IB Mathematics
Analysis and Approaches SL
The Exploration (I.A.)
WHAT IS AN EXPLORATION?
The mathematical exploration is the internally assessed component of the mathematics courses. It is a short report written by the student based on a topic chosen by him or her. It should focus on the mathematics of the particular area chosen.
The emphasis is on mathematical communication (including formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing and thoughtful reflection. A student should develop his or her own focus, with the teacher providing feedback via, for example, discussion and interview. This will allow all students to develop an area of interest for them, without the time constraint as in an examination.
In addition to testing the objectives of the course, the exploration is intended to provide students with opportunities to increase their understanding of mathematical concepts and processes, and to
develop a wider appreciation of mathematics. It is intended that, by doing the exploration, students benefit from the mathematical activities undertaken and find them both stimulating and rewarding.
Particularly, the exploration allows students to use their mathematics to:
enjoy mathematics, and develop an appreciation of the elegance and power of mathematics
apply and transfer skills to alternative situations, to other areas of knowledge and to future developments
appreciate how developments in technology and mathematics have influenced each other
appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics
appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives
appreciate the contribution of mathematics to other disciplines
TIMELINE
October 16 (A) or 19 (B)- topic due
October 22 (A) or 23 (B) - introduction due
December 1 (A) or 2 (B) - body/mathematical exploration due December 7 (A) or 8 (B) - conclusion/bibliography due
EXPECTED SKILLS AND STRATEGIES
These skills and strategies are expected from you:
Choosing a topic
• Identifying an appropriate topic – choose one
that you are interested in so that you can show personal engagement.
• Developing a topic
• Devising a focus that is well defined and
appropriate
• Ensuring that the topic lends itself to a concise
exploration
Communication
• Expressing ideas clearly
• Identifying a clear aim for the exploration
• Focusing on the aim and avoiding irrelevance
• Structuring ideas in a logical manner
• Including graphs, tables and diagrams at
appropriate places
• Editing the exploration so that it is easy to follow
• Citing references where appropriate!!!
Mathematical presentation
• Using appropriate mathematical language and
representation
• Defining key terms and variables, where
required
• Selecting appropriate mathematical tools
(including information and communication technology)
• Expressing results to an appropriate degree of
accuracy
Personal engagement
• Working independently
• Asking questions, making conjectures and
investigating mathematical ideas
• Reading about mathematics and researching
areas of interest
• Looking for and creating mathematical models
for real-world situations
• Considering historical and global perspectives
• Exploring unfamiliar mathematics
Reflection
• Discussing the implications of results
• Considering the significance of the exploration
• Looking at possible limitations and/or extensions
• Making links to different fields and/or areas of
mathematics
• Reflection does not have to be in a section on its
own – it is possible to reflect as you go.
Use of mathematics
• Demonstrating knowledge and understanding
• Applying mathematics in different contexts
• Applying problem-solving techniques
• Recognizing and explaining patterns, where
appropriate
• Generalizing and justifying conclusions
• The mathematics that you use must be at the
level of the IB standard level course. If the level of mathematics is below this level or only at prior knowledge level then you will not give yourself the best opportunity to gain a
reasonable mark. Using mathematics that is at a level higher than standard level is not required and will not attract higher marks.
The finished product should:
• have page numbers inserted on each page
• be stapled or bound
Authenticity
Plagiarism
This includes copying quotes, information and ideas, directly or paraphrased, from books and websites.
Collusion
This includes working closely with another student such that the work between the two students is similar.
Collusion, plagiarism or any other forms of academic dishonesty are considered by the College to be acts of serious misconduct and will be dealt with accordingly.
Ensuring academic honesty
To prevent plagiarism, you need to cite your sources correctly and include any sources in your bibliography. If you have questions on how to properly cite your sources, seek advice from your teacher or from the school librarian. Please use the link to the Massey University website interactive for correct referencing methods.
(http://owll.massey.ac.nz/referencing/apa-interactive.php)
While you might discuss ideas with other students, you should never giver another student your work, either in print or electronically.
Checklist
Item Yes Partially No
Is the work entirely yours?
Have you chosen a topic that you are interested in and developed your own ideas? Is it evident in your exploration?
Have you explained the reason why you have chosen your topic in your exploration?
Is the aim of your exploration included in your introduction? Do you have an introduction and conclusion? Is your exploration organized?
Have you defined key terms/variables?
Have you used appropriate mathematical language (notation, symbols and terminology) consistently throughout your exploration?
** Calculator/computer notation should not be used. **
Have you used more than one form of mathematical representation? Are all graphs, tables and diagrams sufficiently described and labeled? Are formulae, graphs, tables and diagrams in the main body of the text? No full-page graphs and no separate appendices.
Have you used technology to enhance your exploration?
Have you explained what you are doing at all times? Explanatory comments should be seen throughout your exploration?
Have you used mathematics that is commensurate with the Standard Level course (or beyond)?
Is the mathematics in your exploration correct?
Have you reflected on your finding at appropriate places in your exploration, particularly in your conclusion?
Have you considered limitations and extensions in your reflection? Have you considered the assessment criteria when writing your exploration? Have you self-assessed your exploration?
Is your exploration approximately 12 to 20 pages long? Have you referenced your work in a bibliography?
Have you had someone else read your exploration to ensure that the communication is good? Does it have flow and coherence? Is it easily understandable? Does it read well?
Have you made sure there is no identifying information in/on your IA? Have you submitted a first draft to your teacher and used the feedback to improve your report?
Topics Covered in Previous Math Courses
Algebra
• Arithmetic sequences and series • Geometric sequences and series • Exponents and logarithms
Functions and Equations
• Functions (linear, quadratic, etc…) and
their key features
• Composite functions • Inverse functions
• Transformations of graphs
• Solving equations of various forms
Circular Functions and Trigonometry
• Length of arc • Area of a sector • Unit circle
• Trigonometric ratios and their
relationships
• Trigonometric identities
• Trigonometric functions and their key
features
• Transformations of trigonometric
functions
• Solutions of triangles
Vectors
• Components of a vector
• Algebraic and geometric approaches of
sum and difference, multiplication by scalar, magnitude, unit and base vectors, and position vectors
• Scalar product
• Perpendicular and parallel vectors • Angle between vectors
• Vector equation in two and three
dimensions
• The angle between lines
• Distinguishing between orthogonal and
parallel lines
• Determining and finding the point of
intersection of two lines
Topics Covered in This Math Courses
Probability and Statistics
• Concept of population, sample, random
sample, discrete and continuous data
• Presentation of data using frequency
distributions and histograms, box and whisker plots
• Statistical measures and their
interpretations
• Measures of central tendency (mean, median, mode, range)
• Measures of spread (variance, standard
variation)
• Effects of constant changes to data • Linear correlation of bivariate data • Scatter diagrams (regression, prediction
and contextual interpretation
• Concepts of trials and outcomes • Probability of an event
• Use of Venn diagrams, tree diagrams, and
table outcomes
• Combined events, mutually exclusive events
• Conditional probability
• Probabilities with and without
replacement
• Concept of discrete random variables and
their probability distributions
• Expected value (mean) • Binomial distribution
• Normal distributions and curves • Standardization of normal variables
Calculus
• Limits and convergence
• Derivatives and its interpretation as a
gradient function and as rate of change
• Tangents, normal, and their equations • Local minimum and maximum points • Points of inflection
• Graphical behavior of functions
• Optimization
• Indefinite and definite integration • Areas underneath and between curves • Volumes of revolution
• Kinematic problems involving
