Revision Worksheet

Sub – Mathematics

Class – X

Q1. If radii of two concentric circles are 4 cm and 5 cm, then find the length of each

chord of one circle which is tangent to the other.

Q2. In figure if < AOB = 1250 then find <COD

A

B

D C

Q3. In figure AB is a chord of the circle and AOC is its diameter such that < ACB= 500

If AT is the tangent to the circle at the point A, then Find <BAT.

C

B

500

A

Q4. If ½ is a root of the equation. x 2 + K x - 5

4 = 0, then value of K

Q5. State whether the following quadratic equations have two distinct real roots.

Justify your answer.

a) x2 – 3x + 4 b) 2 x2 - 3

2 x +

1

2 = 0

Q6. Is 0.2 a root of the equation x 2 - 0.4 = 0 ? Justify your answer.

Q7. Find the roots of the quadratic equation by using the quadratic formula in each

of the following.

a) x 2 + 2 2 x - 6 = 0

b) 1

2 x2 - 𝑛 x + 1 = 0

Q8. Find the roots of the following quadratic equation by the factorization

a) 2 x2 + 5

3 x – 2 = 0 b) 3 x2 + 5 5X – 10 = 0

Q9. Find whether the following equation have real roots. If real roots exists, Find

them.

a) - 2 x2 + 3 x + 2 = 0 b) 5 x2 – 2 x – 10 = 0

1250

o

500

.2.

Q10. Justify whether it is true to say that -1, −3

2, -2 ,

5

2 forms an AP as

a2 – a1 = a3 – a2

Q11. For tha AP -3, -7, -11, ……….. can we find directly

A30 – a20 without actually finding a30 and a20 ? Give reason for your answer.

Q12. Is O a term of the AP= 31, 28, 25, ……..?

Justify your answer.

Q13. The sum of the first five terms of an AP and the sum of the first seven terms of

same AP is 167. If the sum of the first ten terms of this AP is 235. Find the sum of its

first twenty terms.

Q14. Find the sum of those integers between 1 and 500 which are multiples of 2 as

well as of 5.

Q15. Find the formula for finding distance between two points (x,y) and (x2, y2).

Q16. Find the distance of the point P (6, 8) from the origin.

Q17. If AOBC is a rectangle whose three vertices are A (0,3) O (0,0) and B (5,0), then

find the length of its diagonal.

(0,3) A C

(0,0) O B (5,0)

Q18. Find the perimeter of a triangle with vertices (0,4), (0,0) and (3,0).

Q19. Find the area of a triangle with vertices A(3,0), B(7,0) and c(8,4)

Q20. Find the point which lies on the perpendicular bisector of the line segment

joining the points A (-2,-5) and B (2,5).

Q21. Draw a line segment of length 7 cm. Find a point P on it which divides it in the

ratio 3:5.

Sub – Mathematics

Class – X

Q1. Which of the following is not a quadratic equation?

a) 2 (x – 1)2 = 4x2 – 2x + 1

b) 2x – x2 = x2 + 3

c) ( 2𝑥 + 3)2 = 3 x2 – 5 x

d) x2

Q2. Which of the following equations has 2 as a root?

a) x2 – 4x + 5 = 0

b) x2 + 3x – 12 = 0

c) 2x2 – 7x + 6 = 0

d) 3x2 – 6x – 2 = 0

Q3. Value (s) of k for which the quadratic equation 2x2 – k x + k = 0 has equal root

is /are?

Q4. Write whether the following statements are true or false. Justify your answer

i) Every quadratic equation has exactly one root.

ii) Every quadratic equation has at least one real root.

iii) Every quadratic equation has at least two roots.

iv) Every quadratic equation has at most two root.

Q5. Find the roots of the quadratic equation by using the quadratic formula in each

of the following.

a) x2 + 2 2x – 6 = 0 b) 5x2 + 13x + 8 =0

Q6. Find area of the largest triangle that can be inscribed in a semi-circle of radius r

units.

Q7. Find the area of the circle that can be inscribed in a square of side 6 cm.

Q8. Find the radius of a circle whose circumference is equal to the sum of the

circumference of two circles of radii 15 cm and 18 cm.

Q9. In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the

shaded region.

Q10. Find the coordinate of the point which is equidistant from the three vertices of

the ⧍ AOB as shown in the figure.

(0, 2y)

O (2x, 0)

Q11. Find the area of the triangle triangle whose vertices are (-8, 4), (-6, 6)

and (-3,9).

Q12. If P (9a-2, -b) divides line segment joining A (3a + 1, -3) and B (8a, 5) in the

ratio 3:1, then find the value of a and b.

Q13. A vertical tower stands on a horizontal plane and is surmounted by a vertical

flagstaff of height h. At a point on the plane, the angles of elevation of the bottom

and the top of the flag staff are a and b respectively, Prove that the height of the

tower is ℎ 𝑡𝑎𝑛 𝛼

𝑡𝑎𝑛𝛽 −𝑡𝑎𝑛𝛼

Q14. The angle of elevation of the top of a tower 30 m high from the foot of another

tower in the same plane is 600 and the angle of elevation of the top of the second

tower from the foot of the first tower is 300. Find the distance between the two

towers and also the height of the tower.

Q15. From the top of a tower h m high, angles of depression of two objects which

are in time with the foot of the tower are 𝛼 and 𝛽 where (𝛽 > 𝛼). Find the distance

between the two objects.

Q16. The angle of elevation of the top of a vertical tower from a point on the ground

is 600. From another point 10 m vertically above the first, its angle of elevation is

450. Find the height of the tower.

Q17. In figure, AB is a chord of the circle and AOC is its diameter such that

<ACB=500. If AT is the tangent to the circle at the point A, then find < BAT

C

B

A T

Q18. If two tangents inclined at an angle of 600 are drown to circle of radius 3 cm,

then find the length of each tangent.

500

O

.2.

Q19. In figure, if o is the center of a circle, PQ is a chord and the tangent PR at P

makes an angle of 500 with PQ, then find <POQ.

P

R

Q

Q20. If AB is a chord of a circle with centre O. AOC is a diameter and AT is the

tangent at A. Prove that <BAT = <ACB.

Q21. Draw a ⧍ABC with AB = 5 cm, BC= 6 cm & <ABC = 600. Construct a similar

triangle with scale factor 5/7 Justify it.

500

O

Enrichment Sheet

Sub: Mathematics

Class – IX Paper-I

1. Prove that there is one and only one circle passing through three non collinear points. 2. Prove that an angle in a semicircle is a right angle. 3. In a circle of radius 5 cm, AB & CD are two parallel chords of length 8 cm and 6 cm respectively. calculate the distance between the chords if they are i) On the same side of the centre. ii) On the opposite sides of the centre. 4. Prove that two circles can not intersect at more than two points. 5. Two circles of radii 10 cm and 8 cm intersect each other and the length of the common chord is 12 cm. Find the distance between their centres. 6. ABCD is a parallelogram. If P&Q are any two points on the sides AB and BC respectively, prove that Arewa (⧍ CPD)= Area (⧍ AQD) 7. Find the area and perimeter of the rhombus, length of whose diagonals are 16 cm and 24 cm respectively. 8. ABC is a triangle in which D is mid point of AD. Prove that Area ⧍ BED = ¼ Area(⧍ABC) 9. Show that the diagonals of C parallelogram divides it into four ⧍’s of equal area. 10. A point O inside a rectangle ABCD is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the areas of the other pair of triangles. 11. Prove that the bisectors of the angles of a ||gm enclose a rectangle.

..2.. 12. Show that the quadrilateral formed by joining the mid points of the pair of adjacent sides of a i) rectangle is rhombus ii) rhombus is rectangle. 13. Prove mid point theorem and its converse. 14. Prove that the diagonals of a square are equal and perpendicular to each other. 15. Draw the graph of 2x+y = 6 and find the coordinates of the points where it cuts the coordinate axes. 16. A tent is in the form of right circular cylinder surunded by a cone. The diameter of the cylinder is 24m. The height of the cylindrical portion is 11m while the vertex of the cone is 16m above the ground. Find the area of the canvas required for the tent. 17. Find the length of the longest pole that can be put in a room of dimensions 10m x 10m x 5m. 18. Internal & external diameters of a hallow hemispherical vessel are 20cm & 28cm respectively. Find the cost of painting the vessel all over at 14 paise per cm2. 19. A cone, hemisphere and a cylinder stand on equal bases and have the same height. Find ratio of their volumes. 20. Surface area of sphere is 144𝜋 cm2. Find its volume

Enrichment Sheet

Sub: Mathematics

Class – IX Paper-II

1. A hollow spherical shall is made of a metal of density 4.5 g/cm3. If its internal & external radii are 8cm and 9cm respectively, find the weight of the shall. 2. A hemispherical bowl is made of steel 0.5 cm thick. The inside radius of the bowl is 4 cm. find the volume of steel used in making the bowl. 3. A cylinder and a cone have equal radii of their bases and equal heights. If their curved surfaces are in the ratio 8:5, show that the ratio of radius and height of each is 3:4. 4. A cone of height 8 m has a curved surface area 188.4 sq. meter. Find its volume (Take 𝜋 = 3.14). 5. The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110 cm. Find the height and the volume of cylinder. 6. In a cyclic quadrilateral ABCD if <B - <C = 600, find the measure of <B & <D. 7. If two sides of a cyclic trapezium are parallel, prove that remaining two sides are equal and the diagonals are also equal. 8. Prove that the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it. 9. Constract a circle with any circular object (bangle), Write steps to find out its centre. 10. Find the length of a chord which is at a distance of 8 cm from the centre of a circle of radius 17 cm.

..2.. 11. Show that the figure formed by joining the mid points of adjacent sides of a quadrilateral is a parallelogram. 12. Show that the bisectors of the angles of a parallelogram enchase a rectangle. 13. If O is a point within a quadrilateral ABCD, show that OA + OB + OC +OD > AC + BD. 14. In a parallelogram ABCD, if <A = 1150, find all other angles. 15. Draw graph of the eqn. 3x + 2y = 12. At what points it cut the x – axis & y axis. Find the one enclosed by the line & the coordinate axis. 16. Construct an equilateral ⧍ one whose altitude measures 5 cm.

Enrichment Sheet

Sub: English

Class – IX &X

Que1. You are Lakshmi/Lakshman.Recently you read in a newspaper about the

depletion of green coverage in many areas in India.Write an article on the topic ‘Green

India’ in not more than 120 words.

Que 2.Write a story with a title in 150-200 words using the following hints.

Annual Atheletic Meet-Ravi participates-prepares for months-wins 100mts.and 200

mts.-loses the 400mts. by 58secs. Champion Trophy-someone else’s possession.

Que 3. Imagine yourself as Samina/Sajid.Write a diary entry for the day when you

heard about the harmful effects of using mobile phones in about 100-120 words.

Que 4. Complete the following passage by choosing the most appropriate options from

the given below.

Last night I was watching a match (a)_______________ India and Australia.My friends

(b)_________________whistling and clapping while my mother cooked for all of us.I

(c)_________________always loved to watch a match.

(a)(i) Among (ii) between (iii) for (iv) by

(b)(i) Keep (ii) kept (iii) keeps (iv) had kept

(c)(i) Have (ii) am (iii) had (IV) have been

Que 5.There is one error in each line. Write the incorrect word and the correction in

your answer sheet.

Obstacles are these frightful things (a)____________ ________________

That you see when you took your eyes (b)________________ ___________

Of your goal. But remember, airplane ( c)__________ _______________

takes off against the wind, not to it. (d) _____________ _____________

Que 6.Read the conversation given below and complete the paragraph that follows-

Mohan: I am going to Delhi tomorrow.

Sohan: When will you return?

Mohan: I shall come next week.

Sohan: Please bring a pair of jeans for me.I shall make you the payment.

Mohan: What size and colour do you want?

Sohan: My waist is 32 inches and I want a royal blue colour.

Mohan told Sohan (a)____________.Sohan asked him (b) _____________.

Mohan replied that he would return in coming week.Sohan then replied Mohan

(c)_____________ and he would make the payment.

Que 7.Rearrange the following words and phrases to form meaningful sentences-

Must/be/not waste/and/we/time/attentive

What/the /listen/teacher/is teaching/carefully to

All/written on /read/the board/the/ things.

Enrichment Sheet

Sub: English

Class XI

Ques 1.Read the following passages carefully and make note making?

Everyone needs a holiday,both to relax and to have a change of environment. The

holiday makers feel relaxed and refreshed at the end of the holiday and look forward to

the resumption of their duties, be it at school, office or factories, with renewed

vigour.This is the reason why all establishments grant their employees annual leave.

With the end of the Academic year the schools and universities grant their pupils a long

holiday during mid-summer. This will last until early September when the new school

term starts. Of course the parents will like to take advantage of this and take their leave

to coincide with the children’s vacation. This has become a traditional holiday season in

most European countries particularly in England.

With the coming of August, the traditional holiday season in Britain reaches its peak

point and most of the holiday resorts are packed to capacity. In order to avoid the

crowd, some prefer to take their holiday a little earlier if facilities so warrant. Those

who have already taken their holidays can console themselves not only with reflections

on the happy days spent in country, at the seaside or abroad, but also with the thought

that holiday expenses are over for the year and that by taking an earlier holiday they

have missed the August rush.

The main thing, of course, is the weather and that would be hazardous to prophesy.

But whatever the weather is like, the essence of a holiday for most is the carefree

atmosphere in which it can be enjoyed.”Take all you need but leave your worries

behind” is the sound advice for the holiday maker. Private worries are not always easy

to escape from.However,even the pessimist would admit that for the moment things

appear brighter than they have been.

Holiday time is surely a time for shedding serious preoccupations and seeking the

pleasures that appeal to us. It is true that we may not always succeed in finding them;

indeed there are people who maintain that the great thing about a holiday is that it

gives you an ampler appreciation of home comforts a view no doubt more widely held

among the elderly than you.

2.Cable and satellite mark the end of the era when TV –Television-took place on a

Mainly national basis.Increasingly, messages are transmitted across national borders. In

Europe, satellite has also been an important way in which migrant communities can

keep in touch with the TV systems of their country of origin, because satellite dishes

can pick up much more distant signals. The new era of TV has been called

“narrowcasting” (rather than broadcasting) by some commentators, because the

audiences for TV channels are becoming smaller and more specific.TV stations

increasingly aim at particular segments of the population, rather than at the mass

audience.

Some have argued that proliferation of channels has not meant a new diversity, but

rather lowering of standards, and the replacement of public-service broadcasting by

cartles of commercial owners, such as Murdoch’s News International and the German

company Bertelsmann. While the American system offers a new diversity to those who

can afford the Bertelsmann. While the American System offers a new diversity to those

who can afford the extra subscription costs, the low-cost programming on Italy’s many

cable channels suggest that overhasty degradation can reduce the overall quality of

nation’s broadcasting.

Many writers now use the term “convergence “to refer to an increasing overlap

between telecommunications,computers,the internet, and mass media forms such as

TV.TV is according to some forecasters,about to become the basis of new home

information and entertainment systems. Great power may come to reside in the hands

of the companies who control the distribution systems that determine the range and

type of services reaching homes and businesses.The debates about the power of TV to

influence people’s behavior and belief has been going on ever since the medium has

became widely popular in the Westin the 1950s.There are three main strands of

concern:the impact of TV on social behavior,particularly crimes of violence,its effort on

the political process;and whether it causes a deterioration in cultural standards.

A great deal of research has been carried out on the extent to which TV influences

social behavior.The main concerns have been about whether TV makes people lazier

and less varied in their social habits,and in particular whether it causes more violence in

society.

The research shares the problem of much social science,when faced with controversy:it

is difficult to provide efinite proof of cause and effect.Arguably,to show programmes to

children in a laboratory and then test whether they become more aggressive only

illustrateshow children behave in a laboratory,rather than in the home or the

playground.Even where violent behaviour clearly does occur in response to a violent

programme ,there is still the question of how to separate the TV cause from other

causes,such as family upbringing neighbourhood life,and so on.Many have been willing

to accept the difficulties of such proof,on the grounds that authority figures might use

evidence of links between TV violence and real violence as a justification for controlling

what is shown,and ,in a broader sense for social control.Others have argued that,given

the very large amount of broader sense,for social control.Others have argued

that,given the very large amount of violence on TV (a consequence of the fact that

most narratives are based around conflict that is often resolved by violence),and given

the sheer amount of time that many people watch it,it is difficult to believe that these

images could have no effect .Some think that TV encourages the view that the world is

a more violent place than it really is.The argument has also centred on appropriate

broadcast times for programmes that are primarily aimed at adult audiences.In Britain

a “watershed” time of 9 p.m. acts as a guide to broadcasters,based on the assumption

that children are no longer watching TV by then.With access within households to video

recording of programmes,this guidelines has less relevance than in pre video years.

3. Governments have seized on tourism as a way of creating employment and bringing

income-preferably foreign exchange-into troubled economies.For years tourism’s

capacity to filter wealth through communities has been a major argument in its

favour.The tourist spends money on accommodation,food,and souvenirs,bringing

income to suppliers of these goods and services,whose money will in turn circulate

through the economy.

But if the hotels are foreign-owned,local people have little gain.Nor are they better off

if tourists,though,stay among thembut come prepared to be self sufficient.In both

cases tourists are strongly resented by the locals,who see huge increases in prices as

the only visible result of tourism’s economic impact.

Job creating is another common advantage of tourism.Governments subsidise tourism

projects in the expectation of increasing employment opportunities in the new hotels

and restaurants.But such work is frequently poorly paid and is seasonal.Local people

may be neither willing to do small and mean unskilled jobs nor highly trained enough to

be managers or tour operators.They stand on the sidelines while foreign staff and

migrants fill the vacancies.Social tensions surface all too easily in such situations.

Any kind of change brings tensions,and economic development tends to increase the

generation gap.The young learn new skills while the older generation finds its tradition

devalued or rejected. Tourists bring with them very different cultures and ideas. Their

dress and behavior may be very attractive to the younger generation but not to the

older one. On the beaches and bar strips of Asia, Africa and the Pacific you can see how

readily young people have been lured from their villages by the promise of bright light

and money.

In relation to the environment,even the most blinkered tourism enthusiast is faced

with the truth that tourists destroy the very things they have come for. In Kenya ,a

country that depends heavily on tourism, there is a real danger of ‘tourist pollution ‘in

most popular game parks. Animals in the Masai Mara Reserve are constantly disturbed

by tourist bases, their prey scattered ,their feeding grounds damaged. If the animals

disappear,so may tourism.

Enrichment Sheet

Sub: Hindi

Class IX

Á01- foxzg djks vkSj lekl dk uke crkvks %&

1- HkkbZ& cgu

2- ihrkacj

3- ns”koklh

4- deyu;u

5- egkRek

Á02- vFkZ ds vk/kkj ij fuEufyf[kr okD;ksa ds Hksn crkb, %&

1- ;fn og ifjJe djrk rks lQy gks tkrkA

2- vkidh ;k=k “kqHk gksA

3- D;k og vkxjk tk jgh gS\

4- ?kweus er tkvksA

5- vksg! Fdruk lqanj n`”; gSA

Á03- fuEufy[kr okD;ksa es vysdkj dk uke crkb, %&

1- pk: panz dh pqpy fdj.ks [ksy jgh g Sty Fky esaA

2- dud& dud rs lkS xquh ekndrk vf/kdk;A

Ok [kk, ckSjk, tx] ;k ik, ckSjk;AA

3- pju /kjr fpark djr fpror pgq¡ vksjA

lqcju dks [kkstr fQjr dfo] O;fHkpkjh pksjAA

4- ftl ohjrk ls “k=qvksa dk lkeuk mlus fd;kA

vleFkZ gks mlds dFku es ekSu ok.kh us fy;kAA

5- es?k vk, cM+s cu Bu l¡oj dsA

Á04- fuEufyf[kr iz”uksa ds mRrj nhft, %&

1- es?k :ih esgeku ds vkus ls okrkoj.k esa D;k ifjorZu gq,\

2- jke Lo:i dk viuh csVh dks mPp f”k{kk fnyokuk vkSj fookg ds fy,

fNikuk] ;g fojks/kkHkkl mudh fdl foo”krk dks mtkxj djrk gS\

3- lj Vkel ^gs* ds eSuk ij n;k& Hkko ds D;k dkj.k Fks\

4- ^izsepanz ds QVs twrs* IkkB esa Vhys “kCn dk iz;ksx fdu lanHkksZ dks bafxr djus

ds fy, fd;k x;k gksxk\

Enrichment Sheet

Sub: Hindi

Class X

Á01- funsZ”kkuqlkj mRrj nhft, %&

¼d½ tks euq’; ifjJe djrs gS mUgs vf/kd le; rd fujk”k ugh jguk iM+rkA

¼ljy okDl esa cnfy,½

¼[k½ v/;kid vius f”k’;ksa dks vPNk cukuk pkgrk gSA ¼feJ okD; esa cnfy,½

¼x½ nks ufn;ksa ds feyus ds LFkku dks laxe dgrs gSaA ¼la;qDr okD; esa cnfy,½

Á02- funsZ”kkuqlkj mRrj nhft, %&

¼d½ jkr Hkj dsls tkxk tk,xk\ ¼crkb,½

¼[k½ rqe nku nksxsA ¼deZokP; esa cnfy,½

¼x½ ?kk;y py ugha ldrkA ¼HkkookP; esa cnfy,½

¼?k½ D;k eq>s /kks[kk fn;k gS\ ¼okP; ifjorZu dhft,½

Á03- fuEufyf[kr okD;ksa esa js[kafdr inksa dk ikB& ifjp; fyf[k, %&

¼d½ vkuan cgqr HkkX;”kkyh gSA

¼[k½ og chekj gS blfy, vkt vodk”k ij gSA

¼x½ rfey cgqr izkphu Hkk’kk gSA

¼?k½ esjs ?kj ds lkeus uhe dk isM+ gSA

Á04+- fuEufyf[kr dkO;& iafDr;ksa es iz;qDr jlksa dk uke fyf[k, %&

¼d½ oSjkX; NksM+ ck¡gks dh foHkk l¡Hkkyks

pV~Vkuksa dh Nkrh ls nw/k fudkyks

gS :dh tgk¡ Hkh /kkj f”kyk,¡ rksM+ks

ih;w’k panzekvks dks idM+ fupksM+ks

¼[k½ ^^ gk! o`n~/kk ds vrqy /ku gk! o`n~/krk ds lgkjs!

gk! izk.kksa ds ijefiz; gk! ,d esjs nqykjsA

gk! “kksHkk ds lIr le gk! :Ik yko.; gkjs!

gk! csVk gk! gn; /ku gks! Uks= rkjs gekjsA**

¼x½ vks>jh dh >hjh dk¡/ks vk¡rfu dh lsYQh ck¡/ks]

ewM ds deaMy [kij fd, dksfjdsA

tksfxu >qVqu >qaM& >qaM cuh rkilh& lh]

rhj rhj cSBh lks lej lfj [kksfj dSA

lksfur lkS lkfu& lkfu xwnk [kkr lrqvk ls]

izsr ,d fo;r cgksfj ?kksfj & ?kksj dSA

^rqylh* cSrky Hkwr] lkFk fy, HkwrukFk]

gsfj& gsfj g¡dsr gS gkFk tksj& tksj dSA

¼?k½ ;g ns[k] xxu eq>esa y; gS]

;g ns[k] iou eq>es y; gS]

Ekq>es y; gS lalkj ldyA

vejRo Qwyrk gS eq> esa]

lagkj >wyrk gS eq> esaA

Á05- iz”uksa ds mRrj nhft, %&

1- bl vkRedF; es ysf[kdk ds firk us jlksbZ dks ^HkfV;kj [kkuk* dgdj D;ksa

lacksf/kr fd;k\

2- ij”kqjke ds vuqlkj lsod dkSu gS\ os jke dks viuk lsod ekuus ls bsdkj

D;ks djrs gS\

3- lH;rk vkSj laLd`fr ls d;k rkRi;Z gS\