Southside High School
IB Math Studies
Mr. Howard

Texts: Mathematics for the International Student: Studies SL by Haese & Harris Publications,
Other Texts as appropriate

Pre-requisites: Algebra I, Honors Algebra II, Honors Geometry, Pre-Calculus
Units:1

Topics to be covered in IB Math Studies as recommended by the IB Curricula Standards

Topic 1—Introduction to the graphic display calculator 3 hrs
Topic 2—Number and algebra 14 hrs
Topic 3—Sets, logic and probability 20 hrs
Topic 4—Functions 24 hrs
Topic 5—Geometry and trigonometry 20 hrs
Topic 6—Statistics 24 hrs
Topic 7—Introductory differential calculus 15 hrs
Topic 8—Financial mathematics 10 hrs
Note: More Detailed Standards of the above Topics may be found below.

Unit Grading system:
Major Grades ------------------------- 40%
Classwork/Homework --------------- 50%
Problem of the Day/Journal -------- 10%
(The Project will count as two Unit Grades in the Second Quarter)
Each Quarterly Grade will consist of the straight average of Unit grades during the quarter. There will be six to eight unit grades each quarter.
Semester Exam ----------------------- 20% of first Semester Grade

PROJECT:
An individual piece of work completed during the course involving the collection and/or generation of data, and the analysis and evaluation of that data. Projects may take the form of mathematical modeling, investigations, applications, statistical surveys, etc.
FAILURE TO DO A MATH STUDIES PROJECT WILL RESULT IN A FORFEITURE OF THE IB DIPLOMA.

Project Due Dates:
Topic 9/29/06
Raw Data 11/13/06
Rough Draft 12/8/06
Completed Project 12/20/06
Returned for Correction 1/12/07
Corrected Papers Due 2/16/07

Cheating: Any student found guilty of cheating will be given a zero on the work. The parents will be notified by the teacher. Cheating includes giving help on a test or assignment, as well as receiving help in any form. Plagiarism is a form of cheating and includes information obtained through computer sources.

Daily Materials:
You are expected to come to class prepared to do work. Doing work for another class is unacceptable. You will need your textbook, pens or pencils, paper, a graphing calculator, a ruler, graph paper, any handouts, a folder, and a notebook with plenty of loose-leaf paper to keep your materials organized.
Class Participation:
You are expected to participate in class on a daily basis by taking part in questioning, activities, and classwork. Comments that are constructive and relevant are always welcome if contributed at an appropriate time and in a respectful manner. Listening is an important part of participation as is bringing all required materials.

Attendance:
1. It is extremely important that you attend class everyday! Missed explanations are almost impossible to make up. Attendance will be taken during each class. The school attendance and tardy policy will be followed.
2. Assignments may be made up if absence is excused and admission slip is shown within two days of absence. An unexcused absence will result in a zero on each missed assignment.
3. Any student exceeding 10 absences may be denied course credit.

Class Standards:
1. Respect one another.
2. Be prepared for class. Be in seat when bell rings and bring all materials to class and use them accordingly.
3. Stay on task.
4. Obey all rules in the student Handbook.

Rewards:
1. Positive calls/notes home
2. Self-fulfillment and self-confidence
3. Content mastery and good grades
4. Smiles J

Consequences:
1st Offense: Warning
2nd Offense: Conference with teacher, parent contact
3rd Offense: Referral to office, parent contact
**** Severe disruptions will result in an immediate office referral ****

If you need extra help, do not hesitate to ask! I will be happy to arrange a time to help you. I am available after school on most Monday, Tuesday, and Thursday afternoons and during lunch on most days. If problems occur, do not wait to seek help.
Thank You,
Mr. Howard

Syllabus content
Topic 1—Introduction to the graphic display calculator 3 hrs
Aims
The aim of this section is to introduce the numerical, graphical and listing facilities of the graphic display calculator (GDC).
Details
© International Baccalaureate Organization 2004 12
Content Amplifications/exclusions Teaching notes
1.1 Arithmetic calculations, use of the GDC to
graph a variety of functions.
Appropriate choice of “window”; use of “zoom”
and “trace” (or equivalent) to locate points to a
given accuracy.
Explanations of commonly used buttons.
Entering data in lists.
Extensive use of the GDC is expected
throughout the course. A time allowance has
been made in individual sections to allow for
this extensive use.
See teacher support material.
Topic 2—Number and algebra 14 hrs
Aims
The aim of this section is to introduce students to some basic elements and concepts of mathematics. A clear understanding of these is essential for further
work in the course.
Details
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Content Amplifications/exclusions Teaching notes
2.1 The sets of natural numbers, ; integers, ;
rational numbers, and real numbers,
Not required: proof of irrationality, for example,
of 2 .
Approximation: decimal places; significant
figures. Percentage errors.
Included: an awareness of the errors that can
result from premature rounding.
2.2
Estimation. Included: the ability to recognize whether the
results of calculations are reasonable, including
reasonable values of, for example, lengths,
angles and areas.
For example, lengths cannot be negative.
2.3 Expressing numbers in the form 10k^a × where
1 10and a k ≤ < ∈ .
Operations with numbers expressed in the form
10k a × where 1 10and a k ≤ < ∈ .
Awareness and use of scientific mode on the
GDC.
All answers should be written in the form
10k a × where 10 a k ≤ < ∈ . It is not
acceptable to write down calculator displays in
an examination.
Work should include examples on very large
and very small numbers in scientific, economic
and other applications.
2.4 SI (Système International) and other basic units of
measurement: for example, gram (g), metre (m),
second (s), litre (l), metre per second (m s–1),
Celsius and Fahrenheit scales.
Included: conversion between different units. Link with the form of the notation in 2.3, for
example, 6 5km 5 10 mm.
Topic 2—Number and algebra (continued)
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Content Amplifications/exclusions Teaching notes
Arithmetic sequences and series, and their
applications.
Included: simple interest as an application.
Link with simple interest 8.2.
2.5
Use of the formulae for the nth term and the sum
of the first n terms. The formulae can be verified using numerical
examples.
Students may use a GDC for calculations, but
they will be expected to identify clearly the first
term and the common difference.
Geometric sequences and series, and their
applications.
Included: compound interest as an application.
Link with compound interest 8.3.
2.6
Use of the formulae for the nth term and the sum
of n terms.
Not required: use of logarithms to find n, given
the sum of a series; sums to infinity.
The formulae can be verified using numerical
examples.
Students may use a GDC for calculations, but
they will be expected to identify clearly the first
term and the common ratio.
Solutions of pairs of linear equations in two
variables by use of a GDC.
Included: revision of analytical methods. 2.7
Solutions of quadratic equations: by factorizing;
by use of a GDC.
Optional: knowledge of quadratic formula.
Standard terminology, such as zeros or roots and
factors should be taught.
Link with quadratic functions in 4.3.
Topic 3—Sets, logic and probability 20 hrs
Aims
The aims of this section are to enable students to understand the concept of a set and to use appropriate notation, to enable them to translate between verbal
and symbolic statements, to introduce the principles of logic to analyse these statements, and to enable students to analyse random events.
Details
© International Baccalaureate Organization 2004
Content Amplifications/exclusions Teaching notes
3.1 Basic concepts of set theory: subsets; intersection;
union; complement.
Discuss notation for set relations and sets of prime numbers, multiples
and factors can be used as examples.
3.2 Venn diagrams and simple applications. Included: diagrams with up to three subsets of
the universal set.
Not required: knowledge of de Morgan’s laws.
3.3 Sample space: event, A; complementary event,
A′ .
Alternative notations for the complement of a
set are recognized.
3.4 Basic concepts of symbolic logic: definition of a
proposition; symbolic notation of propositions.
3.5 Compound statements: implication, ⇒ ;
equivalence, ⇔; negation, ¬; conjunction, ∧ ;
disjunction, ∨ ; exclusive disjunction.
Translation between verbal statements, symbolic
form and Venn diagrams.
Knowledge and use of the “exclusive disjunction”
and the distinction between it and “disjunction”.
Included: an emphasis on analogies between
sets and logic.
Topic 3—Sets, logic and probability (continued)
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Content Amplifications/exclusions Teaching notes
3.6 Truth tables: the use of truth tables to provide
proofs for the properties of connectives;
concepts of logical contradiction and tautology.
A maximum of three propositions will be used
in truth tables.
Truth tables can be used to illustrate the
associative and distributive properties of
connectives, and for variations of implication
and equivalence statements.
3.7 Definition of implication: converse; inverse;
contrapositive.
Logical equivalence.
3.8 Equally likely events.
Probability of an event A.
Probability of a complementary event,
In general, probability should be introduced and
taught in a practical way using coins, dice,
playing cards and other examples to demonstrate
random behaviour.
3.9 Venn diagrams; tree diagrams; tables of
outcomes. Solution of problems using “with
replacement” and “without replacement”.
Examples: cards, dice and other simple cases of
random selection.
3.10 Laws of probability.
Combined events:
Mutually exclusive events:
Independent events:
Conditional
Students should be encouraged to use the most
appropriate method in solving individual
questions.
In examinations: no questions involving playing
cards will be set.
Experiments using, for example, coins, dice and
packs of cards can enhance understanding of
experimental relative frequency versus
theoretical probability.
Teachers should emphasize that some problems
of probability might be more easily solved with
the aid of a Venn diagram or tree diagram.
Topic 4—Functions 24 hrs
Aims
The aim of this section is to develop understanding of some of the functions that can be applied to practical situations. Extensive use of a GDC is to be
encouraged in this section.
Details
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Content Amplifications/exclusions Teaching notes
4.1 Concept of a function as a mapping.
Domain and range. Mapping diagrams.
Examples should include functions defined on
the sets and as domains.
In the notation, the letters f and x can each be
replaced by any other letter.
4.2 Linear functions and their graphs.
Teachers should illustrate with examples from
real-world problems, such as temperature
conversion graphs and car hire charges.
Link with equation of a line in 5.2.
4.3 The graph of the quadratic function:
Properties of symmetry; vertex; intercepts.
Axis of symmetry,
Properties should be illustrated with a GDC.
The form of the equation of the axis of symmetry
may initially be found by investigation.
Link with the quadratic equations in 2.7.
4.4 The exponential expression:
Graphs and properties of exponential functions.
Growth and decay; basic concepts of asymptotic
behaviour.
In examinations: students will be expected to
use graphical methods, including GDCs, to
solve problems.
Real-world examples, such as population growth,
radioactive decay, and the cooling of a liquid can
be used.
Link with compound interest in 8.3.
Topic 4—Functions (continued)
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Content Amplifications/exclusions Teaching notes
4.5 Graphs and properties of the sine and cosine functions:
In examinations: students will be expected to
use graphical methods to solve problems.
GDCs should be in degree mode.
Amplitude and period. Examples of periodic phenomena may include,
for example, tides, length of day and rotating
wheels.
4.6 Accurate graph drawing. Students are expected to draw accurate graphs
of all the previous functions.
4.7 Use of a GDC to sketch and analyse some
simple, unfamiliar functions and higher polynomials.
Students need to recognize and identify
horizontal and vertical asymptotes only.
4.8 Use of a GDC to solve equations involving
simple combinations of some simple, unfamiliar
functions.
Topic 5—Geometry and trigonometry 20 hrs
Aims
The aims of this section are to develop the ability to draw clear diagrams, to represent information given in two dimensions, and to develop the ability to apply
geometric and trigonometric techniques to problem solving.
Details
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Content Amplifications/exclusions Teaching notes
5.1 Coordinates in two dimensions: points; lines;
midpoints.
Distances between points.
5.2 Equation of a line in two dimensions: Gradient; intercepts.
Points of intersection of lines; parallel lines;
perpendicular lines.
Included: for lines with gradients for parallel lines, for
perpendicular lines, Link with linear functions in 4.2.
5.3 Right-angled trigonometry. In examinations: problems incorporating
Pythagoras’ theorem will be set.
Use of the ratios of sine, cosine and tangent. Use of the inverse trigonometric functions on a
GDC is expected, but a detailed understanding
of the functions themselves is not expected.
Topic 5—Geometry and trigonometry (continued)
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Content Amplifications/exclusions Teaching notes
The sine rule:
Not required: radian measure. In all areas of this section, students should be
encouraged to draw sufficient, well-labelled
diagrams to support their solutions.
5.4
The cosine rule
Area of a triangle:
Construction of labelled diagrams from verbal
statements.
In examinations: students will not be asked to
derive the sine and cosine rules.
The ambiguous case could be taught, but will
not be examined.
Geometry of three-dimensional shapes: cuboid;
prism; pyramid; cylinder; sphere; hemisphere;
cone.
Included: surface area and volume of these
shapes.
5.5
Lengths of lines joining vertices with vertices,
vertices with midpoints and midpoints with
midpoints; sizes of angles between two lines
and between lines and planes.
Included: only right prisms and square-based
right pyramids.
Topic 6—Statistics 24 hrs
Aims
The aims of this section are to introduce concepts that will prove useful in further studies of inferential statistics, and to develop techniques to describe and
analyse sets of data
Details
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Content Amplifications/exclusions Teaching notes
6.1 Classification of data as discrete or continuous. Student, school and/or community data can be
used.
6.2 Simple discrete data: frequency tables;
frequency polygons.
6.3 Grouped discrete or continuous data: frequency
tables; mid-interval values; upper and lower
boundaries.
Frequency histograms.
Stem and leaf diagrams (stem plots).
A frequency histogram uses equal class
intervals.
6.4 Cumulative frequency tables for grouped
discrete data and for grouped continuous data;
cumulative frequency curves.
Box and whisker plots (box plots).
Percentiles; quartiles.
6.5 Measures of central tendency.
For simple discrete data: mean; median; mode.
For grouped discrete and continuous data:
approximate mean; modal group; 50th percentile.
Students should use mid-interval values to
estimate the mean of group data. They may link
the median to the 50th percentile and to
cumulative diagrams.
Students should be familiar with sigma notation
( ∑ ).
Topic 6—Statistics (continued)
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Content Amplifications/exclusions Teaching notes
6.6 Measures of dispersion: range; interquartile
range; standard deviation.
Included: an awareness of the concept of
dispersion and an understanding of the
significance of the numerical value of the
standard deviation, n s . Students are expected to
use a GDC to calculate standard deviations.
Students should understand the concept of
population and sample. They should also be
aware that the population mean,
µ, and the
population standard deviation, σ, are generally
unknown, and that the sample mean, x , and the
sample standard deviation, n s , serve only as
estimates of these quantities.
Initially, the calculation of standard deviation
from first principles should be demonstrated.
Students should be aware that the IBO notation
may differ from the notation on their GDCs.
Scatter diagrams; line of best fit, by eye, passing
through the mean point.
Bivariate data: the concept of correlation.
6.7
Pearson’s product–moment correlation coefficient:
Interpretation of positive, zero and negative
correlations.
A GDC can be used to calculate r when raw
data is given.
Topic 6—Statistics (continued)
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Content Amplifications/exclusions Teaching notes
6.8 The regression line for y on x: Understanding of outliers is expected. y is the dependent variable.
Use of the regression line for prediction
purposes.
Students should be aware that the regression
line is less reliable when extended far beyond
the region of the data. A GDC can be used to
calculate the equation of the regression line
when raw data is given.
6.9 The χ-square
test for independence: formulation of
null and alternative hypotheses; significance
levels; contingency tables; expected
frequencies;
degrees of freedom; use
of tables for critical values; p-values.
Included: h by k contingency tables
In examinations: questions on various commonly
used significance levels (1%, 5%, 10%) will be
set.
The GDC can be used to calculate the χ-square
value
when raw data is given.
p-values will be used to deal with both the upper
and lower one-tailed tests, but not with two-tailed
tests.
Topic 7–Introductory differential calculus 15 hrs
Aims
The aim of this section is to introduce the concept of the gradient of the graph of a function, which is fundamental to the study of differential calculus, so that
students can apply the concept of the derivative of a function to solving practical problems.
Details
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Content Amplifications/exclusions Teaching notes
7.1 Gradient of the line through two points, P and Q,
that lie on the graph of a function.
Behaviour of the gradient of the line through two
points, P and Q, on the graph of a function as Q
approaches P.
Tangent to a curve.
Not required: formal treatment of limits.
Included: solving problems involving a particular
function for given values of h and x.
The derivative as the gradient function;
In examinations: questions on differentiation
from first principles will not be set.
The concept of a limit should be introduced
using numerical and graphical investigations.
7.2 The derivative of functions of the polynomial form
Included: negative integer values for n.
7.3 Gradients of curves for given values of x.
Values of x where f (x) ′ is given.
Equation of the tangent at a given point.
Not required: equation of the normal.
Topic 7—Introductory differential calculus (continued)
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Content Amplifications/exclusions Teaching notes
7.4 Increasing and decreasing functions.
Values of x where the gradient of a curve is 0
7.5
Local maximum and minimum points. Included: the concept of a function changing
from increasing to decreasing and vice versa as a
test for local maxima and minima.
Awareness of points of inflexion with zero
gradient is to be encouraged, but will not be
examined.
Topic 8–Financial mathematics 10 hr
Aims
The aim of this section is to build a firm understanding of the concepts underlying certain financial transactions. Students can use any correct method (for
example, iterative processes and finding successive approximations) that is valid for obtaining a solution to a problem in this section.
Details
© International Baccalaureate Organization 2004 26
Content Amplifications/exclusions Teaching notes
8.1 Currency conversions. Included: currency transactions involving
commission.
8.2
Simple interest: use of the formula
Crn =I
where C = capital, r = % rate, n = number of
time periods, I = interest.
In examinations: questions that ask students to
derive the formula will not be set.
Link with arithmetic sequences in 2.5.
8.3 Compound interest:
Depreciation.
In examinations: questions that ask students to
derive the formula will not be set.
Included: the use of iterative methods, successive
approximation methods or a GDC to find n (the
number of time periods).
Not required: use of logarithms.
Compound interest can be calculated yearly,
half-yearly, quarterly, monthly or daily.
Link with geometric sequences 2.6 and
exponential functions 4.4.
8.4 Construction and use of tables: loan and
repayment schemes; investment and saving
schemes; inflation.