Calculus
Curriculum 2002-2003
American School of Alexandria, Egypt
GRADE LEVEL: Grade 12 students
OVERVIEW: Calculus is rigorous course that is intended to be a college preparatory class designed for students planning to
enter math and science related majors. The course includes a review of the crucial PreCalculus skills plus additional topics
such as limits, derivative and integrals. At this time it is offered as a non-AP course.
PREREQUISITES: Passing grade in PreCalculus
TEXT: Holt Calculus with Analytic Geometry- 1994
OTHER RESOURCES: Resources that accompany the text book: Solution Manual (no teacher edition), Instructional Overhead
Transparencies, Chapter Test Generator
SPECIAL INSTRUCTIONAL PRACTICES:
This is an optional course. It is not required for graduation. Students in the class are generally heading towards
math/science university majors, or are good students who want a strong transcript.
Many students applying to Egyptian Universities are required to take 2 SAT II exams, and many of the students taking
Calculus understandably opt to take one of them in Math IC or Math IIC. I recommend getting a copy of an
SAT II Math book as a reference. There are topics on the tests that are stressed but are not necessarily
stressed in Calculus… statistics in particular. I only had one student in Calculus last year and she did not take
the test, so I do not know that much about it. There is one SAT II book in the library that gives the basic
information, but it only has general information and only one practice test.
This class is generally very very small. The first year it was offered we had two students and the second year we had
one student.
In the 2002-2003 school year chapters 1-5 or 6 were covered.
EVALUATION OF COURSE, GRADING SCALE: Flexible, generated by teacher.
Quarter Grade Semester Grade Yearly Grade
15% Homework 40% 1st Quarter 50% 1st Semester
45% Tests/Quizzes 40% 2nd Quarter 50% 2nd Semester
30% Citizenship 20% Final Exam
10% Presentations/Projects
LOCALLY AVAILABLE RESOURCES: None that we have found.
STANDARD 1: Elementary Functions The student will analyze the rate of change of function
The student will understand elementary functions and with respect to change in its independent variable.
their inverses.
2.1 Demonstrate his/her understanding of the definition
1.1 Understand limits and continuity in functions of a derivative
1.1.1 find a the indicated limit of an expression 2.1.1 identify the correct definition of the derivative
1.1.2 find a left- or right-handed limit at a point of as the limiting value of the secant line slope in a
discontinuity in a function function or graph of functions
1.1.3 find limits at infinity and infinite limits in a 2.1.2 find the slope of the tangent line at x = 2, for a
function function
1.1.4 determine whether a function is continuous or 2.1.3* find the equation of the line tangent to the
discontinuous function f (x) at x = a
2.1.4* find the equation of a normal tangent
2.2 Find the derivative of various types of functions
STANDARD 2: Differential Calculus 2.2.1* analyze statements that explain what must be
true of a function for it to be differentiable
2.2.2* differentiate a polynomial function
2.2.3* differentiate a trigonometric function (e.g., sin,
cos and tan).
2.2.4* differentiate an exponential or a logarithmic 3.4.2 determine the area of the region over the
function interval [a,b] having f (x) as an upper bound
2.2.5* differentiate a composite function and g(x) as a lower bound
2.2.6* differentiate a function which is the sum, 3.4.3 determine the volume of the solid obtained by
product and/or quotient of several functions revolving a bound region, defined by f (x) over
2.2.7* find the derivative of y with respect to x of a the interval [a,b] about the x-axis or y-axis
function written in the form f (x,y) which gives
the relation between two given variables
2.3 Use the derivative to analyze the graph of functions
2.3.1* determine the first derivative of a given
function or a *given graph
2.3.2* find the interval over which a function is
increasing or decreasing
2.3.3* finds the interval over which a function is
concave upward or downward
2.3.4* identify the points of inflection of a function
2.3.5* connect f' and f" with the graph of f
2.3.6 compute a relative and/or an absolute maximum
or minimum given an equation and an interval
2.3.7 determine the vertical and/or horizontal
asymptotes of a function
2.4 Solve problems which require the use of a derivative
2.4.1 find the average rate of change of a given
function over an interval
2.4.2 find the instantaneous rate of change of a
function at a given point (e.g., velocity,
acceleration and marginal cost
2.4.3 solve a maximum-minimum problem situation
2.4.4* solve related rate problems
STANDARD 3: Integral Calculus
The student will integrate expressions to solve
problems.
3.1 Take the antiderivative of a function
3.1.1* write the general solution of the first order
equation f (x), from f' (x)
3.1.2* find the specific solution of an equation
involving f' (x) given the value of a and f (a)
3.1.3* find specific velocity, distance and cost
functions given initial conditions
3.2 Master the techniques of integration
3.2.1* choose appropriate equivalencies for u and du
to be used in performing the integration of a
specific integral
3.3 Define and list the properties of the definite
integral
3.3.1* utilize properties of integrals to rewrite and
solve problems
3.3.2* evaluate the definite integral of f(x) from x = a
to x = b.
3.3.3* evaluates a definite integral using u and du
substitution
3.4 Apply definite integral to a variety of geometric and
physical problems
3.4.1 determine the average value of the function f
(x) in a given interval