PACING GUIDE: Pre - Calculus

PACING GUIDE: Pre - Calculus

REVIEW: Chapter P A.1 Radicals and Rational Exponents A.2 Polynomials and Factoring A.3 Fractional Expressions

8 days

CHAPTER 1: Functions and Graphs

12 days

Objectives:

Recognize whether a relation is also a function. Given functions f and g, find f + g, f - g, fg, f/g, f g, and g f. Determine whether a function is invertible. Read and interpret inverses (where applicable) from graphs in application settings. Determine the inverse of a function displayed in table form. Determine the equation of the inverse when algebraically possible. Sketch the inverse graph of an invertible function, manually and using the graphing calculator. Determine the domain, range, intercepts, and intervals where the function is increasing or decreasing for

polynomial functions, piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential functions, trigonometric functions, families of functions, and the composition of these functions. Observe symmetries about points and about lines for piecewise functions, absolute value functions, rational functions, trigonometric functions, families of functions, and the composition of these functions using the graphing calculator. Verify algebraically where possible.

1.1 Modeling and Equation Solving ? 2 day 1.2 Functions and Their Properties ? 2 day 1.3 12 Basic Functions ? 2 day 1.4 Building Functions from Functions ? 1 day 1.5 Inverses ? 1 day (skip examples 1 and 2: Parametric mode) 1.6 Graphical Transformations ? 2 day 1.7 Modeling with Functions ? 2 day

CHAPTER 2: Polynomial, Power, and Rational Functions

15 days

Objectives:

Determine graphically relative maximum and minimum values where they exist for piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential functions, trigonometric functions, families of functions, and the composition of these functions.

Determine any horizontal, vertical, and oblique asymptotes for rational functions, logarithmic functions, exponential functions, trigonometric functions and the composition of these functions algebraically. Verify using the graphing calculator.

Observe and describe both rigid and non-rigid transformations of polynomial functions, piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential functions, trigonometric functions, families of functions, and the composition of these functions.

Write an equation for both rigid and non-rigid transformations or composition of functions. Graph piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential

functions, trigonometric functions, families of functions, and the composition of these functions manually and using the graphing calculator.

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2.1 Linear and Quadratic Functions and Modeling ?2 days 2.2 Power Functions with Modeling ? 2 days 2.3 Polynomial Functions of Higher Degree with Modeling ? 2 days 2.4 Real Zeros of Polynomial Functions ? 2 days 2.5 Complex Zeros and the Fundamental Theorem of Algebra ? 2 days 2.6 Graphs of Rational Functions ? 2 days 2.7 Solving Equations in One Variable ? 2 days 2.8 Solving Inequalities in One Variable ? 1 days

CHAPTER 3: Exponential, Logistic, and Logarithmic Functions

17 days

Objectives:

Determine graphically relative maximum and minimum values where they exist for piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential functions, trigonometric functions, families of functions, and the composition of these functions.

Determine any horizontal, vertical, and oblique asymptotes for rational functions, logarithmic functions, exponential functions, trigonometric functions and the composition of these functions algebraically. Verify using the graphing calculator.

Observe and describe both rigid and non-rigid transformations of polynomial functions, piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential functions, trigonometric functions, families of functions, and the composition of these functions.

Write an equation for both rigid and non-rigid transformations or composition of functions.

Graph piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential

functions, trigonometric functions, families of functions, and the composition of these functions manually and using the graphing calculator.

3.1 Exponential and Logistic Functions ? 2 days 3.2 Exponential and Logistic Modeling ? 3 days 3.3 Logarithmic Functions and Their Graphs ? 2 days 3.4 Properties of Logarithmic Functions ? 2 days 3.5 Equation Solving and Modeling ? 2 days 3.6 Mathematics of Finance ? 3 days

CHAPTER 4: Trigonometric Functions

15 days

Objectives:

Convert an angle measurement in radians or decimal degrees to an equivalent measurement.

Calculate the length of an arc of a circle, given the radius and central angle measure.

Use the definitions of trigonometric functions to evaluate the trigonometric functions.

State the exact values of the trigonometric functions for 0, /6, /4, /3, and /2 radians.

Find reference values and use the symmetries of the unit circle to determine the exact values of the trigonometric

functions for 0, /2, , 3/2, 2/3, 3/4, 5/6, 7/6, 5/4, 4/3, 5/3, 7/4, and 11/6 radians.

Evaluate an expression involving trigonometric functions of real numbers without a calculator.

Estimate an expression involving trigonometric functions of real numbers using a calculator.

State the definitions of the inverse sine, cosine, and tangent functions.

Using a calculator, estimate an expression involving the inverse sine, cosine or tangent functions.

Without using a calculator, evaluate an expression exactly involving the inverse sine, cosine or tangent functions.

Using a calculator, estimate the value of an expressing involving the composition of a trigonometric and an inverse

trigonometric function.

State the domain, range, and period for each of the six trigonometric functions. Verify these values using the

graphing calculator.

Sketch the graphs of all six trigonometric functions.

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 Sketch the graphs of y = a f(bx + c) + d where f is a trigonometric function, and discuss amplitude, period, phase shift and vertical shift.

Given the graph of a trigonometric function, determine the amplitude, period, phase shift and vertical shift. Use that information to write the equation of the function.

Sketch the graphs of y = sin-1x, y = cos-1x, and y = tan-1x.

4.1 Angles and Their Measures ? 1 days 4.2 Trigonometric Functions of Acute Angles ? 2 days 4.3 Trigonometry Extended: The Circular Functions ? 2 days 4.4 Graphs of Sine and Cosine: Sinusoids ? 2 days 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant ? 2 days 4.6 Graphs of Composite Trigonometric Functions ? 2 days 4.7 Inverse Trigonometric Functions ? 2 days 4.8 Solving Problems with Trigonometry ? 2 days

CHAPTER 5: Analytic Trigonometry + Section 7.1

7 days

Objectives:

Use the Law of Sines and the Law of Cosines to determine parts of a triangle. State and use the following identities: Negative angle identities, Cofunction identities, Reciprocal identities,

Tangent-cotangent identities, Pythagorean identities Prove identities involving the trigonometric functions. Solve equations involving trigonometric and inverse trigonometric functions. Determine the point(s) of intersection for systems of non-linear functions algebraically and using the graphing

calculator.

5.1 Fundamental Identities ? 2 days 5.2 Proving Trigonometric Identities ? 2 days 5.5 The Law of Sines ? ? days 5.6 The Law of Cosines ? ? days 7.1 Solving Systems of Two Equations ? 2 days

Section 10.3 More on Limits

4 days

Review

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