Sierra Sands Unified School District
Curriculum Guides 2003-2004

Mathematics - AP Calculus Semester 1

Mathematics

The California Achievement Test, Version 5 (CAT/5) Mathematics tests include both computational skills and critical-thinking skills.

The Mathematics Computation section of the CAT/5 includes computation with whole numbers, decimals, fractions, integers, percents, order of operations, and algebraic expressions.

The Mathematics Concepts and Applications section of the CAT/5 emphasizes problem-solving and critical-thinking skills. Objectives include estimation, pattern recognition, number sequences, functions, and shapes.

The HSEE field test in mathematics addresses the standards adopted by the California State Board of Education through Algebra I. The mathematics test will include statistics, data analysis and probability, number sense, measurement and geometry, mathematical reasoning, and algebra. Students also will be asked to demonstrate a strong foundation in arithmetic, including work with decimals, fractions, and percents. The math test will consist of all multiple-choice items.


The STAR blueprints provide standards for Mathematics assessment.


Calculus and Pre-Calculus

    Differential Equations: Solution Methods
The learner will be able to understand the solution methods of certain elementary differential equations, as well as their use in many different situations, including growth and decay problems.
Strand Source
Differential Equations CA: Content Standards, 1998, Calculus, 27.0
  
    Derivatives: Formulas
The learner will be able to use formulas to determine the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 4.4
  
    Limit: Knowledge
The learner will be able to display an understanding of the formal and graphical definitions or interpretations of limits of function values, including one sided limits, limits at infinity, and infinite limits.
Strand Source
Limits CA: Content Standards, 1998, Calculus, 1.0
  
    Calculus Concepts: Intermediate Value
The learner will be able to illustrate an understanding of the intermediate value theorem.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 3.0
  
    Extreme Value Theorem: Comprehend
The learner will be able to comprehend the Extreme Value Theorem.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 3.0
  
    Calculus Concepts: Rolle's Theorem
The learner will be able to understand Rolle's Theorem.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 8.0
  
    Calculus Concepts: Understand/L'Hopital
The learner will be able to understand L'Hopital's Rule.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 8.0
  
    Apply Calculus Concepts: L'Hopital's
The learner will be able to apply L'Hopital's Rule.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 8.0
  
    Intermediate Value Theorem: Application
The learner will be able to apply an understanding of the intermediate value theorem.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 3.0
  
    Extreme Value Theorem: Application
The learner will be able to apply an understanding of the extreme value theorem.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 3.0
  
    Calculus Concepts: Apply/Rolle's Theorem
The learner will be able to apply Rolle's Theorem.
Strand Source
Applying Calculus Concepts CA: Content Standards, 1998, Calculus, 8.0
  
    Derivatives: Mean Value Theorem
The learner will be able to comprehend the Mean Value Theorem.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 8.0
  
    Derivatives: Chain Rule/Proof
The learner will be able to understand the chain rule and its proof.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 5.0
  
    Derivatives: Higher Order
The learner will be able to calculate higher order derivatives (second derivative, third derivative, etc.).
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 7.0
  
    Derivatives: Composite/Chain Rule
The learner will be able to calculate the derivative of composite functions using the chain rule.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 5.0
  
    Derivatives: Mean Value Theorem
The learner will be able to use the Mean Value Theorem.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 8.0
  
    Derivatives: Sketch Graphs
The learner will be able to apply derivatives in manually sketching function graphs.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 9.0
  
    Derivatives: Implicit Differentiation
The learner will be able to apply the concept of implicit differentiation in many different problem types originating in a variety of curriculum areas.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 6.0
  
    Derivatives: Derive Formulas
The learner will be able to derive formulas for determining derivatives.
Strand Source
Derivatives/Antiderivatives CA: Content Standards, 1998, Calculus, 4.4
  
    Limits: Apply Theorems
The learner will be able to apply theorems used for evaluating the limits of sums, products, quotients, and function compositions.
Strand Source
Limits CA: Content Standards, 1998, Calculus, 1.1
  
    Limits: Estimate/Graphing Calculator
The learner will be able to make estimates of limits with the application of graphing calculators.
Strand Source
Limits CA: Content Standards, 1998, Calculus, 1.2
  
    Limits: Verify/Graphing Calculator
The learner will be able to verify limits with the application of graphing calculators.
Strand Source
Limits CA: Content Standards, 1998, Calculus, 1.2
  
    Limits: Apply
The learner will be able to apply special limits such as the limit of (sin(x))/x and/or (cos(x))/x as the value of x approaches zero.
Strand Source
Limits CA: Content Standards, 1998, Calculus, 1.3
  
    Limits: Prove Theorems
The learner will be able to create proofs of theorems that relate to the evaluating the limits of sums, products, quotients, and function composition.
Strand Source
Limits CA: Content Standards, 1998, Calculus, 1.1
  
    Limits: Prove
The learner will be able to create proofs for special limits such as (sin(x))/x and/or (cos(x))/x as the value of x approaches zero.
Strand Source
Limits CA: Content Standards, 1998, Calculus, 1.3
  
    Problem Solving: Derivative
The learner will be able to apply the derivative to obtain solutions to problems in a variety of curriculum areas involving the rate of change of a function.
Strand Source
Problem Solving CA: Content Standards, 1998, Calculus, 4.2
  
    Differentiation: Understand/Definition
The learner will be able to understand the formal definition of the derivative of a function at a point.
Strand Source
Differentiation CA: Content Standards, 1998, Calculus, 4.0
  
    Differentiation: Understand/Concept
The learner will be able to understand the concept of differentiability.
Strand Source
Differentiation CA: Content Standards, 1998, Calculus, 4.0
  
    Differentiation: Understand/Slope
The learner will be able to illustrate an understanding of the derivative of a function as the slope of the line tangent to the curve.
Strand Source
Differentiation CA: Content Standards, 1998, Calculus, 4.1
  
    Differentiation: Understand/Rate
The learner will be able to illustrate an understanding of the interpretation of the derivative of a function as the instantaneous rate of change.
Strand Source
Differentiation CA: Content Standards, 1998, Calculus, 4.2
  
    Differentiation: Comprehend
The learner will be able to comprehend the relationship between differentiability and continuity.
Strand Source
Differentiation CA: Content Standards, 1998, Calculus, 4.3
  
    Differentiation: Solve/Related Rates
The learner will be able to apply differentiation in obtaining solutions to related rates problems in both theoretical and real world contexts.
Strand Source
Differentiation CA: Content Standards, 1998, Calculus, 12.0
  
    Differentiation: Solve Optimization Prob
The learner will be able to apply differentiation in obtaining solutions to optimization problems in both theoretical and real world contexts.
Strand Source
Differentiation CA: Content Standards, 1998, Calculus, 11.0
  

Functions

    Functions: Continuity/Definition
The learner will be able to display a comprehension of the formal definition and graphical interpretation of the concept of continuity of a function.
Strand Source
Functions CA: Content Standards, 1998, Calculus, 2.0
  
    Functions: Identify Attributes
The learner will be able to identify the various attributes of a given function, including maxima/minima, points of inflection, and increasing/decreasing intervals.
Strand Source
Functions CA: Content Standards, 1998, Calculus, 9.0
  
    Functions: Convergence/Divergence
The learner will be able to comprehend the definition of convergence and divergence of a function as the domain variable approaches a fixed number or infinity.
Strand Source
Functions CA: Content Standards, 1998, Calculus, 1.0
  

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