(Project) Mathematics Project Guide For CBSE By Vasant Valley School

(Project) Mathematics Project Guide For CBSE By Vasant Valley School

General Instructions:
- The project should be hand written
- Credit will be given to original and creative use of material/pictures/drawings/methods of illustrating
- The project must be presented in a neatly bound simple folder.

Any one of the following projects may be chosen:

A) Linear Equations
Project Assignment Think of a question that asks about a cause and effect relationship between two measurable quantities. (eg.. does fingernail length affect typing speed?)

1. Write two different "how does _____ affect _____" questions.
2. Select the question that makes the most sense to you and explain why you have chosen it.
3. Write a hypothesis to answer your question.
4. Graph your data using appropriate choices of scales and axis.
5. In pencil, draw your "best" line.
6. Find the equation of your line.

Respond to the following questions
7. What do the variables in your equation represent? What does the equation represent?
8. Was your data positively correlated, negatively correlated or neither? Give possible explanations for the relationships or absence of relationships that you see in the data.
9. Use your equation to predict two data points not represented by the data. How good do you think these estimates are? why?
10. What information does the slope indicate?

Present your findings in a 3-4 pages handwritten report. Graph must be included.

B) Integer trains
You can use rods of integer sizes to build "trains" that all share a common length. A "train of length 5" is a row of rods whose combined length is 5. Here are some examples:

Notice that the 1-2-2 train and the 2-1-2 train contain the same rods but are listed separately. If you use identical rods in a different order, this is a separate train.
How many trains of length 5 are there?
Repeat for length 6
Repeat for length 7
Come up with a formula for the number of trains of length n. (Assume you have rods of every possible integer length available.) Prove that your formula is correct.
Come up with an algorithm that will generate all the trains of length n.
Create trains of lengths 6,7. Record any findings, conclusions in 3-4 pages of handwritten work.

C) Area of an Arbelos

Objective: Prove that the area of the arbelos (white shaded region) is equal to the area of circle CD.

What is an arbelos?
The arbelos is the white region in the figure, bounded by three semicircles. The diameters of the three semicircles are all on the same line segment, AB, and each semicircle is tangent to the other two. The arbelos has been studied by mathematicians since ancient times, and was named, apparently, for its resemblance to the shape of a round knife (called an arbelos) used by leatherworkers in ancient times.

An interesting property of the arbelos is that its area is equal to the area of the circle with diameter CD. CD is along the line tangent to semicircles AC and BC (CD is thus perpendicular to AB). C is the point of tangency, and D is the point of intersection with semicircle AB. Can you prove that the area of circle CD equals the area of the arbelos?

To do this project, you should do research that enables you to use the following terms and concepts:

right triangles,
circumscribing a circle about a triangle,
similar triangles,
area of a circle,
Tangents are perpendicular to radii at the point of contact.
Materials and Equipment
For the proof, you'll need :

pencil,
paper,
compass, and
straight edge.
Experimental Procedure

Do your background research,
Organize your known facts, and
Spend some time thinking about the problem and you should be able to come up with the proof.
Present your findings in a 3-4 pages handwritten report.
D) The Birthday paradox

Objective : The objective of this project is to prove whether or not the birthday paradox holds true by looking at random groups of 23 or more people.

Introduction: The Birthday Paradox states that in a random gathering of 23 people, there is a 50% chance that two people will have the same birthday. Is this really true?

Experimental Procedure
1) First you will need to collect birth dates for random groups of 23 or more people. Ideally you would like to get 10-12 groups of 23 or more people so you have enough different groups to compare. Here are a couple of ways that you can find a number of randomly grouped people.

You could use birthday lists from your own school for different classes.
Take the class lists of about 12 sections. Pass these around each of these classes and collect the birth date data
Use the birth dates of players on major teams. (Note: this information can easily be found on the internet).
2) Next you will need to sort through all the birth dates you have collected and see if the Birthday Paradox holds true for the random groups of people you collected. How many of your groups have two or more people with the same birthday? Based on the birthday paradox, how many groups would you expect to find that have two people with the same birthday?

3) Tabulate/Organize your data and findings in a 3-4 pages handwritten report

E) Perimeters of Semi Circles
Objective: The objective of this project is to prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle.

Introduction : The figure below shows a semicircle (AE) with a series of smaller semicircles (AB, BC, CD, DE,) constructed inside it. As you can see, the sum of the diameters of the four smaller semicircles is equal to the diameter of the large semicircle. The area of the larger semicircle is clearly greater than the sum of the four smaller semicircles. What about the perimeter?

Materials and Equipment
For the proof, you'll need :

pencil,
paper,
compass, and
straight edge.
Here's a suggestion for your display: in addition to your background research and your proof, you can make a model of� the Figure� with colored paper. Use a compass and straightedge to construct the semicircles. Cut pieces of string or yarn equal to the arc-lengths of the semicircles. You can use these to demonstrate that the perimeter lengths are indeed equal. Repeat for 3 different measurements of semi circles.

Experimental Procedure

Do your background research,
Organize your known facts,
Perform the experiments for 3 different semi circles
Tabulate your findings
Mathematically prove the result
Present your work in 3-4 handwritten pages.

Thanks to CBSEPORTAL for this info

CBSE Grading system

CBSE Grading system

With the academic year 2009-10, CBSE moves to the next level of education!
Class IX & X students will now be evaluated on a 9-point Grading System that is based on Continuous and Comprehensive Evaluation (CCE).
The academic year gets divided into 2 terms, each having two types of assessment:
Formative = Evaluation of class work, homework, assignment and project work
Summative = Term End Exams

April - September

Two Formative Assessments each of 10% weightage = 20% Two Formative Assessments each of 10% weightage = 20%

October - March

Term End Exam / Summative = 20% Term End Exam / Summative = 40%
Total = 100%

9-Point Grading System Roadmap

Grade Marks Range
A1 91-100
A2 81-90
B1 71-80
B2 61-70
C1 51-60
C2 41-50
D 33-40
E1 21-32
E2 00-20


Class X (2009-10) Board Exams happen, however, instead of marks - Grades are given
Class IX (2009-10) CCE gets operational from October 2009
Class X (2010-11) CCE gets implemented & Board Exams become optional
Grading system is based on yearlong performance.

Reserve Bank of India (RBI) Young Scholars Award Scheme

Reserve Bank of India (RBI) Young Scholars Award Scheme

To encourage learning about the Reserve Bank of India (RBI) among the youth of the country, the RBI conducts a major awareness and sensitization exercise on the role of the Reserve Bank and the banking system across the country. This exercise, the ‘RBI Young Scholars Award Scheme’, exposes youngsters to an actual banking and financial environment and inculcates a sense of pride in the selected ones of having had the opportunity to associate themselves with a prestigious organisation, the central bank of the country.

1. Eligibility: (A) Educational Qualification: All students across India who have completed 10 + 2 years of formal education or its equivalent from recognized institutions/boards in 2009 or before and are currently pursuing their undergraduate studies. However, those having enrolled for or having acquired degree(s) higher than graduation will not be eligible. Candidates who have qualified and worked at RBI as a Young Scholar in any of the previous years are not eligible to apply.

(B) Age : Candidates should be of age 18 years or more but less than 23 years as on September 1, 2009.

2. Number of Seats: A maximum of 150 young scholars would be awarded scholarship by the RBI every year under the scheme. Out of these, a maximum of 50 candidates will be selected through a test conducted in English medium. The rest, up to a maximum number of 100 shall be selected on regional basis through a test conducted in vernacular medium.

3. Entrance Examination: The entrance exam will be conducted in English, Hindi and 11 other regional languages. The regional languages will be Assamese, Bengali, Gujarati, Kannada, Malayalam, Marathi, Oriya, Punjabi, Tamil, Telugu and Urdu. The exam will be held at around 100 different locations spread all across the country. The List of Centres is given in this notification.

4. Examination Pattern and Syllabus : The examination will be of objective type with multiple choices for answers. The paper will be of approximately 90 minutes duration and will have questions related to role and functioning of the RBI, the trend of banking industry in India and general economic and financial environment of the country.

5. How to prepare for the Exam: Candidates willing to appear for the exam may take help of the material available on RBI Website www.rbi.org.in/youngscholars and www.rbi.org.in/commonman.aspx . The latest issue of RBI’s Annual Report and the Report on Trends & Progress of Banking will form part of the syllabus.

6. Placements and Project Assignment: The selected All India candidates and the Regional Candidates will be placed at the nearest Regional Office designated for the purpose, depending on the size of the office. The selected candidates will be required to work within the RBI on projects/assignments allocated to them by the respective Regional Director of RBI. They will be expected to complete the same in a reasonable time, subject to a maximum of 3 calendar months.

7. Stipend: During their stint with the RBI, they will be paid a consolidated monthly stipend of Rs.7500/- per head. For broken periods, the amount will be calculated on a pro rata basis.
8. Accommodation: During their stay with the RBI, the selected scholars who do not have a place to reside at the centre of placement will be assisted with accommodation for the duration of their project.

9. How to Apply: Candidates willing to apply for the scholarship may apply in the prescribed application form available on http://www.rbi.org.in/youngscholars.aspx either on line or offline. There is no fee for application or examination.

(A) Guidelines for Online Application

Candidates should have a valid email ID.

Go to the website and follow the instructions.

After applying online, the registered candidates should obtain a system generated printout of the registered information and sign at the appropriate place. A recent photograph should be pasted on the print-out and sent along with attested copies of the certificate on the address given below :

Project CoordinatorRBI Young Scholars Award SchemeProject No. 8709,Post Box No: 7632Malad (W),Mumbai- 400 064.

(B) Guidelines for filling Application Offline

Go to the website www.rbi.org.in/youngscholars

Download the application form for off-line mode.

Fill the form completely and paste your photograph at the appropriate place, sign at appropriate space and attach attested copies of all the relevant documents.

Project CoordinatorRBI Young Scholars Award SchemeProject No. 8709,Post Box No: 7632Malad (W),Mumbai- 400 064.

All applications – sent online or offline – should be sent to the given address by ordinary post only.Superscribe the envelope ‘Application for the RBI Young Scholars Award Scheme 2009-10′.

10. Last Date for Receipt of Application

The application and/or print-outs of application made online should reach the address mentioned above before October 21, 2009 by ordinary post. For the candidates staying abroad and for those posting print-out from Andaman & Nicobar Islands, Lakshadweep, Minicoy Islands, Assam, Meghalaya, Arunachal Pradesh, Mizoram, Manipur, Nagaland, Tripura, Sikkim, Ladakh Division of J & K State, Lahaul and Spiti District and Pangi Sub-Division of Chamba District of Himachal Pradesh, the last date for receipt of Print-out will be October 28, 2009. A print-out received after the last date will not be entertained.

The Reserve Bank of India/Institute of Banking Personnel Selection (IBPS) will not be responsible for any loss of application/print-out in transit or for rejection of application print-out because of non-receipt of print-out on or before the stipulated date.

Class 12 marks for IIT: Cut-off not changed

Class 12 marks for IIT: Cut-off not changed

NDTV Correspondent, Tuesday October 20, 2009, New Delhi

The government has been forced to clarify its stand on just how Class 12 results will affect admission to IIT.On Monday, Kapil Sibal announced that starting in 2011, Class 12 marks will play a greater role in determining who gets into IIT. Sibal is the Minister for Human Resource Development. He said that students often ignore their Class 12 board exams to focus on entrance exams for IIT, and the new policy hopes to address that.Sibal says his remarks were misreported by some parts of the media, which said that the new guidelines mean that students will need to score much higher in their boards if they want to get into IIT. Currently, students who clear the IIT entrance exam have to prove they've scored at least 60 per cent in their Boards.Raising this minimum worries states like Bihar, where students do not have equal access to good schools. Students here perform well in the entrance exam, however, and this guarantees them admission in IIT.Sibal has clarified that the current policy has not been changed, and there is no cause for concern. What role Class 12 results will play in IIT admission will be decided by a new committee headed by Dr Anil Kakodkar, chairperson of the Atomic Energy Commission. The committee is expected to submit its guidelines in January for review.