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. |