figure PQRS is a parallelogram. Find the value of x and y.

. The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. find its volume.

A die is thrown 100 times and the outcomes are recorded as follows:

4 5 6

18 15 10

If the die is thrown once again, what is the probability of getting:

with the following outcomes: Head: 455, Tail

SECTION-C

carry three marks each.

. (a) Find the mean of the square of the first five natural numbers.

(b) Find the mean of the cubes of first 4 odd prime numbers.

. Convert the following frequency distribution into a continuous grouped frequency table:


WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm, find YX.

, AB=6 cm, AC+BC=5 cm but construction of

sphere are 12 cm and 10 cm. find its volume.

: 455, Tail: 745. Compute the

. Convert the following frequency distribution into a continuous grouped frequency table:



Class - Interval Frequency

150 -153

154 - 157

158 - 161

162 - 165

166 -169

170 - 173

7

7

15

10

5

6

In which interval would 153.5 and

13. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to

both SR and PQ, then show that ar(

14. In the figure, AB and CB are chords of a circle equidistant from the center O.

diameter DB bisect ∠ABC and ∠

15. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.

16. In the figure, PQRS is a trapezium in which PQ

A line through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid

point of side QR.

17.In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate

the value of a and b.



Frequency

In which interval would 153.5 and 167.5 be included?

. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to

both SR and PQ, then show that ar(∆PSQ) =ar(∆SRQ).

In the figure, AB and CB are chords of a circle equidistant from the center O.

∠ADC.

. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.

In the figure, PQRS is a trapezium in which PQǁSR, QS is a diagonal and X is the mid

through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid

In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate


. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to

In the figure, AB and CB are chords of a circle equidistant from the center O. Prove that the

. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.

ǁSR, QS is a diagonal and X is the mid-point of PS.

through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid-

In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate



18. A dome of a building is in the form of a hemisphere. From inside, it was white washed at the cost

of Rs.997.92. If the cost of white washing is 400 paisa square meter, find the volume of air inside

the dome. (�� =22

7).

Question numbers 19 to 28 carry

19. The following table gives the life times of 400 lamps

Life time

(in hrs)

300-400 400-

No. of

lamps

14 56

Represent the given information with the help of a histogram and a

(ii) How many lamps have a life time of 700 or more hours?

20. ABCD is a rectangle, E, F, G and H are mid

ar(EFGH)=16 cm2, Find ar(ABCD).

21. I the given figure, O is the Centre

and CD respectively and PQ=1 cm. If AB

22. Construct ∆ABC in which AB=6.7 cm,



uilding is in the form of a hemisphere. From inside, it was white washed at the cost


SECTION-D

to 28 carry four marks each.

The following table gives the life times of 400 lamps

-500 500-600 600-700 700-800 800

60 86 74 62

Represent the given information with the help of a histogram and a frequency polygon.

(ii) How many lamps have a life time of 700 or more hours?

E, F, G and H are mid-point of sides AB, BC, CD and DA respectively

, Find ar(ABCD).

Centre of a circle of radius r cm, OP and OQ are perpendicular to AB

and CD respectively and PQ=1 cm. If ABǁCD, AB=6 cm, and CD=8 cm, determine r.

ABC in which AB=6.7 cm, ∠A=55o and AC- BC=1.2 cm.


uilding is in the form of a hemisphere. From inside, it was white washed at the cost


800-900 900-1000

48

frequency polygon.

point of sides AB, BC, CD and DA respectively. If

of a circle of radius r cm, OP and OQ are perpendicular to AB

ǁCD, AB=6 cm, and CD=8 cm, determine r.



23. PQRS is a square and ∠ABC=90

∠BAC=45o.

24. Roof top of a house in a village is rectangular shaped of dimensions 22 m by 20 m. The owner of

house has connected drain of root top with a cylindrical vessel on ground through a circu

so that the whole rain water collected on the roof top can be stores in a cylindrical vessel. The

radius of the cylindrical vessel is 2 cm, A certain day recorded rainfall of 5 cm.

(a) Find the height of water filled in the cylindrical tank.

(b) Find the volume of water filled in the cylindrical tank.

(c) Which moral value is depicted in this problem?

25. Volume of a hollow sphere is 11352

outer surface area of the sphere.

26. The length, breath and height of a cuboidal tank are 150 cm, 120 cm and 110 cm respectively.

The tank has129600 cm3 of water in it. 100 porous brick each having dimensions 20 cm×10 cm

are placed in the tank. Calculate in the rise in the water level of the tank

own volume.

27. There are 100 students in class IX of a school. Mathematics teacher asks all the students to

prepare a cylindrical container with base at the bottom but open at the top, using cardboard

Each student has to make one container of diameter 8.4 cm and height 11.2 cm. The cost of the

cardboard is Rs. 10 per 100 cm

cardboard.

28. A die is tossed 120 times and the outcomes are recorded as follows:

Outcomes 1 Even no < 6

Frequency 25 40

Find the probability or getting:



ABC=90o as shown in the figure. If AP= BQ=CR, then Prove that

. Roof top of a house in a village is rectangular shaped of dimensions 22 m by 20 m. The owner of

house has connected drain of root top with a cylindrical vessel on ground through a circu



(a) Find the height of water filled in the cylindrical tank.

Find the volume of water filled in the cylindrical tank.

(c) Which moral value is depicted in this problem?

11352

7 cm3. If the outer diameter is 16 cm, find the inner radius and

of the sphere.

length, breath and height of a cuboidal tank are 150 cm, 120 cm and 110 cm respectively.

of water in it. 100 porous brick each having dimensions 20 cm×10 cm

are placed in the tank. Calculate in the rise in the water level of the tank, if each absorbs

. There are 100 students in class IX of a school. Mathematics teacher asks all the students to


one container of diameter 8.4 cm and height 11.2 cm. The cost of the

cardboard is Rs. 10 per 100 cm2. Find the amount spent by the teacher for the purchase of the

. A die is tossed 120 times and the outcomes are recorded as follows:

Even no < 6 Add no > 1 6

35 20


as shown in the figure. If AP= BQ=CR, then Prove that

. Roof top of a house in a village is rectangular shaped of dimensions 22 m by 20 m. The owner of

house has connected drain of root top with a cylindrical vessel on ground through a circular pipe



. If the outer diameter is 16 cm, find the inner radius and

length, breath and height of a cuboidal tank are 150 cm, 120 cm and 110 cm respectively.

of water in it. 100 porous brick each having dimensions 20 cm×10 cm

, if each absorbs1

10 of its

. There are 100 students in class IX of a school. Mathematics teacher asks all the students to


one container of diameter 8.4 cm and height 11.2 cm. The cost of the

. Find the amount spent by the teacher for the purchase of the



(a) an even number

(b) An odd number greater than 1.

SECTION-E

(Open Text)

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

Theme: Energy Consumption and Electricity Bill

29. From a linear equation. If the total bill of a house in Delhi is above Rs. 3000 for a month

assuming that the consumption is x units as per Delhi tariff slabs shown in the actual bill.

30. Obtain a liner equation to find the number of units consumed by each of the following

appliances when used for x hours a day?

(i) Lamp (100 watts)

(ii) Washing Machine

(iii) Computer

31. What does the Electric energy cost to run an Electric 1 KW for x hours and 2KW of Geyser for y

hours a day? If 20 units of total electric energy is used per day represent this situation as a liner

equation and draw its graph.

Does the graph of above equation passes through origin?



Mathematics

Class -IX


Time: 3 Hours Max. Marks: 90


(i) All questions are compulsory.

(ii) The question paper consists of 31 question divided into five section A, B, C, D and E.

Section-A comprises of 4 question of 1 mark each, Section-B comprises of 6 question of 2

marks each, Section-C comprises of 8 question of 3 marks each and Section-D comprises of

10 question of 4 marks each.Section E comprises of two questions of 3 marks each and 1

question of 4 marks from Open Text theme.

(iii) There is no overall choice.

(iv) Use of calculator is not permitted.

SECTION-A


1. Area of parallelogram is 64 cm2. If base of the parallelogram is 16cm, find the height of the

corresponding attitude.

2. Find the side of a cube of its total surface area is 486 cm2.

3. The mean of the set of number 6, 3, x, 4 ,3, 5 and y is given as 5. What is the value of x+y?

4. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32.

SECTION-B


5. PQTS and PTRQ are two parallelograms. Show that ar (∆PST) = ar (∆QTR) = 1

3ar(PQRS).



6. Draw a line segment of length 7.6 cm. Bisect Measure the length of each part.

7. In the figure, ABCD is a square. Find the measure of ∠CDB.

8. The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.

9. Teachers and students are selected at random to make teams of 20 members each on sports

day to participate in the event of “Tug of War’’. The number of volunteers are as follows:

TEACHERS STUDENTS

Male Female Male Female

12 18 20 10

Find the probability that the person chosen at random

(a) is a male

(b) is a female student.

10. An experiment is performed 400 times and three possible events A, B and C. Possible

occurrence of the three events are recorded. Out of the following which records are Possible

(give reason to support y our answer).

(a) A-176, B-54, C-170

(b) A-200, B-100, C-75

(c) A-180, B-170, C-50

(d) A-175, B-125, C-200

SECTION-C

Question numbers 11 to 18 carry three marks each.

11. Ten observations 6, 14, 15, 17, x+1, 2x-13, 30, 34, 43 are written in an ascending order. The

median of the data is 24. Also, find their mean.

12. Draw Bar Diagram for the given expenditure of a family on different heads in the month:

Head Expenditure



Food 4000

Education 2500

Clothing 1000

House rent 3500

Others 2500

Savings 1500

13. ABCD is a parallelogram and O is the point of intersection of its diagonals. If ar(∆AOD)=4 cm2,

find area (ABCD).

14. Two concentric circle, shown in the given figure, have a common center O. A line l Intersects

the outer circle at A and B and the inner circle at C and D. If AB =x and CD=y, prove that

AC=BD=1

2(x-y).

15. Draw two lines AB and CD such that they intersect at point O and not perpendicular to each

other. Measure ∠ AOD and ∠ AOC. Bisect the greater angle.

16. A square ABCQ is inscribed in an isosceles right ∆PQR such that A and C are mid-points of PQ

and QR respectively as shown in the figure. Find the measure of ∠ PBA.

17. (a) Is it possible to construct ∆ABC if perimeter of the triangle is 11 cm, base angles are

60A∠ = ° and ∠ B=70o.

(b) Is it possible to construct ∆EFG, if EF+FG+GE=11cm, ∠ E=105o and ∠ F=90o.

(c) Is it possible to construct ∆XYZ if perimeter is 12.5cm, ∠ X=75o and ∠ Y=30o

18. A boy has a spherical ladoo whose radius is 4 cm. A girl has 8 spherical ladoos each of radius

2 cm. Find the ratio of the volumes of ladoos girl has to the ladoo boy has.

SECTION-D



Question numbers 19 to 28 carry four marks each.

19. The following data represents the population of girl child (per 1000 boy child) in a state.

Years Number of Girls

2007-2008

2008-2009

2009-2010

2010-2011

2011-2012

875

900

925

945

1000

(a) Draw a bar graph to represent the above data.

(b) What change in the value over the period of time is depicted by the state?

20. In a question PQRS, diagonal PR and QS intersect each other at O such that ar(∆POS) =

ar(∆QOR). If distance between sides PQ and SR is 4 cm, PQ =3 cm and SR =7 cm, find

ar(∆PQRS).

21. In the given figure, if y =36oand z =40odetermine x. If y and z were complementary angle,

show that x would have been 1

2right angle.

22. Construct ∆XYZ in which XY =5 cm, ∠ X = 60oand sum of the other two sides is 7.6 cm.

23. In the parallelogram ABCD of the given figure, ∠ PAQ is an obtuse angle. Two equilateral

triangle ABP and ADQ are drawn outside the parallelogram. Prove that ∆CPQ is also an

equilateral triangle.



24. The patients in a hospital are given soup daily in a cylindrical bowl of diameter 7 cm. On a

particular day, the girl of NCC decided to cook the soup for the patients. If they fill the bowl

with soup to a height of 6 cm, then how much soup (in litres) is to be cooked for 200

patients? Which value is depicted by the girls?

25. A pit is 20 m long, 6m wide and 80 cm deep. Calculate the number of planks, each with

dimensions 5 m× 25 cm× 10cm that can be store in the pit.

26. Radha has a piece of canvas whose area is 550 m2. She uses it to make a conical tent with a

base diameter of 14 m, Find the volume of the tent that can be made with it.

27. The capacity of a closed cylindrical vessel of height 2 m is 30.8 litres. Haw many square

metres of metal sheet would be needed to make it?

28. The following table gives the distance (in km) that 40 students of a class have to travel from

their residence to their school.

Distance (In km) No. of students

0-5

5-10

10-15

15-20

20-25

25-30

30-35

5

11

11

9

1

1

2

Find the probability that randomly choosen student lives at a distance of:

(a) more than 35 km.

(b) 10-15 km.

(c) atleast 25 km.

In between 15-25 km.

SECTION-E



(Open Text)


Theme: Childhood Obesity in India

29. Taking the height as 170 cm, form a liner equation in two variable taking BMI as x and weight

as y kg.

30. A person wants to burn 300 cal in a day. Which two two physical activities can he choose and

for how much time? Write a liner equation for the same and give two values.

31. Rajat went to a party. He ate 2 slice of pizza and 1 cheese burger and 200 ml cola dark.

(a) Calculate the total calories he took.

(b) T burn the total calories, he choose walking and running stairs. He plans to spend ‘t’

minutes in walking and ‘s’ minutes running stairs. Write a linear equation for the same

and draw the graph.

***********



Mathematics

Class -IX


Time: 3 Hours Max. Marks: 90


1. All questions are compulsory.

2. The question paper consists of 31 question divided into five section A, B, C, D and E. Section-

A comprises of 4 question of 1 mark each, Section-B comprises of 6 question of 2 marks

each, Section-C comprises of 8 question of 3 marks each and Section-D comprises of 10

question of 4 marks each. Section E comprises of two questions of 3 marks each and 1

question of 4 marks from Open Text theme.

3. There is no overall choice.

4. Use of calculator is not permitted.

SECTION-A


(1) In ∆XYZ, P is the mid-point of side YZ. Find the ratio ar(∆XYZ):ar(∆XYZ).

(2) If the total surface area of a cube is 96 cm2, then find its volume.

(3) Find the mean of first 10 odd numbers.

(4) In a frequency distribution, the mid-point of a class – interval is 20 and the width of the class

is 8. Find the lower limit of the class - interval.

SECTION-B


(5) ABCD is a trapezium with E being any point AB. IF ADǁEC and DEǁBC find the ratio

ar(∆DAE):ar(∆BEC).

(6) Using protractor, draw ∠DEF=60o. Construct another angle equal to ∠DEF, using compass.

(7) In the figure, ABCD is a parallelogram with ∠B=110o. Find the value of x and y.



(8) 20 circular plats each of radius 7 cm and thickness 1.5 cm are placed one above the other to

form a solid right ciruclar cylinder. Find the total surface area of the cylinder so formed.

(9) Three coins are tossed simultaneously 250 times with following frequencies of different

outcomes:

Number of tails 0 1 2 3

Frequency 45 65 52 88

Compute the probability of getting:

i. At most 2 heads

ii. All heads

(10) Following table shows the birth months of the 80 students of Class XII.

Jan Feb Mar Apr May June

5 6 7 4 10 3

July Aug Sep Out Nov Dec

5 10 6 8 8 8

Find the probability that a student selected at random was born a month in which the

Independence day or Republic day are celebrated.

SECTION-C

Question numbers 11 to 18 carry three marks each.

(11) The average monthly salary of 12 workers in a factory Rs. 12,850. IF the salary of the

manager is included, the average becomes 13,550, what is the manager’s salary?

(12) The median of the following observations arranged in ascending order, is 25. Find x. 11, 13,

15, 19, x+2, x+4, 30, 35, 39, 46. Also find mean.

(13) In ∆PQR, base QR is divided at X such that QX= 1

2 XR. If ar(∆PQR)= 81cm2, find ar(∆PQX).

(14) In the given figure, AB is a chord equal to the radius of the given circle with center O.

Calculate the value of a and b.



(15) Construct a line segment of suitable length and using ruler and compasses divide it into four

equal parts. Measure each equal part. Write steps of construction.

(16) In the figure, PQRS is a parallelogram whose diagonals intersect at O. Find the value of x and

y. Also, find the angle of the parallelogram.

(17) Draw an angle of 70o with the help of protractor. Now construct angle of (i) 35o (ii) 140o,

using compass.

(18) A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm.

Find the outer curved surface area of the bowl.

SECTION-D

Question numbers 19 to 28 carry four marks each.

(19) A batsman’s run in 80 one day matches are as follows:

Runs 20-29 30-39 40-49 50-59 60-69 70-79 80-89

No of

Matches

1 1 8 13 20 22 3

What is the probability that in the next match the batsman will score:

(a) atleast 70 runs,

(b) atmost 59 runs.

(20) PQRS is a parallelogram in which QR is produced to E such QR=RE. PE intersects SR at F. If

ar(∆SFQ)=3 cm2, find ar(PQRS).

(21) In the give figure, P is any point on the chord BC of a circle such that AB=AP. Prove that

CP=CQ. If ∠BAP=50o, find ∠CQP and ∠BRQ.



(22) Construct ∆MNO, when NO= 3.6cm, MN=MO=4.4cmand ∠N=75o.

(23) In the figure, ABCD and ABPQ are two parallelograms. Prove that ∆ADQ ≅ ∆BCP.

(24) The “Caring old people organisation” needs money to build the old age home which requires

164000 bricks. Bricks measure 10 cm ×8 cm× 4 cm and cost of brick depends on its volume

at the rate of Rs.1 per 100cm3. It also requires 4 cylindrical cans of paint of radius 14 cm and

height 30 cm. The cost of paint is Rs.1 per 20 cm3. How much money is required by

organization? If “company A gives the money to the organization”, then what common value

is depicted by company A and the organization?

(25) A closed cubical box of edge 20 cm is made up of wood of thickness 2 cm. Find the:

(a) volume of the wood used to make it.

(b) volume of air trapped in it.

(26) How many full bags of wheat can be emptied into a conical tent of radius 8.4 m and height 3.5

cm, if space for the wheat in each bag is 1.96 m3?

(27) The curved surface area of cylindrical pillar is 264 m2and its volume is 924 m3. Find the

diameter and height of the pillar.

(28) The table shows the prefers snacks of 100 children:

Prefered

Snack

Number of children

Lays chips

Crax

Cheese Balls

Uncle chips

Fun flips

22

10

15

24

29

Find the probability that the child chosen at random likes:



(a) crax and funflips

(b) lays chips and cheese balls

(c) only uncle chips.

SECTION-E

(Open Text)


Theme: Childhood Obesity in India

(29) Two friend examined their BMI as 27 and 31, however both have equal height of 150 cm.

Determine weight of both friends. Also state the health status of both friends.

(30) You want to burn 250 calories with the help of home activities for x min and running or y

min. Then what will be the liner equation for this? Write it in standard from and write value

of a, b and c.

(31) It is given that infants from age of one onward grow up to adolescence at a rate of 2 kg every

year for weight.

(a) Write a liner equation in 2 variable establishing a relation between age and weight

assuming age to be x and weight as y, if weight at 1 year of age and is given as 3 kg.

(b) Write two solution for the above equation.

Documents

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