Precalc Objectives

Chapter 1:

1. Be able to sketch graphs of equations.

2. Be able to find x-and y-intercepts of graphs of equations algebraically.

3. Be able to algebraically determine symmetry of graphs of equations.

4. Be able to find equations and sketch the graphs of circles.

5. Be able to solve linear equations in one variable.

6. Be able to solve quadratic equations by factoring, using square roots, completing the square, and using the Quadratic Formula.

7. Be able to use linear and quadratic equations and inequalities to model and solve real-life problems

8. Understand the imaginary unit i.

9. Be able to do arithmetic computations using complex numbers, including using complex conjugates to write quotients and finding complex solutions of quadratic equations.

10. Be able to solve polynomial equations, equations using radicals, and equations involving fractions or absolute value.

11. Be able to solve linear, polynomial, and rational inequalities in one variable.

12. Be able to solve inequalities involving absolute values.

Chapter 2:

1. Be able to find the slope of a line and use slope to graph the line.

2. Be able to use slope to identify parallel and perpendicular lines.

3. Be able to use linear equations in two variables to model and solve real-life problems.

4. Know the definition of a function and be able to determine whether a relation is a function using the definition and the Vertical Line Test.

5. Be able to find the domains of functions.

6. Be able to identify even and odd functions, algebraically and graphically.

7. Be able to identify and graph common functions (linear, quadratic, cubic, square root, reciprocal, piecewise-defined.)

8. Understand the effect of transformations and be able to use transformations to graph common functions (vertical and horizontal shifts, reflections, stretch/shrink).

9. Be able to find combinations and compositions of functions, and their domains.

10. Be able to determine whether functions have inverses (algebraically and using the Horizontal line test to determine 1-1) and find the inverse functions (algebraically).

Chapter 3:

1. Be able to write a quadratic function in standard form and sketch the graph.

2. Be able to use quadratic functions to model and solve real-life problems.

3. Be able to use the leading coefficient test to determine the end behavior of graphs of polynomial functions.

4. Be able to use zeros of polynomials (and their multiplicity) to sketch the graphs of polynomial functions.

5. Be able to use both long division and synthetic division of polynomials. Know the restrictions on synthetic division.

6. Know and be able to use the Factor Theorem.

7. Understand the Fundamental Theorem of Algebra.

8. Know and be able to use the Linear Factorization Theorem.

9. Be able to find rational and complex zeros of polynomials.

Chapter 4:

1. Be able to find the domain of rational functions.

2. Understand what is meant by an asymptote and be able to find vertical, horizontal, and slant asymptotes of rational functions.

3. Be able to use asymptotes to sketch a rational function.

4. Be able to use rational functions to model and solve real-life problems.

5. Be able to find partial fraction decompositions of rational expressions.

6. Understand what is meant by conic sections and know how the definition of the four basic conic sections.

7. Be able to recognize, graph, and write equations of ellipses, parabola, and hyperbola (with center at the origin or shifted.)

8. Be able to use conics to model and solve real-life problems.

Chapter 5:

1. Understand and be able to recognize, evaluate, and graph exponential functions (any base).

2. Understand and be able to recognize, evaluate, and graph logarithmic functions (any base).

3. Be able to use logarithmic functions to model and solve real-life applications.

4. Be able to use properties of logarithms to expand or condense logarithmic expressions.

5. Be able to change the base of either a logarithmic or exponential expression.

6. Be able to solve exponential and logarithmic equations.

7. Be able to use exponential functions to model and solve real-life applications. Know and be able to use the five most common types of logarithmic and exponential models.

Chapter 6:

1. Understand the definition of an angle and be able to convert between degree and radian measures of an angle.

2. Be able to use angles to model and solve real-life problems.

3. Know and be able to use the right triangle definitions of the trigonometric functions. KNOW THEM ABSOLUTELY.

4. Know and be able to use the fundamental trigonometric identities.

5. Be able to evaluate trigonometric functions with or without a calculator. Be able to use reference angles in evaluating trigonometric functions.

6. Know and be able to sketch the basic graphs of the six trigonometric functions. Know the definition of amplitude and period, and be able to sketch translations.

7. Understand inverse trigonometric functions and be able to evaluate them. Be able to evaluate the compositions of trigonometric functions.

8. Be able to use trigonometric functions to model and solve real-life problems.

Chapter 7:

1. Know and be able to use the fundamental trigonometric identities.

2. Be able to verify trigonometric identities.

3. Be able to solve trigonometric equations using algebra, the Quadratic Formula, multiple angle formulas, and inverse trigonometric functions.

4. Be able to use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations.

5. Be able to use multiple angle, power reducing, half angle, product to sum and sum to product formulas to rewrite and evaluate trigonometric functions.

6. Be able to use trigonometric functions to model and solve real-life problems.

Chapter 8:

1. Know and be able to use the Law of Sines.

2. Be able to find the area of oblique triangles.

3. Know and be able to use the Law of Cosines.

4. Be able to use Heron’s Formula to find the area of a triangle.

5. Be able to use the Law of Sines and the Law of Cosines to model and solve real-life problems.

Chapter 9:

1. Be able to use substitution, graphing, and elimination to solve systems of equations in two variables. Know how to interpret the solution of a system of equations.

2. Be able to use Gaussian elimination to solve systems of linear equations in three or more variables.

3. Be able to solve systems of inequalities in two variables.

4. Be able to use systems of equations in two or more variables and inequalities in two variables to model and solve real-life problems.