I Review all areas of mathematics. This includes algebra, trigonometry, and geometry necessary for calculus.(This should take approximately 4 weeks based on need.)Parts II through IV should take approximately two weeks each. The other parts are done based on time left).
II Identify and apply properties of elementary functions.
A) Identify the domain and range of a function.
B) Solve problems using the rules of sum, product, quotient and composition of two function.
C) Determine the inverse of functions.
D) Graph functions using symmetry and asymptotes.
E) Determine the zeros of a function.
III Demonstrate the ability to apply the concept of limits.
A) Solve problems using the laws of limits to constants, sums, products and quotients.
B) Determine if a function is continuous at a point in an open interval.
C) Use the concept of limit to define derivative of a function.
IV Demonstrate the ability to apply the rules of differentiation to find derivatives of elementary functions.
A) Find the derivative of an elementary function.
B) Find the derivative of an implicit function of x using inplicit differentiation.
C) Find the derivative of a sum, a product or a quotient.
D) find the derivative of a composite function(chain rule)
V Demonstrate the ability to apply the concepts of differentiation.
A) Use the derivative to find the slope of a curve at a point.
B) Find the equation of a tangent line at a point on the curve.
C) Find the equation of a normal line at a point on the curve.
D) Sketch curves using the concept of derivative.
E) Solve problems using velocity and acceleration of a particle moving along a line.
F) Solve exrema value problems.
G) Solve problems using average and instantaneous rates of change and related rates of change.
The following areas are covered in AP calculus and introduced in calculus.
VI Demonstrate the ability to find the general antiderivatives of elementary functions.
A) Find the antiderivative of constant functions
B) Find the antiderivative of polynomial functions.
C) Find the antiderivtive of powers of algebraic functions.
D) Find the antiderivative of sums and differences of algebraic function.
VII Demonstrate the ability to find the definite integral of elementary functions.
A) Find the definite integral of constant functions using the Fundamental Theorm of Calculus.
B) Find the definite integral of polynomial functions using the Fundamental Theorem of Calculus.
C) Find the definite integral of powers of algebraic functions using the Fundamental Theorm of Calculus.
D) Find the definite integral of sums and differences of algebraic functions using the Fundamental Theorem of Calculus.
E) Evaluate a definite integral by use of substitution.
F) Evaluate a definite integral by the method of integration by parts.
VIII Demonstrate the ability to apply the concepts of integration.
A) Approximate the area under the curve by using integration.
B) Approximate the area between two curves by using integration.
C) Find the volume of a solid of revolution.
D) Find the length of a line and surface area of revolution.
Precalculus follows state standards and uses the book PRECALCULUS WITH LIMITS A GRAPHING APPROACH THIRD EDITION
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