Hillwoods School Gandhinagar SUMMER HOLIDAY HOMEWORK

CLASS – VI

ENGLISH- Imagine yourself as a tourist-guide and explain about any Indian monument to

the tourist/s. Write the information in dialogue form. Also paste the picture of the monument .

MATHS : Name any five Indian heritage‟s sites. Find the Height in metres.

i) convert it into cm and write it in Indian and International system of numeration and round

off to nearest 10,100 and 1000.

ii) convert height in metres , Kilometres and mm.

iii) Find the area and write it in ascending order.

SCIENCE: - Scientific & Technological development in Indian Heritage.

SST : - Prepare a file for the project on Heritage on the basis of given points. You have to

choose any five states of India .Beautify your file with different pictures and colours.

i) Religion ii) Monuments iii) Dressing features ( Costumes ) iv) Food style

v) Language vi) Festivals vii) Rivers viii) Dance forms

ix) Famous personalities x) Sculptures and architectures

[ Note: Paper colour code for Project ]

English – Yellow

Maths – Blue

Hindi – Pink

Science – Green

Sanskrit – White

SST - Orange

Hillwoods School Gandhinagar SUMMER HOLIDAY HOMEWORK

CLASS – VII

TOPIC: - FORESTS

ENGLISH: Prepare a thought provoking colourful poster on the topic „SAVE FORESTS

AND WILDLIFE‟ on a A-4 size sheet. Add catchy slogans to make it more attractive.

MATHS: Choose any 5 states in India and mention their forest area (in square km).

Represent the above data using BAR GRAPH and PICTOGRAPH. Take appropriate scale.

SCIENCE: Visit a zoo/national park/Sanctuary and write the name of species of plants &

animals seen along with their pictures

OR

Survey of Current Status of Forests in India. Compare it with the past & Predict the Future.

SST: „Deforestation is manmade disaster‟. Describe what are man made disasters and how

humans are destructing the environment by doing Deforestation. Provide any two evidences

which proves it.

[Note: Paper colour code for Project ]

English – Yellow

Maths – Blue

Hindi – Pink

Science – Green

Sanskrit – White

SST - Orange

Hillwoods School Gandhinagar SUMMER HOLIDAY HOMEWORK

CLASS – VIII

ENGLISH: Imagine you and your friends have visited a nearby slum during Summer

Vacation, for a week, to create awareness among the slum dwellers, about the importance of

natural resources and its judicious use. Draft a report about your experience and

achievements during the visit.

MATHS: Using DOUBLE BAR GRAPH compare the usage of five different natural

resources between two countries.

SCIENCE: Prepare a working model on the topic “Steps to conserve natural resources”.

Principle involved in the model should be in chart paper.

SOCIAL SCIENCE : Prepare a project on NATURAL RESOURCES. Beautify your file

with different pictures and colours. Classification of Natural Resources, Uses and methods of

conservation of Natural resources.

Hillwoods School Gandhinagar SUMMER HOLIDAY HOMEWORK

CLASS – IX ENGLISH: Write two each of the following writing skills .

i) Diary

ii) Articles

MATHS : To make a spiral of root 7 and to prepare a project on congruency and similarity of

triangles.

SCIENCE: To prepare a working model on basic principles of science.

SST : Project on Disaster Management given by CBSE-(Any one topic to be taken)

1) Natural Disaster

Meaning, types of disaster, steps taken before, during and after disaster, Mitigation

strategies for-

Earthquakes, Floods, Cyclones, Drought ( Any 2 )

2) Man-made Disaster

Meaning, types of disaster, steps taken before, during and after disaster, Mitigation

strategies for-

Road, Rail & Air accidents, Terrorist attack

3) Chemical & Biological/Industrial Disaster

Meaning, types of disaster, steps taken before, during and after disaster, Mitigation

strategies ,and

Case Study for-

Bhopal Gas Tragedy of 1984 in India , Anthrax Scare of 2001 in US & Gas Well

Blowout of 2003 in China

Hillwoods School Gandhinagar SUMMER HOLIDAY HOMEWORK

CLASS – X

ENGLISH- Write two each of the following writing skills .

i) Letter Writing( Formal)

ii) Articles

iii) Story Writing

MATHS : Make the algebraic expression for the pair of linear equations for all three cases

and draw the graph for the same…(take a real life examples related to you).

SST : - Project on any one topic:

1. Consumer Awareness-meaning, intro of COPRA, need of implementing COPRA, role of

consumer movements, consumer rights and duties

2. Social Issue- any 2 social issues, case study, reasons, role of society and government, laws

taken to overcome on it and present scenario.

3. Sustainable Development- meaning, challenges of global world, planning for the future,

educating ourselves for a sustainable future, role of government, measuring the wealth of

nation and national strategies.

SCIENCE: - To prepare a working model on basic principles of science.

Hillwoods School Gandhinagar SUMMER HOLIDAY HOMEWORK

CLASS – XII

ENGLISH- Write two each of the following writing skills .

i) Note making

ii) Speech and Debate

iii) Advertisement

PHYSICS:-

1) Complete Experiment File and Activity file.

2) Do Worksheet of Ch-1 & 10 as Assignment form.

3) Prepare the Layout of Investigatory Project.

CHEMISTRY-

1) Complete practical File.

2) Complete worksheet questions in notebook for chapter-solutions, Haloalkanes & Haloarenes,

Alcohol, Phenol & ether.

3.Planning & completion of investigatory project.

BIOLOGY :

1) Prepare the layout of the investigatory project

2) Do worksheet of chapters 1 to 8

3) Complete practical records

4) Prepare unit 1 for class test.

MATHS :-

1) Do worksheet of chapter 1:- Relation and Functions

2) Do Sample Questions :-

Matrices:-

1. Express the matrix

𝐴 = 3 2 71 4 3−2 5 8

𝑎𝑠 𝑡𝑕𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑎 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑎𝑛𝑑 𝑎 𝑠𝑘𝑒𝑤 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑎𝑡𝑟𝑖𝑥

2. Find the inverse of the matrix by elementary transformation 𝐴 = 1 2 −2−1 3 00 −2 1

3. 𝐼𝑓 𝐴 = 2 −1 1−1 2 −11 −1 2

.Show that 𝐴3 − 6𝐴2 + 9𝐴 + 4𝐼3 = 0. 𝐻𝑒𝑛𝑐𝑒 𝑓𝑖𝑛𝑑 𝐴−1

4. Construct a 2x3 matrix A=[𝑎𝑖𝑗 ] 𝑤𝑕𝑜𝑠𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑎𝑟𝑒 𝑔𝑖𝑣𝑒𝑛 𝑏𝑦 𝑎𝑖𝑗 =

(𝑖+2𝑗 )2

2

5. 𝐹𝑜𝑟 𝑤𝑕𝑎𝑡 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑥 𝑎𝑛𝑑 𝑦 𝑎𝑟𝑒 𝑡𝑕𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑚𝑎𝑡𝑟𝑖𝑐𝑒𝑠 𝑒𝑞𝑢𝑎𝑙?

𝐴 = 𝑥 + 10 𝑦2 + 2𝑦0 −4

, B= 3𝑥 + 4 3

0 𝑦2 − 5𝑦

6. Find A and B if 2A+B=

3 2 −30 4 1

𝑎𝑛𝑑 A-2B= 6 −6 0−4 2 −1

7. Find the inverse of the matrix by elementary transformation 𝐴 = 3 −1 −22 0 −13 −5 0

8. Construct a 2x3 matrix A=[𝑎𝑖𝑗 ] 𝑤𝑕𝑜𝑠𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑎𝑟𝑒 𝑔𝑖𝑣𝑒𝑛 𝑏𝑦 𝑎𝑖𝑗 =𝑖−𝑗

𝑖+𝑗

9. 𝐹𝑜𝑟 𝑤𝑕𝑎𝑡 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑥 𝑎𝑛𝑑 𝑦 𝑎𝑟𝑒 𝑡𝑕𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑚𝑎𝑡𝑟𝑖𝑐𝑒𝑠 𝑒𝑞𝑢𝑎𝑙?

𝐴 = 2𝑥 + 1 2𝑦

0 𝑦2 − 5𝑦 , B= 𝑥 + 3 𝑦2 + 2

0 −6

10. A square matrix A , of order 3 , has |A|=5, find |A.adjA|.

11. Find inverse of

3 27 5

using elementary transformation

12.

If A= 2 1 11 0 10 2 −1

, Find 𝐴−1, 𝑢𝑠𝑖𝑛𝑔 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑟𝑜𝑤 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛.

13.

Find x if 𝑥 −5 −1 1 0 20 2 12 0 3

𝑥41 = 0

14.

If A= 1 3 20 1 4

and B= 1 40 12 3

. Show that AB≠BA

15. Find A and B if 2A+3B=

1 −2 32 0 −1

𝑎𝑛𝑑 A-2B= 3 0 1−1 6 2

ITF:

1. Prove :-tan−1

1+𝑥2+ 1−𝑥2

1+𝑥2− 1−𝑥2 =

𝜋

4+

1

2cos−1 𝑥2 , −1 < 𝑥 < 1

2. Prove that tan−1 1 + tan−1 2 + tan−1 3 = 𝜋

3. Prove that cot−1 7 + cot−1 8 + cot−1 18 = cot−1 3

4. Write the principal value of 𝑐𝑜𝑠−1(1

2) − 2𝑠𝑖𝑛−1(

−1

2)

5. Prove that sin−1 8

17+ sin−1 3

5=cos−1 36

85

6. Write the principal value of 𝑡𝑎𝑛 −1 3 − 𝑠𝑒𝑐−1 −2

7. Prove that tan−1 1

2+ tan−1 1

5+tan−1 1

8=

𝜋

4

8. Prove that sin[cot−1{cos(tan−1 x)}] =

x2+1

x2+2

9. Prove that 𝑖𝑓

1

2≤ 𝑥 ≤ 1 𝑡𝑕𝑒𝑛 cos−1 𝑥 + cos−1

𝑥

2+

3−3𝑥2

2 =

𝜋

3

10.

𝐹𝑜𝑟 𝑡𝑕𝑒 𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑣𝑎𝑙𝑢𝑒𝑠 , 𝑒𝑣𝑎𝑙𝑢𝑎𝑡𝑒 sin−1(− 3

2) + cos−1 3

2.

11. 𝑃𝑟𝑜𝑣𝑒 𝑡𝑕𝑎𝑡 :-cos−1

𝑐𝑜𝑠𝛼 +𝑐𝑜𝑠𝛽

1+𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛽 = 2 tan−1(𝑡𝑎𝑛

𝛼

2tan

𝛽

2)

12. Prove :-tan−1

1+𝑥2+ 1−𝑥2

1+𝑥2− 1−𝑥2 =

𝜋

4+

1

2cos−1 𝑥2 , −1 < 𝑥 < 1

13. 𝑃𝑟𝑜𝑣𝑒 𝑡𝑕𝑎𝑡 :-cos−1

𝑐𝑜𝑠𝛼 +𝑐𝑜𝑠𝛽

1+𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛽 = 2 tan−1(𝑡𝑎𝑛

𝛼

2tan

𝛽

2)

14. Prove that tan−1 2 + tan−1 3 =3𝜋

4

ACCOUNTANCY

Worksheet : Ch :1 (part B) Accounting for share capital

Project: Comprehensive story with accounting data

BUSINESS STUDIES:

Project :

Topics : Business Environment , Marketing , Stock Exchange, Principles of Management

ECONOMICS :

Worksheet:

Ch: 1,2,3

COMPUTER SCIENCE:

Solve 5 Questions each from the Ch-1 and Ch-9 Assignments mailed to you in your

notebook.

INFORMATICS PRACTICES:

Solve the Questions from Worksheet for Ch-3 and Ch-4 in your notebook.

15. Prove :-tan−1

1+𝑥+ 1−𝑥

1+𝑥− 1−𝑥 =

𝜋

4−

1

2cos−1 𝑥, 0 < 𝑥 < 1

16. Prove that cos(sin−1 1

5 2) = sin(4 cos−1 3

10)

17. Prove that

cot−1 1+𝑠𝑖𝑛𝑥 + 1−𝑠𝑖𝑛𝑥

1+𝑠𝑖𝑛𝑥 − 1−𝑠𝑖𝑛𝑥 =

𝑥

2 𝑥 ∈ (0,

𝜋

4)