PRE-CALC PACING CHART FOR Precalculus by Demana, Waits ...

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Precalculus Pacing Guide Aug 27, 2012. Page 1 of 3. PACING GUIDE: Pre - Calculus. REVIEW: 8 days. • Chapter P. • A.1 Radicals and Rational Exponents.
PACING GUIDE: Pre - Calculus REVIEW:  Chapter P  A.1 Radicals and Rational Exponents  A.2 Polynomials and Factoring  A.3 Fractional Expressions CHAPTER 1: Functions and Graphs

8 days

12 days

Objectives:         

1.1 1.2 1.3 1.4 1.5 1.6 1.7

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.

Modeling and Equation Solving – 2 day Functions and Their Properties – 2 day 12 Basic Functions – 2 day Building Functions from Functions – 1 day Inverses – 1 day (skip examples 1 and 2: Parametric mode) Graphical Transformations – 2 day 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.

Precalculus Pacing Guide Aug 27, 2012 Page 1 of 3.

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Linear and Quadratic Functions and Modeling –2 days Power Functions with Modeling – 2 days Polynomial Functions of Higher Degree with Modeling – 2 days Real Zeros of Polynomial Functions – 2 days Complex Zeros and the Fundamental Theorem of Algebra – 2 days Graphs of Rational Functions – 2 days Solving Equations in One Variable – 2 days Solving Inequalities in One Variable – 1 days

CHAPTER 3: Exponential, Logistic, and Logarithmic Functions

17 days

Objectives:    



3.1 3.2 3.3 3.4 3.5 3.6

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.

Exponential and Logistic Functions – 2 days Exponential and Logistic Modeling – 3 days Logarithmic Functions and Their Graphs – 2 days Properties of Logarithmic Functions – 2 days Equation Solving and Modeling – 2 days 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.

Precalculus Pacing Guide Aug 27, 2012 Page 2 of 3.

  

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

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.

Angles and Their Measures – 1 days Trigonometric Functions of Acute Angles – 2 days Trigonometry Extended: The Circular Functions – 2 days Graphs of Sine and Cosine: Sinusoids – 2 days Graphs of Tangent, Cotangent, Secant, and Cosecant – 2 days Graphs of Composite Trigonometric Functions – 2 days Inverse Trigonometric Functions – 2 days Solving Problems with Trigonometry – 2 days

CHAPTER 5: Analytic Trigonometry + Section 7.1

7 days

Objectives:     

5.1 5.2 5.5 5.6 7.1

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.

Fundamental Identities – 2 days Proving Trigonometric Identities – 2 days The Law of Sines – ½ days The Law of Cosines – ½ days Solving Systems of Two Equations – 2 days

Section 10.3 More on Limits

4 days

Review

Precalculus Pacing Guide Aug 27, 2012 Page 3 of 3.