Maths HL IA 09

Maths HL IA 09, ib sh!t

[ Pobierz całość w formacie PDF ]
MATHL/PF/M09/N09/M10/N10
MATHEMATICS
Higher Level
The portfolio - tasks
For use in 2009 and 2010
© IBO 2008
22 pages
For final assessment in 2009 and 2010
– 2 –
MATHL/PF/M09/N09/M10/N10
CONTENTS
Introduction
Type I tasks
INVESTIGATING DIVISIBILITY
INVESTIGATING RATIOS OF AREAS AND VOLUMES
THE SEGMENTS OF A POLYGON
PARABOLA INVESTIGATION
Type II tasks
DESIGNING A FREIGHT ELEVATOR
MODELLING THE HEIGHTS OF SAPLINGS
MODELLING PROBABILITIES IN GAMES OF TENNIS
MODELLING THE COURSE OF A VIRAL ILLNESS AND ITS TREATMENT
Criteria
Developing your own tasks
Old tasks
For final assessment in 2009 and 2010
– 3 –
MATHL/PF/M09/N09/M10/N10
Introduction
What is the purpose of this document
This document contains new tasks for the portfolio in mathematics HL. These tasks have been produced
by the IB, for teachers to use in 2009 and 2010. It should be noted that any tasks previously produced and
published by the IB will no longer be valid for assessment after November 2008. These include all the
tasks in any teacher support material (TSM). To assist teachers to identify these tasks, a list is included at
the end of this document.
What happens if teachers use these old tasks?
The inclusion of these old tasks in the portfolio will make the portfolio non-compliant, and such
portfolios will therefore attract a 10-mark penalty. Teachers may continue to use the old tasks as practice
tasks, but they should not be included in the portfolio for final assessment.
Why are these changes being made?
An interim version of the TSM for the current course was first published in 2004, with the full TSM
published in 2005. There were concerns that these documents were available for sale potentially giving
students access to the student work and its accompanying assessment. Teachers also expressed concerns
that model answers soon became easily available on the internet and felt that this made it difficult to
ensure students’ work was their own. There were also frequent requests for more tasks to be published by
the IB, as many teachers are apprehensive about producing their own tasks.
What other documents should I use?
All teachers should have copies of the mathematics HL subject guide (second edition, September 2006),
including the teaching notes appendix, and the TSM (September 2005). Further information, including
additional notes on applying the criteria, are available on the Online Curriculum Centre (OCC).
Important news items are also available on the OCC, as are the diploma programme coordinator notes,
which contain updated information on a variety of issues.
Can I use these tasks before May 2009?
These tasks should only be submitted for final assessment from May 2009 to November 2010. Students
should not include them in portfolios before May 2009. If they are included, they will be subject to a
10-mark penalty.
For final assessment in 2009 and 2010
– 4 –
MATHL/PF/M09/N09/M10/N10
Type I – mathematical investigation
While many teachers incorporate a problem-solving approach into their classroom practice, students also
should be given the opportunity formally to carry out investigative work. The mathematical investigation
is intended to highlight that:
•
the idea of investigation is fundamental to the study of mathematics
•
investigation work often leads to an appreciation of how mathematics can be applied to solve
problems in a broad range of fields
•
the discovery aspect of investigation work deepens understanding and provides intrinsic motivation
•
during the process of investigation, students acquire mathematical knowledge, problem-solving
techniques, a knowledge of fundamental concepts and an increase in self-confidence.
All investigations develop from an initial problem, the starting point. The problem must be clearly stated
and contain no ambiguity. In addition, the problem should:
•
provide a challenge and the opportunity for creativity
•
contain multi-solution paths, that is, contain the potential for students to choose different courses of
action from a range of options.
Essential skills to be assessed
•
Producing a strategy
•
Generating data
•
Recognizing patterns or structures
•
Searching for further cases
•
Forming a general statement
•
Testing a general statement
•
Justifying a general statement
•
Appropriate use of technology
For final assessment in 2009 and 2010
– 5 –
MATHL/PF/M09/N09/M10/N10
INVESTIGATING DIVISIBILITY
HL TYPE I
Background
In order to satisfactorily complete this assignment, the following areas of the core curriculum should have
been covered:
Factorization of polynomials
Mathematical induction
Pascal’s triangle
Binomial theorem and notation
n
r
x
. Determine if the expression is always
divisible by the corresponding
x
. If divisible use mathematical induction to
prove
your results by
showing whether ( 1)
P n n n
for
x
{2, 3, 4, 5}
P k P k
is always divisible by
x
. Using appropriate technology, explore
more cases, summarize your results and make a conjecture for when
( )
x
nn
is divisible by
x
.
2.
Explain how to obtain the entries in Pascal’s Triangle, and using appropriate technology, generate
the first 15 rows. State the relationship between the expression
( 1)
P k
P k
and Pascal’s
Triangle. Reconsider your conjecture and revise if necessary.
Write an expression for the
x
th
row of Pascal’s Triangle. You will have noticed that
x
kk
,
ï‚¥
. Determine when
k
is a multiple of
x
.
r
3.
Make conclusions regarding the last result in part 2 and the form of proof by induction used in this
assignment. Refine your conjecture if necessary, and prove it.
4.
State the converse of your conjecture. Describe how you would prove whether or not the converse
holds.
For final assessment in 2009 and 2010
1.
Factorize the expression ()
( )
[ Pobierz całość w formacie PDF ]

zanotowane.pl

doc.pisz.pl

pdf.pisz.pl

mement.xlx.pl