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Math 1113 Objectives
OpenStax Algebra & Trigonometry
CHAPTER 2: EQUATIONS AND INEQUALITIES
Section 2.1: The Rectangular Coordinate System and Graphs
Plot ordered pairs in the Cartesian coordinate system.
Graph equations by plotting points.
Graph equations with a graphing utility.
Find x- and y-intercepts.
Use the distance formula.
Use the midpoint formula.
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Page 84: Section Exercises
Section 2.2: Linear Equations in One Variable
Solve equations in one variable algebraically.
Solve a rational equation.
Find the slope of a line given two points on the line.
Find a linear equation (slope-intercept and point-slope forms).
Given the equations of two lines, determine whether their graphs are parallel or perpendicular.
Write the equation of a line that is parallel or perpendicular to a given line.
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Page 100: Section Exercises
Section 2.3: Models and Applications
Set up a linear equation to solve a real-world application.
Use a formula to solve real-world applications, such as d = rt, perimeter, or area
problems.
Given a formula with two or more variables, solve for one of the variables.
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Section 2.4: Complex Numbers
Add and subtract complex numbers (combine like terms).
Multiply complex numbers (use FOIL and i2 = −1).
Given a complex number, find its complex conjugate (a + bi ⇔ a − bi).
Divide complex numbers (mult. top and bottom by comp. conj. of denominator).
Simplify powers of i (use the fact that i2 = −1).
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Section 2.5: Quadratic Equations
Solve quadratic equations by factoring.
Solve quadratic equations by the “square-root property.”
Solve quadratic equations by “completing the square.”
Solve quadratic equations by using the quadratic formula.
Use the discriminant b2 − 4ac to determine the types of solutions of a quadratic
equation ax2 + bx + c = 0.
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Section 2.6: Other Types of Equations
Solve equations involving rational exponents.
Solve equations using factoring.
Solve radical equations (isolate the radical and square both sides).
Solve absolute value equations (isolate absolute value and interpret).
Solve other types of equations (“quadratic in form” and rational equations).
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Section 2.7: Linear and Absolute Value Inequalities
Use interval notation: −3 ≤ x < 5 is the interval [−3, 5).
Use properties of inequalities (like equations, except when mult./div. by a negative).
Solve inequalities in one variable algebraically.
Solve absolute value inequalities (isolate absolute value and interpret).
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Page 149: Section Exercises
p. 151: Chapter 2 Review, Vocabulary
p. 155: Chapter 2 Review Exercises (see solutions manual)
p. 158: Chapter 2 Practice Test (see solutions manual)
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