1: Precalculus and Limits

1.A: General Learner Expectations

1.A.1: Students are expected to understand that functions, as well as variables, can be combined, using operations, such as addition and multiplication, and demonstrate this, by:

1.A.1.1: describing the relationship among functions after performing translations, reflections, stretches and compositions on a variety of functions

Absolute Value with Linear Functions
Rational Functions
Translating and Scaling Sine and Cosine Functions
Translations

1.A.1.2: drawing the graphs of functions by applying transformations to the graphs of known functions

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

1.A.1.3: expressing final algebraic and trigonometric answers in a variety of equivalent forms, with the form chosen to be the most suitable form for the task at hand

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Sine, Cosine, and Tangent Ratios
Using Algebraic Expressions

1.A.2: Students are expected to understand that functions can be transformed, and these transformations can be represented algebraically and geometrically, and demonstrate this, by:

1.A.2.1: describing the relationship among functions after performing translations, reflections, stretches and compositions on a variety of functions

Absolute Value with Linear Functions
Rational Functions
Translating and Scaling Sine and Cosine Functions
Translations

1.A.2.2: drawing the graphs of functions by applying transformations to the graphs of known functions

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

1.A.2.3: expressing final algebraic and trigonometric answers in a variety of equivalent forms, with the form chosen to be the most suitable form for the task at hand

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Sine, Cosine, and Tangent Ratios
Using Algebraic Expressions

1.B: Conceptual Understanding

1.B.1: Students will demonstrate conceptual understanding of the algebra of functions, by:

1.B.1.3: expressing the sum, product, difference and quotient, algebraically and graphically, given any two functions

Addition and Subtraction of Functions

1.B.1.5: illustrating the difference between the concepts of equation and identity in trigonometric contexts.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Translating and Scaling Sine and Cosine Functions

1.B.2: Students will demonstrate conceptual understanding of the transformation of functions, by:

1.B.2.1: describing the similarities and differences between the graphs of y = f(x) and y = af [k(x+c)]+d, where a, k, c and d are real numbers

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

1.B.2.2: describing the effects of the reflection of the graphs of algebraic and trigonometric functions across any of the lines y = x, y = 0, or x = 0

Absolute Value with Linear Functions
Introduction to Exponential Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

1.B.3: Students will demonstrate conceptual understanding of equivalent forms, by:

1.B.3.1: describing what it means for two algebraic or trigonometric expressions to be equivalent.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax2+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

1.C: Procedural Knowledge

1.C.1: Students will demonstrate competence in the procedures associated with the algebra of functions, by:

1.C.1.2: finding the sum, difference, product, quotient and composition of functions

Addition and Subtraction of Functions

1.C.1.2.a: primary and reciprocal ratio

Simplifying Trigonometric Expressions

1.C.1.2.c: sum and difference sin (A±B) cos (A±B)

Sum and Difference Identities for Sine and Cosine

1.C.1.2.d: Pythagorean

Simplifying Trigonometric Expressions

1.C.2: Students will demonstrate competence in the procedures associated with the transformation of functions, by:

1.C.2.1: sketching the graph of, and describing algebraically, the effects of any translation, reflection or dilatation on any of the following functions or their inverses:

1.C.2.1.a: linear, quadratic or cubic polynomial

Absolute Value with Linear Functions
Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translations
Zap It! Game

1.C.2.1.b: absolute value

Absolute Value with Linear Functions
Translating and Scaling Functions

1.C.2.1.d: exponential

Exponential Functions
Introduction to Exponential Functions

1.C.3: Students will demonstrate competence in the procedures associated with the construction of equivalent forms, by:

1.C.3.2: rationalizing expressions containing a numerator or a denominator that contains a radical

Simplifying Radical Expressions

1.D: Problem-Solving Contexts

1.D.1: Students will demonstrate problem-solving skills, by:

1.D.1.3: translating problem conditions into equation or inequality form.

Comparing and Ordering Decimals
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Using Algebraic Equations

2: Derivatives and Derivative Theorems

2.B: Conceptual Understanding

2.B.2: Students will demonstrate conceptual understanding of derivative theorems, by:

2.B.2.7: describing the second derivative geometrically.

Graphs of Derivative Functions

2.B.3: Students will demonstrate conceptual understanding of the derivatives of trigonometric functions, by:

2.B.3.1: demonstrating that the three primary trigonometric functions have derivatives at all points where the functions are defined

Graphs of Derivative Functions

2.C: Procedural Knowledge

2.C.1: Students will demonstrate competence in the procedures associated with derivatives, by:

2.C.1.1: finding the slopes and equations of tangent lines at given points on a curve, using the definition of the derivative

Graphs of Derivative Functions

2.C.2: Students will demonstrate competence in the procedures associated with derivative theorems, by:

2.C.2.1: finding the derivative of a polynomial, power, product or quotient function

Graphs of Derivative Functions

2.C.2.5: finding the slope and equations of tangent lines at given points on a curve

Graphs of Derivative Functions

2.C.2.6: finding the second and third derivatives of functions.

Graphs of Derivative Functions

2.C.3: Students will demonstrate competence in the procedures associated with derivatives of trigonometric functions, by:

2.C.3.1: calculating the derivatives of the three primary and three reciprocal trigonometric functions

Graphs of Derivative Functions

2.C.3.3: using the power, chain, product and quotient rules to find the derivatives of more complicated trigonometric functions

Graphs of Derivative Functions

3: Applications of Derivatives

3.A: General Learner Expectations

3.A.1: Students are expected to understand that calculus is a powerful tool in determining maximum and minimum points and in sketching of curves, and demonstrate this, by:

3.A.1.6: fitting mathematical models to situations described by data sets.

Least-Squares Best Fit Lines
Solving Using Trend Lines

3.C: Procedural Knowledge

3.C.1: Students will demonstrate competence in the procedures associated with maxima and minima, by:

3.C.1.4: determining vertical, horizontal and oblique asymptotes, and domains and ranges of a function

Exponential Functions
General Form of a Rational Function
Radical Functions

4: Integrals, Integral Theorems and Integral Applications

4.B: Conceptual Understanding

4.B.1: Students will demonstrate conceptual understanding of antiderivatives, by:

4.B.1.2: showing that many different functions can have the same derivative

Graphs of Derivative Functions

4.B.2: Students will demonstrate conceptual understanding of area limits, by:

4.B.2.2: establishing the existence of upper and lower bounds for the area under a curve.

Riemann Sum

4.C: Procedural Knowledge

4.C.1: Students will demonstrate competence in the procedures associated with antiderivatives, by:

4.C.1.2: finding the family of curves whose first derivative has been given

Graphs of Derivative Functions

5: Calculus of Exponential and Logarithmic Functions

5.A: General Learner Expectations

5.A.1: Students are expected to understand that exponential and logarithmic functions have limits, derivatives and integrals that obey the same theorems as do algebraic and trigonometric functions, and demonstrate this, by:

5.A.1.5: fitting mathematical models to situations described by data sets.

Least-Squares Best Fit Lines
Solving Using Trend Lines

5.B: Conceptual Understanding

5.B.1: Students will demonstrate conceptual understanding of the calculus of exponential and logarithmic functions, by:

5.B.1.1: defining exponential and logarithmic functions as inverse functions

Logarithmic Functions

6: Numerical Methods

6.B: Conceptual Understanding

6.B.1: Students will demonstrate conceptual understanding of the principles of numerical analysis, by:

6.B.1.2: identifying when a particular numerical method is likely to give poor results

Estimating Population Size

6.B.1.5: describing the basis of a limit, derivative, equation root or integral procedure in geometric terms

Graphs of Derivative Functions

7: Volumes of Revolution

7.D: Problem-Solving Contexts

7.D.1: Students will demonstrate problem-solving skills, in one or both of the following, by:

7.D.1.1: deriving formulas for the volume of a cylinder, cone and sphere

Prisms and Cylinders

9: Applications of Calculus to Biological Sciences

9.B: Conceptual Understanding

9.B.1: Students will demonstrate conceptual understanding of the links between calculus and the biological sciences, by:

9.B.1.1: defining exponential and logarithmic functions as inverse functions

Logarithmic Functions

Correlation last revised: 9/24/2019

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