IB MATH SL

Introduction & Summer Assignment 2015

Name _____________________________________________ We are excited to welcome you as the newest member of Hauppauge’s IB Mathematics SL Program. The IB Diploma Programme Mathematics Standard Level Course is for students with knowledge of basic mathematical concepts who are able to apply simple mathematical techniques correctly. The course will provide you with a sound mathematical background to prepare for future studies in subjects such as chemistry, economics, psychology and business administration. You will be introduced to important mathematical concepts through the development of mathematical techniques in a way that emphasizes subject comprehension rather than mathematical rigor.  You will, where possible, apply the acquired mathematical knowledge to solve realistic problems.  Your success in the Mathematics Standard Level Course is measured by combining your grades on an external and internal assessment. The internal assessment is comprised of a portfolio consisting of a mathematical exploration to be chosen, researched and reported by you.  

Upon your arrival in September, we ask that you have the following items with you:  

1. An empty binder. 

2. Pens (blue or black).  Pencils are not permitted on the IB exam and therefore will not be used. 

3. A TI‐84+ graphing calculator which has been reset for use.  Arrangements will be made in 

September for students who wish to loan this calculator from our department. 

4.   Completed Summer Assignment‐ (see directions on the next page) 

 

 Any mathematical concepts which will need to be reviewed will take place upon your arrival to class.  If you should have any questions, please do not hesitate to contact us at   concannond@hauppauge.k12.ny.us  maere@hauppauge.k12.ny.us  We look forward to our upcoming year.  Enjoy your summer. 

  

The Summer Assignment consists of the following: Assignment 1: Memorize the attached notation and command terms list. Since IB is an

international course some key terms that we use are referred to differently and students must be comfortable referring to terms using various words or symbols.

Assignment 2: Read over the grading criteria for the Mathematical Exploration and grade the sample exploration.

Assignment 3: Your submission of your Mathematical Exploration Synopsis. Assignment 4: Completed IB questions based on prior knowledge.                           

ASSIGNMENT #1          MEMORIZE NOTATION/COMMAND TERMS LIST  

NOTATION Number Sets 

Absolute Value  IB will refer to this as modulus 

Line Segments  Line segment,  , will be written as   

Angles  We write Angle A as  A  or  A .   

IB will use the following notation:   

Repeating Decimals      IB Notation 13  0. 3  0. 3 .123123123123  0. 123 0. 123

 

Slope  IB will refer to this a the gradient 

 

COMMAND TERMS Calculate  Obtain a numerical answer showing the relevant stages in the working 

Determine  Obtain the only possible answer 

Draw  Represent by means of a labeled, accurate diagram or graph, using a pencil.  A ruler should be used for straight lines.  Diagrams should be drawn to scale. Graphs should have points correctly plotted and joined in a straight line or curve.  

Find  Obtain an answer, showing relevant stages in that working. 

Hence  Use the proceeding work to obtain the required result 

Hence or otherwise  It is suggested that the preceding work is used, but other methods could also receive credit.  

Show that  Obtain the required result (possible using information given) without the formalily of proof.  “Show that” questions do not generally require the use of a calculator.  

Sketch  Represent by means of a diagram or graph (labelled as appropriate)  The sketch should give a general idea of the required shape or relationship, and should include relevant features.  

Solve  Obtain the answer(s) using algebraic and/or numerical and/or graphical methods. 

Write down  Obtain the answer(s), usually by extracting information.  Little or no calculation is required.  Working does not need to be shown.  

Internal Assessment AKA “The Exploration”  20% of the IB grade which you will earn for this course will be the result of your submitted work for a mathematical exploration. This exploration will be graded locally by your teacher and moderated externally by International Baccalaureate personnel. International Baccalaureate has said that the purpose of the IA is to “enable students to demonstrate the application of their skills and knowledge, and to pursue their personal interests, without the time limitations and other constraints that are associated with written examinations.” Yourultimatetaskistoselectatopicwithinmathematics,toexplore,andtowriteapaperdemonstratingyourabilitytocommunicate,reflect,bepersonallyengaged,usepropermathematicsandmathematicpresentation. The goal is to pick a topic for the IA now, and hand in the completed final draft in January. The details:

Length: 6-12 pages (including graphs, diagrams, charts, etc.) Detailed bibliography to be included with direct quotes acknowledged In order to complete this assignment, there will be benchmarks to complete before the rough draft is written. These dates are subject to change.

Process  Date Due 

Choose a topic/Synopsis  Friday 9/11/2015 

Introduction o Outline the aim and purpose in a clear and succinct manner. o Justify the exploration choice o Briefly discuss the area of mathematics that will be used.  o Evidence of some research. 

Friday 10/9/2015 

Body/Mathematical Exploration o Describe the method, followed by an investigation o Record your results (tables, lists etc) o Analyze the results (graphs, diagrams, calculations etc) and form 

conjectures. 

Friday 11/6/2015 

Submit first draft hard copy and to turnitin.com which includes:   

Conclusion and Bibliography o Summarize your findings in response to your aim. Restate any rules, 

conjectures or models that you found. o Comment on any limitations to your approach, or to your findings.  o Comment on possible extensions and real life connections. Relate it to 

your personal knowledge and to your previous knowledge.  o Including a reflection on what you have learned and what you have taken 

away from this experience will reflect personal engagement. 

Friday 11/20/2015 

Teacher to review & comment on draft 

Meet with teacher (in class) 12/14 ‐ 12/23 

Final writing 

Revise draft 

Submit to turnitin.com (where required) 

Friday 1/8/2016 

GRADING THE INTERNAL ASSESSMENT The internal assessment is graded out of 20 marks and then converted into a numerical grade from 1-7. There are 5 criteria in which the exploration is judged. Students should be familiar with the 5 criterion and aware of how they are marked within these categories. The 5 criteria are seen below. Please read each of the explanations carefully, noting what must be present within your exploration to receive full marks.

 

 

 

 

 

 

ASSIGNMENT #2          READ THE EXPLORATION AND COMPLETE THE SCORING RUBRIC Read the following Exploration Sample. As you read, keep in mind the 5 criteria that the paper will be judged on. At the end of the exploration there is a grading sheet. Please grade the exploration by assigning a value within each category and a final score out of 20 by adding the values for each category together. Also, give a brief explanation as to why you gave the score you did within each category making sure to explain why if you deducted points.

Name_______________________________ IB MATH SL SAMPLE SCORING RUBRIC

Give a numerical score and comment for each criteria. CRITERIA  SCORE  COMMENTS 

 

   

 

 

   

 

   

   

 

   

TOTAL SCORE:  

             /20 

Additional Comments:  

 

 

 

 

ASSIGNMENT #3          1 PAGE SYNOPSIS OF YOUR INTENDED EXPLORATION  MATHEMATICAL EXPLORATIONN SYNOPSIS

Your next assignment for this summer is to research a possible topic of interest and submit to me a one-page synopsis of your intended exploration. It is expected that you will briefly explain the topic that you have chosen as well as the mathematical exploration that you plan to undertake. To assist you in your efforts, please re-read the criteria in which you will be graded and use the suggested topic list on the next page from which you may choose something of interest (your topic does not need to appear on this list- this is merely provided to assist you). It cannot be stressed enough that this exploration is NOT intended to be a research paper. There is a significant difference between presenting a paper about quadratics and instead investigating and presenting quadratics in a way that may help you perfect your dive or improve your volleyball serve. Your topic of choice MUST be important to you in that you can apply the mathematics of the SL course to something that is relevant to YOUR life. In addition, it is importasnt to note that this exploration must be based in mathematics and your paper must explore mathematical content. It is important that you choose a topic in which you can clearly descirbe the mathematics you use. Also, make sure that the mathematics is commensurate with the level of the course.

One-page exploration synopsis due date: FRIDAY, SEPTEMBER 11, 2015 We would also ask that you save an electronic copy of all work done in connection with the mathematical exploration as we will need to upload all submissions to the Turn-It-In service. Account information will be provided upon your return.

SAMPLE PAPER TOPIS ALLIGNED WITH IB MATH CURRICULUM

Unit1:Functions Define functions graphically, algebraically, numerically and verbally Types of functions and defining domain & range Dilation and translation of functions and graphs Composition of Functions Inverse of a function Even/odd functions

The development of functions [Rene Descartes (France), Gottfried Wilhelm Leibniz (Germany) and Leonhard Euler (Switzerland).] Shifting supply and demand curves Kinematics Hardy-Weinberg equation The birth of complex numbers

Unit2:ExponentialFunctionsandLogarithms Shapes of functions Identifying functions graphically and numerically Properties of logarithms Logarithm equations Logarithm functions Logistic functions for restrained growth

Calculation of pH Banking (i.e. compound interest) Scientific models (i.e. growth and decay) Earthquakes (i.e. the Richter Scale) The history of logarithms and Napier’s rods Fermat’s belief for a formula for prime numbers and Euler’s proof that he was wrong The mathematics of music

Unit3:SequencesandSeries Definition of Sequences and Series Arithmetic, geometric and other sequences Series and partial sums Binomial theorem

Compound interest and population growth Fibonacci sequence Discovery of the golden ratio Koche’s snowflake (history and limits of areas and permiters) Sierpinski’s gadget Mendelbrot set Canter and his research with infinity Euler and the number e Perfect numbers How can fractals be used to measure coastlines? Chaos theory Julia Sets Graphical iterations Math and the Mona Lisa

Unit4:PeriodFunctionandRightTriangleTrig Measurement of rotation Sine and cosine function Values of sine, cosine, tangent, cotangent, secant, cosecant Inverse trigonometric functions

History of the derivation/calculation of pi History of the derivation of Pythagorean theorem Simple harmonic motion

Unit5:GraphingPeriodFunctions Cycle of sinusoidal graphs Finding equations by looking at graphs Graphs of tangent functions Radian measures of angles Sector, segments, areas and perimeters Circular functions Solving trig functions graphically and algebraically

Tides Turning of wheels Modeling rock formations

Unit6:Identities Pythagorean, Reciprocal and Quotient properties Identities and algebraic transformations of identities Double angle identity and Quadratic Trigonometric Equations

The witch of agnesi curve and its corresponding derivation

Unit7:Non‐rightangletriangletrig Oblique triangles Law of sine and cosine Area of triangles

Aircraft heading to counter wind Land surveying

Unit8:DescriptiveStatistics Displaying data Measure of center Measure of spread Percentiles Variance and standard deviation

Psychology studies Advertising/misleading statistics Biology studies

Unit9/10:Probability Experimental probabilities Sample spaces Independent and dependent variables Multiplication rule Conditional probabilities Binomial probabilities Discrete and continuous random variables Expected values

Experiments Medical testing (i.e. false positives) Gambling Measuring risk Monte Carlo simulations Pascals’ Triangle DeMorgan’s laws Simpson’s Paradox How are insurance rates computed?

Unit11:NormalDistribution Normal curve Empirical Rule Z-scores Probabilities of normal distribution Inverse probability

Feeding farm animals, amounts determined based on weights Business decisions made based on a normal curve The history, development and significance of the t-distribution Genetics and cancer risk assessment

Unit12:RegressionandLinearfit Least squares line Residuals Correlation coefficient Non-linear regression

Estimations for businesses Economics Psychology Measuring success on standardized tests in education The history and development of the least squares regression line

ASSIGNMENT #4          SAMPLE IB MATHEMATICS SL QUESTIONS Name_____________________________________ IB MATH SL SAMPLE QUESTIONS 1. [Maximum mark: 6 ]

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3. [Maximum mark: 5 ]

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4. [Maximum mark: 6 ]

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5. [Maximum mark: 7 ]

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6. [Maximum mark: 9 ]

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