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# INTERMEDIATE ALGEBRA

Chapter 7 QUADRATIC EQUATIONS AND FUNCTIONS
Section: 7.1 – 7.6

Outcomes: Upon completion of this unit, students will be able to solve quadratic equations and work application
problems involving quadratic equations.

 A B C D F N Specific Competencies Demonstrate the ability to: 7.1 Solving quadratic equations using the square root property. 7.1 Complete the square in one variable. 7.1 Solve quadratic equations by completing the square. 7.1 Solve problems using the Pythagorean Theorem. 7.2 Solve quadratic equations using the quadratic formula. *7.2 Use the discriminant to determine the nature of solutions in a quadratic equation. 7.2 Model and solve problems involving quadratic equations. 7.3 Solve equations that are quadratic in form. *7.4 Graph quadratic functions of the form f(x) = x2 + k. *7.4 Graph quadratic functions of the form f(x) = (x – h)2. *7.4 Graph quadratic functions of the form f(x) = ax2. *7.4 Graph quadratic functions of the form f(x)=ax2 + bx + c *7.4 Find a quadratic function from its graph. 7.5 Graph quadratic functions of the form f(x)=ax2 + bx + c. *7.5 Find the maximum or minimum value of a quadratic function. *7.5 Model and solve optimization problems involving quadratic functions. *7.6 Solve quadratic inequalities.

Chapter 8 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Section: 8.1 – 8.5

Outcomes:
The student will evaluate and graph exponential and logarithmic functions, evaluate using change of
base, find an inverse function, and use properties of exponents and logarithms to solve problems.

 A B C D F N Specific Competencies Demonstrate the ability to: *8.1 Form the composite function. *8.1 Determine whether or not a function is one-to-one. *8.1 Determine the inverse of a function defined by a map or ordered pair. *8.1 Obtain the graph of the inverse function from the graph of the function. *8.1 Find the inverse of a function defined by an equation. *8.2 Evaluate exponential expressions. *8.2 Graph exponential functions. *8.2 Define the number e. *8.2 Solve exponential equations. *8.2 Study exponential models that describe our world. *8.3 Change exponential expressions to logarithmic expressions. *8.3 Change logarithmic expressions to exponential expressions. *8.3 Evaluate logarithmic functions. *8.3 Determine the domain of a logarithmic function. *8.3 Graph logarithmic functions. *8.3 Work with natural and common logarithms. *8.3 Study logarithmic models that describe our world. *8.4 Understand the properties of logarithms. *8.4 Write a logarithmic expression as a sum or difference of logarithms. *8.4 Write a logarithmic expression as a single logarithm. *8.4 Evaluate logarithms whose base is neither 10 nor e. *8.5 Solve logarithmic equations using the properties of logarithms. *8.5 Solve exponential equations. *8.5 Solve equations involving exponential models.

Chapter 9 CONICS Section: 9.1 – 9.6

Outcomes: The student will graph and write equations for parabolas, circles, and ellipses and hyperbolas.

 A B C D F N Specific Competencies Demonstrate the ability to: 9.1 Use the distance formula. 9.1 Use the midpoint formula. *9.2 Write the standard form of the equation of a circle *9.2 Graph a circle. *9.2 Find the center and radius of a circle from an equation in general form. *9.3 Graph parabolas in which the vertex is the origin. *9.3 Find the equation of a parabola. *9.3 Graph parabolas in which the vertex is not the origin. *9.3 Solve applied problems involving parabolas. *9.4 Graph ellipses in which the center is the origin. *9.4 Find the equation of an ellipse in which the center is the origin. *9.4 Graph ellipses in which the center is not the origin. *9.4 Solve applied problems involving ellipses. *9.5 Graph hyperbolas in which the center is the origin. *9.5 Find the equation of a hyperbola in which the center is the origin. *9.5 Find the asymptotes of a hyperbola in which the center is the origin. *9.6 Solve a system of nonlinear equations using substitution. *9.6 Solve a system of nonlinear equations using elimination.

Chapter 10 SEQUENCES, SERIES, AND THE BINOMIAL THEOREM Section: 10.1 – 10.4

Outcomes:
The student will utilize notation of sequences, series, and summations; use induction and binomial
theorem; solve problems using counting principle and probability.

 A B C D F N Specific Competencies Demonstrate the ability to: *10.1 Write the first several terms of a sequence. *10.1 Find a formula for the nth term of a sequence. *10.1 Use summation notation. *10.2 Determine if a sequence is arithmetic. *10.2 Find a formula for the nth term of an arithmetic sequence. *10.2 Find the sum of an arithmetic sequence. *10.3 Determine if a sequence is geometric. *10.3 Find a formula for the nth term of a geometric sequence. *10.3 Find the sum of a geometric sequences and series. *10.3 Solve annuity problems. *10.4 Compute factorials. *10.4 Evaluate a binomial coefficient. *10.4 Expand a binomial.