LSU College of Science
LSU  | Mathematics

Math 1023 Algebra and Trigonometry Topics

Linear Equations

  • Recognizing linear equations
  • Solving linear equations with integer coefficients
  • Solving linear equations involving fractions
  • Solving linear equations involving decimals
  • Solving equations that lead to linear equations

Quadratic Equations

  • Solving quadratic equations by factoring and the zero product property
  • Solving quadratic equations using the square root property
  • Solving quadratic equations using the quadratic formula
  • Using the discriminant to determine the type of solutions of a quadratic equation

Other Types of Equations

  • Solving higher-order polynomial equations
  • Solving equations that are quadratic in form
  • Solving equations involving single radicals

Linear Inequalities

  • Solving linear inequalities
  • Solving three-part inequalities

Absolute Value Equations and Inequalities

  • Solving an absolute value equation
  • Solving an absolute value “less than” inequality
  • Solving an absolute value “greater than” inequality

The Rectangular Coordinate System

  • Plotting ordered pairs
  • Finding the midpoint of a line segment using the midpoint formula
  • Finding the distance between two points using the distance formula

Circles

  • Writing the standard form of an equation of a circle
  • Sketching the graph of a circle
  • Converting the general form of a circle into standard form

Lines

  • Determining the slope of a line
  • Sketching a line given a point and the slope
  • Finding the equation of a line using the point-slope form
  • Finding the equation of a line using the slope-intercept form
  • Writing the equation of a line in standard form
  • Finding the slope and the y-intercept of a line in standard form
  • Sketching lines by plotting intercepts
  • Finding the equation of a horizontal line and a vertical line

Parallel and Perpendicular Lines

  • Understanding the definition of parallel lines
  • Understanding the definition of perpendicular lines
  • Determining whether two lines are parallel, perpendicular, or neither
  • Finding the equations of parallel and perpendicular lines

Relations and Functions

  • Understanding the definitions of relations and functions
  • Determining whether equations represent functions
  • Using function notation; evaluating functions
  • Using the vertical line test
  • Determining the domain of a function given the equation

Properties of a Function’s Graph

  • Determining the intercepts of a function
  • Determining the domain and range of a function from its graph
  • Determining whether a function is increasing, decreasing, or constant
  • Determining relative maximum and relative minimum values of a function
  • Determining whether a function is even, odd, or neither
  • Determining information about a function from a graph

Graphs of Basic Functions; Piecewise Functions

  • Sketching the graphs of the basic functions
  • Analyzing piecewise-defined functions

Transformations of Functions

  • Using vertical shifts to graph functions
  • Using horizontal shifts to graph functions
  • Using reflections to graph functions
  • Using vertical stretches and compressions to graph functions
  • Using combinations of transformations to graph functions

Composite Functions

  • Forming and evaluating composite functions
  • Determining the domain of composite functions

One-to-One Functions; Inverse Functions

  • Understanding the definition of a one-to-one function
  • Determining whether a function is one-to-one using the horizontal line test
  • Understanding and verifying inverse functions
  • Sketching the graphs of inverse functions
  • Finding the inverse of a one-to-one function

Quadratic Functions

  • Understanding the definition of a quadratic function and its graph
  • Graphing quadratic functions written in standard form
  • Graphing quadratic functions using the vertex formula
  • Determining the equation of a quadratic function given its graph

Applications of Quadratic Functions

  • Maximizing projectile motion functions
  • Maximizing functions in economics

The Graphs of Polynomial Functions

  • Understanding the definition of a polynomial function
  • Sketching the graphs of power functions
  • Determining the end behavior of polynomial functions
  • Determining the intercepts of a polynomial function
  • Determining the real zeros of polynomial functions and their multiplicities
  • Sketching the graph of a polynomial function
  • Determining a possible equation of a polynomial function given its graph

Rational Functions and Their Graphs

  • Finding the domain and intercepts of rational functions
  • Identifying vertical asymptotes
  • Identifying horizontal asymptotes
  • Using transformations to sketch the graphs of rational functions
  • Sketching rational functions
  • Sketching rational functions having removable discontinuities

Exponential Functions

  • Understanding the characteristics of exponential functions
  • Sketching the graphs of exponential functions using transformations
  • Solving exponential equations by relating the bases
  • Solving applications of exponential functions

Logarithmic Functions

  • Understanding the definition of a logarithmic function
  • Evaluating logarithmic expressions
  • Understanding the properties of logarithms
  • Using the common and natural logarithms
  • Understanding the characteristics of logarithmic functions
  • Sketching the graphs of logarithmic functions using transformations
  • Finding the domain of logarithmic functions

Properties of Logarithms

  • Using the product rule, quotient rule, and power rule for logarithms
  • Expanding and condensing logarithmic expressions
  • Solving logarithmic equations using the logarithm property of equality
  • Using the change of base formula

Exponential and Logarithmic Equations

  • Solving exponential equations
  • Solving logarithmic equations

Applications of Exponential and Logarithmic Functions

  • Solving compound interest applications
  • Solving exponential growth and decay applications

An Introduction to Angles: Degree and Radian Measure

  • Understanding degree measure and radian measure
  • Converting between degree measure and radian measure
  • Finding coterminal angles using degree measure and radian measure

Applications of Radian Measure

  • Determining the area of a sector of a circle
  • Determining the arc length of a sector of a circle

Triangles (Review)

  • Classifying triangles
  • Using the Pythagorean Theorem
  • Understanding similar triangles
  • Understanding the special right triangles

Right Triangle Trigonometry

  • Understanding the right triangle definitions of the trigonometric functions
  • Using the special right triangles
  • Understanding the fundamental trigonometric identities
  • Understanding cofunctions
  • Evaluating trigonometric functions using a calculator

Trigonometric Functions of General Angles

  • Understanding the four families of special angles
  • Understanding the definitions of the trigonometric functions of general angles
  • Finding the values of the trigonometric functions of quadrantal angles
  • Understanding the signs of the trigonometric functions
  • Determining reference angles
  • Evaluating trigonometric functions of angles belonging to the $\frac{\pi}{3}$, $\frac{\pi}{4}$, and $\frac{\pi}{6}$ families

The Unit Circle

  • Understanding the definition of the unit circle
  • Understanding the unit circle definitions of the trigonometric functions

The Graphs of the Trigonometric Functions

  • Understanding the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions and their properties
  • Sketching graphs of the form $y=A\sin(Bx-C)+D$ or $y=A\cos(Bx-C)+D$
  • Sketching graphs of the form $y=A\tan(Bx-C)+D$ or $y=A\cot(Bx-C)+D$
  • Sketching graphs of the form $y=A\sec(Bx-C)+D$ or $y=A\csc(Bx-C)+D$
  • Determine the equation of a function of the form y=Asin(Bx-C) or y=Acos(Bx-C) given its graph

Inverse Trigonometric Functions

  • Understanding and finding the exact and approximate values of the inverse sine function, the inverse cosine function, and the inverse tangent function
  • Evaluating composite functions involving inverse trigonometric functions of the forms $f∘f^{-1}$, $f^{-1}∘f$, $f∘g^{-1}$, and $f^{-1}∘g$

Trigonometric Identities

  • Substituting known identities to verify an identity
  • Changing to sines and cosines to verify an identity
  • Factoring to verify an identity
  • Separating a single quotient into multiple quotients to verify an identity
  • Combining fractional expressions to verify an identity
  • Multiplying by conjugates to verify an identity

The Sum and Difference Formulas

  • Understanding and using the sum and difference formulas for the cosine, sine, and tangent functions
  • Using the sum and difference formulas to verify identities
  • Using the sum and difference formulas to evaluate expressions involving inverse trigonometric functions

The Double-Angle and Half-Angle Formulas

  • Understanding and using the double-angle formulas and the half-angle formulas
  • Using the double-angle and half-angle formulas to verify identities
  • Using the double-angle and half-angle formulas to evaluate expressions involving inverse trigonometric functions

Trigonometric Equations

  • Solving trigonometric equations that are linear or quadratic in form
  • Solving trigonometric equations using identities
  • Solving other types of trigonometric equations
  • Solving trigonometric equations using a calculator

Right Triangle Applications

  • Solving right triangles
  • Solving applications using right triangles

The Law of Sines

  • Determining if the Law of Sines can be used to solve an oblique triangle
  • Using the Law of Sines to solve the SAA case or the ASA case
  • Using the Law of Sines to solve the SSA (ambiguous) case
  • Using the Law of Sines to solve applied problems involving oblique triangles

The Law of Cosines

  • Determining if the Law of Cosines can be used to solve an oblique triangle
  • Using the Law of Cosines to solve the SAS case
  • Using the Law of Cosines to solve the SSS case
  • Using the Law of Cosines to solve applied problems involving oblique triangles

Area of Triangles

  • Determining the area of oblique triangles
  • Using Heron’s Formula to determine the area of an SSS triangle
  • Solving applied problems involving the area of triangles

Polar Coordinates and Polar Equations

  • Plotting points using polar coordinates
  • Determining different representations of a point $(r, θ)$
  • Converting points from polar to rectangular coordinates and from rectangular to polar coordinates
  • Converting equations from rectangular to polar form and from polar to rectangular form

Graphing Polar Equations

  • Sketching equations of the form $r\cosθ = a$, $r\sinθ = a$, $ar\cosθ + br\sinθ = c$, and $θ = α$
  • Sketching equations of the form $r = a$, $r = a\sinθ$, and $r = a\cosθ$
  • Sketching equations of the form $r = a + b\sinθ$ and $r = a + b\cosθ$
  • Sketching equations of the form $r = a\sin(nθ)$ and $r = a\cos(nθ)$
  • Sketching equations of the form $r^{2} = a^{2}\sin(2θ)$ and $r^{2} = a^{2}\cos(2θ)$

Vectors

  • Understanding the geometric representation of a vector
  • Understanding operations on vectors represented geometrically
  • Understanding vectors in terms of components
  • Understanding vectors in terms of i and j
  • Finding a unit vector
  • Determining the direction angle of a vector
  • Representing a vector in terms of i and j given its magnitude and direction angle
  • Using vectors to solve applied problems involving velocity 

Systems of Equations

  • Verifying solutions to a system of linear equations in two variables
  • Solving a system of linear equations using the substitution method
  • Solving a system of linear equations using the elimination method
  • Solving applied problems using a system of linear equations