AZTEC HIGH SCHOOL

MATHEMATICS DEPARTMENT STANDARDS

 

AP CALCULUS I/11

 

PREREQUISITE – Pre-Calculus with a C- or better

 

DESCRIPTION – Weighted, one year course.  A study of limits, derivatives and integrals.  The use of each is studied in application of applied problems.  Designed to broaden the student’s knowledge, understanding, and skill of use of Calculus.  A preparation for math manipulations for the student planning on engineering, math or science at college.

 

POWER STANDARDS – Skills and knowledge needed to be prepared for Calculus.

 

1.      Understand the unit circle and basic trig identities

2.      Perform operations on functions including finding compositions

3.      Graph and solve all types of functions

4.      Solve problems involving radicals, logarithms, exponents, inequalities, rational expressions, fractions, sequences and series

5.      Solve quadratic equations by factoring, quadratic formula, and by calculator

6.      Factor by grouping and by using difference of cubes

7.      Use the binomial theorem to expand functions

8.      Use basic geometry formulas involving triangles, trapezoids, rectangles, and circles, including area and circumference

9.      Use a graphing calculator to graph, solve, and analyze functions

 

COMMON STANDARDS – These standards will be included in every math class at Aztec High School.

1.   Learn to communicate mathematically

2.   Learn to use mathematics in their daily lives.

3.   Become proficient with appropriate computational tools and techniques.

4.   Learn to reason mathematically.

5.            Become mathematical problem solvers.

 

 

PERFORMANCE STANDARDS – Skills and content that students will learn in this course.

1.Be able to graph in the Cartesian plane and determine functions.

    1. Be able to graph on the real number line and in the Cartesian plane.
    2. Be able to graph equations and lines in the plane.
    3. Be able to determine functions.
    4. Be able to use and apply trigonometric functions.

 

  1. Be able to determine limits.
    1. Be able to use properties of limits.
    2. Be able to use all techniques to evaluate limits.
    3. Be able to solve one-sided limits.
    4. Be able to find infinite limits.

AP CALCULUS PERFOAMANCE STANDARDS (cont.)

 

  1. Be able to find derivatives.
    1. Be able to apply the definition of derivative.
    2. Be able to apply derivatives to velocity, acceleration and other rates of change.
    3. Be able to use the product rule and quotient rule.
    4. Be able to use chain rule.
    5. Be able to use implicit differentiation.
    6. Solve related rate problems

 

  1. Be able to apply differentiation.
    1. Be able to find extreme.
    2. Be able to determine increasing and decreasing functions.
    3. Be able to determine concavity.
    4. Be able to apply Newton’s Method.
    5. Be able to sketch a curve.
    6. Be able to use Rolle’s Theorem and the Mean Value Theorem.

 

  1. Be able to integrate.
    1. Be able to find antiderivative and indefinite integrals.
    2. Be able to find definite integrals and use Reimann sums.
    3. Be able to apply fundamental theorem of calculus.
    4. Be able to integrate by substitution and perform numerical integration.

 

  1. Be able to differentiate and integrate logarithmic exponential and other transcendental functions.
    1. Be able to differentiate and integrate natural logarithmic functions.
    2. Be able to find inverse functions.
    3. Be able to find growth and decay.
    4. Be able to differentiate and integrate inverse trigonometric functions.
    5. Be able to differentiate and integrate hyperbolic functions.

 

  1. Be able to apply integration.
    1. Be able to find area between two curves.
    2. Be able to find volume using disc and shell method.
    3. Be able to find arc length and surfaces of revolution.
    4. Be able to find work, fluid pressure and force.
    5. Be able to find centers of mass and centroids.

 

  1. Be able to use integration techniques and apply L’Hopital’s Rule.
    1. Be able to apply basic integration formulas.
    2. Be able to integrate by parts.
    3. Be able to integrate using partial fractions.
    4. Be able to use integration tables.
    5. Be able to use L’Hopital’s Rule for integration.

AP CALCULUS PERFOAMANCE STANDARDS (cont.)

 

*     9. Be able to determine convergence and divergence of infinite series.

A.    Be able to use integral test and p-series.

B.     Be able to use comparison, alternating, and ratio and root test for convergence.

C.    Be able to find Taylor polynomial.

 

*   10.  Be able to find vectors.

A. Be able to use vectors in the plane.

B. Be able to use vectors in the space.

 

*   11. Be able to apply multiple integration.

A.     Be able to find iterate integrals.

B.      Be able to find area in the plane.

C.     Be able to find double integrals.

D.     Be able to find volume.

 

 

* Time permits/ teacher discretion

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