IB Math Standard Level
Instructor: Salah E. Altaji
Text
Book: Precalculus Sixth
Edition By Larson and Hostetler
Course
Goal: To enable the candidate to develop a
sound basis of mathematical skills and knowledge that will aid in the further study of
subjects with math applications.
Course
Description: IB
math standard level is a two-year course that requires a solid background of Algebra
II and Trigonometry skills. Included in
the course are : Numerical
computations, Algebra
and Coordinate Geometry, Trigonometry, Functions, Calculus, Vectors,
Probability and Statistics.
Materials
Needed:
- Geometry
Set (Ruler, Protractor, Compass, Triangles)
- Pencil
and Eraser
- Folder
with lined Paper/mm graph paper
- Graphic
Display Calculator (Casio 9850/9950 series)
Assessment:
Test #1: .................................
15% Graded HW #1:
………………5% Project:………10%
Test #2....................................20% Graded HW #2:………………10%
Test #3................................
...25% Graded HW #3:………………15%
Teacher
Expectations:-
Come to class on time and bring all necessary materials
- Pay
attention in class and ask questions when in doubt
- Review
previous lessons daily, weekly and monthly
- Return
the homework on time and present it neatly
- Keep all
notes during the two-year course of study
__________________________________________________________________________________
Part I:
1) Algebra
1.1 Sequences and series
1.2 Exponents and Logarithms
1.3
Binomial Theorem
2) Functions and Equations
2.1 Domain, Range, composition, Inverse
and Domain Restrictions of functions
2.2 Graphing Skills (Use of graphic
calculators): horizontal/vertical
asymptotes, max/min
2.3 Transformation of Graphs
(Translations, stretches and reflection(in x/y axis,
graph
of inverse functions)
2.4 The reciprocal function 1/x
2.5 Quadratic Function, its graph,
vertex (h,k), y and
x-intercept
2.6 The quadratic formula and use of discriminant
2.7 The exponential and the
logarithmic functions, their graphs ; solution of ax
= b
2.8
The functions ex and ln x and their
applications in growth and decay
3) Circular Functions and Trigonometry
3.1 The circle: Radian measure; arc
length and area of sector
3.2 Definition of sin x, cos x and tan x and their graphs
The
Pythagorean Identity
3.3 The Double Angle formula for sin 2x
and Cos 2x
3.4 Circular Functions, and their
inverse functions
Composite
functions in the form F(x) = a Sin b (x + c) + d
3.5 Solution of linear and quadratic
trigonometric functions and their graphs
3.6 Solution of triangles using the
Sine/Cosine rules
Finding
the area of a triangle
4) Matrices
4.1
Definition of Matrix in
terms of rows/columns and order
4.2
Basic operation on
Matrices (+/-/x, etc.), identity and Zero Matrix
4.3
Determinant of a
square matrix (2x2 and 3x3), conditions for inverse matrices
4.4
Solving systems of
linear equations using matrices (Max. 3 unknowns)
5) Vector Geometry
5.1
Vectors as
displacements in the plane and in 3 dimensions
components of a
vector (Column representation)
multiplication of a
vector by a scalar
Position Vectors
Magnitude or length of a vector
Sum and
difference of two vectors
Zero Vector and unit vector
5.2
Scalar product of two
vectors
5.3
Perpendicular and
Parallel vectors
Angle between two vectors
Parametric equation of a line and
the angle between two lines
5.4 Common point of two lines;
parallel lines, coincident lines
6) Statistics and Probability
6.1 Population and Sample, Discrete and
continuous data
Frequency tables
6.2 Histograms and mid-interval values
6.3 Measures of Central Tendency (Mean,
mode and Median), variance and standard
deviation, range and IQR
6.4 Cumulative frequency graphs, median
of CFG, quartiles, percentiles
6.5 Trial, outcomes, sample space and
the event
Probability of an event and complementary events
6.6 Probability of combined events, mutually
exclusive events
6.7 Conditional probability and
independent events
6.8 Use of Venn diagrams and
tree/tables to solve problems
6.9 Discrete random variables and their
probability distributions, expected
value (mean for discrete data)
6.10
Binomial distribution
and its mean
6.11 Normal
distribution, its properties and standardization of normal variables
7 ) Calculus
-Limit and Convergence, graphical
representation of convergence
-Derivative of Xn, sin x, cos x, ex and ln x
-The
Chain rule
-Applications of First derivative in Max/Min, velocity, acceleration,
tangents, optimization problems
-Indefinite integration of Xn, Cos x, Sin x, ex
-Application to acceleration and velocity
-Antiderivatives with a boundary condition to determine the
constant term
-Definite integrals
-Areas under the curve
-Volumes of revolution
-Derivatives using the product and quotient rules
-The
second derivative, the significance of the second derivative
-Derivatives
of ax, loga x, tan x
-Graph behavior of functions for large | x |
-Vertical and Horizontal asymptotes
-Points of inflection
-Integration by substitution
External
Assessment:
At the end
of the two year program, students who wish to earn IB certificates must sit for
examinations which are externally assessed by the IB Examinations Office as
follows:
Paper 1: A 1 and half hour exam
that counts 40% of the total grade. The exam includes 15 compulsory short-response
questions on all topics
Paper 2: A 1 and a half hour exam that counts as 40%
of the total grade. The exam includes two
sections.
Award
of Marks For Paper 1:Each question will be worth 6 marks for a total of 90
marks. Full credit will be given to
correct answers irrespective of the demonstration of work. Some marks may be given if the final answer
is wrong but the method is correct.
Award
of Marks For Paper 2:Paper 2 is worth 90 marks with questions that may not be worth the
same number of marks.
Marks may be awarded for the following:
Method:
Display of knowledge, ability to apply learned
concepts and skills in analyzing and solving problems.
Accuracy: Demonstrate a high
degree of accuracy in carrying out computational skills and the presentation of
numerical values
Follow
through: If a question is made up of different parts
and an incorrect answer found in the
early part of the
question is used in another part of the same question, then some marks may be
awarded in the later part despite of the incorrect answer. Candidates are not penalized twice.
Reasoning: Clarity in
explanations or logical arguments
Internal Assessment:(Portfolio)-20%
During the
course of two years, students will apply learned math skills to real-life
applications. It is a requirement for
each candidate to complete 2 assignments in the following areas:
a) Mathematical
Investigation: "
Inquiry into a particular area of mathematics leading to a
general result which was previously unknown
to the
candidate."
b) Mathematical Modeling: " The solution
of real-world problem that requires the application of relatively elementary
mathematical modeling skills."
The
candidates will be assessed according to the following criteria:
A: Use of notation and terminology
B:
Communication
C:
Mathematical Process-developing a model
D:
Results -interpretation
E: Use
of technology
F:
Quality of work
Bimester I Outline
Topic 1:
Functions and their graphs
Lessons 1.1-1.9
Topic 2:
Polynomial and Rational functions
Lessons 2.1-2.7
Topic 3:
Exponential and logarithmic Functions
Lessons 3.1-3.5
Topic 4:
Trigonometry
Lessons 4.1-4.8
Topic 5:
Analytic Trigonometry
Lessons 5.1-5.5
Bimester III Outline
Topic 6: Additional Topics in Trigonometry
Lessons 6.1-6.5
Topic 7:
Systems of equations and Inequalities
Lessons 7.1-7.5
Topic 8:
Matrices and determinants
Lessons 8.1-8.5
Bimester IV Outline
Topic 9:
Sequences and Series and Probability
Lessons 9.1-9.7
Topic 10:
Statistics:
Handouts
-
Histograms and Frequency Distribution
-
Percentiles, Quartiles, Box-and-Whisker Plots
- Measures
of Central Tendency
- Measures
of Variability
-Expected
value for discrete data
- Binomial
distributions and their mean
- Normal
distribution, its properties and standardization of normal variables
-
Cumulative Review
Homeworks:
Homeworks
are assigned daily to insure understanding of learned math skills. Each missing homework
without justification will receive no credit.
In case of absences, it is the responsibility of the student to make up
all missing work. Homeworks
should be presented neatly and should demonstrate all work required for the
solution of problems. It should reflect individual effort. Students will complete approximately 3
cumulative graded assignments.
Projects:
Students are encouraged to
participate in math projects to apply learned math skills to real-life situations. All projects must be typed. Credit will be given for level of
research,
complexity, comprehension, planning and data collection, analysis and
implementation, evaluation.
Participation:
Daily in-school
exercises (written and oral)
are assigned as additional practice. Some exercises may be performed individually while others
may be performed in groups of 3 to 4 students.
All students are expected to be on task and held accountable during
classroom exercises.
Examinations: All examinations
are cumulative until the end of the semester.
Tests are announced a few days prior to testing date allowing for adequate
preparations. Students are evaluated on:
a) Their
understanding of problems and the kind of mathematics used
b) The correct use
of mathematics
c) The use of problem solving strategies and
good reasoning
d) Communication of mathematical ideas
Cheating: Any form of
cheating will not be tolerated in my classroom.
Any work demonstrating evidence of cheating will receive zero credit
plus severe disciplinary actions. I
expect
all students to follow the guidelines set in the school honor code and
technology code.
Absences: It is the responsibility of every
student upon missing any school days to justify the absences with the school's
secretary. Any missing exams or work due
to an
unjustified
absence will receive zero credit. If
absences are anticipated, it is the responsibility of the student to find out
about any missing
assignments or exams.
