IB Math
Standard Level Grade 12
Instructor: Salah
E. Altaji
Text Book: Calculus, by Larson, Hostetler and Edwards(
Sixth Edition)
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 & Eraser)
- Binder
with lined Paper
- Graphic
Display Calculator (Casio CFX-9850/9950 Series)
- mm graph paper
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
- Do the
homework and present it neatly
- Use class time wisely
- Keep all
notes during the two-year course of study
__________________________________________________________________________________
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
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 Matrixin terms of raws/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
Solvings 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
Perpendicular and Parallel vectors
Angle
between two vectors
5.3 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 Probabilityof
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 varibales
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,optimixation 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
Calculus:
a) Differentiation: Include first and second
derivatives
- Informal
treatment of limits and limit convergence
- Differentiation of sums,
products and quotients of:
- polynomials
- exponential functions
- rational functions
b) Applications of Differentiation:
- Graphs and properties of functions involving ex and ln x for x > 0
- Equations of the tangent and normal at a
point on the graph of any of the above functions.
-
Stationary values. Tests for
maxima, minima and points of inflection
- Simple problems involving maxima and minima
- Curve sketching for the functions listed in
section 5-a
-
Use of the formula f(x
+ h) = f(x) + hf ' (x) for small h
-
Velocity and accelaration
c) Integration
-
Integration of polynomials
-
Integration of exponential functions
-
Integration of rational functions
Calculus
Differentiation
, Integration and Applications :
- Finding
areas using integrals
- Finding
the area between two curves using integrals
- Finding
Volumes of revolution
- Solving kinematic problems involving displacement (s), Velocity (v)
and acceleration (a)
- Properties and graphs of Exponential functions
- Differentiation and integration of exponential functions
- Properties and graphs of Natural logarithmic functions
- Differentiation of natural logarithmic functions and Log Rule
-
Integration by
Substitution
- Differentiation of Trigonometric functions such as (sine,
cosine and tangent)
- Integration of Sine, cosine and tangent functions
During
these two bimesters, students will be involved in a cummulative review of the entire Math Methods program in
preparation of the IB
exams. This will involve a review of the
core contents of parts I through VI and the optional topic (Further Calculus)
Students
will complete worksheets and projects on the six parts.
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 assignements or exams.
