Dual Enrollment Program DE Course: Math 1015 Basic Math & Applications

This course covers basic mathematical skills of graphing, formulas for geometric measurement, systems of linear equations and inequalities, review of quadratic equations, logarithms and application to exponential growth and decay, triangle trigonometry and its application to geometry and measurement.

Note: Math 1015 does not serve as a prerequisite for calculus. Credit will not be given for both this course and Math 1021 or Math 1022. Students who take this course are primarily planning to earn an Associate Degree, which is not offered at LSU A&M. Though Math 1015 includes some of the topics covered in Math 1021 College Algebra and Math 1022 Trigonometry, it does not cover those topics at the same depth.

Topics & Objectives

Chapter and section numbers refer to Algebra & Trigonometry, 4th edition

R.2 A Review of Fractions and the Order of Operations
  • Use the properties of real numbers to rewrite expressions
  • Use the order of operations to simplify numeric and algebraic expressions
  • Evaluate algebraic expressions for given values of variables

R.3 The Properties of Integer Exponents
  • Simplify exponential expressions using the product rule
  • Simplify exponential expressions using the quotient rule
  • Simplify exponential expressions using the product-to-power rule
  • Write expressions using positive exponents using the negative-power rule
  • Simplify exponential expressions using the appropriate rule or combination of rules

R.5 Polynomials
  • Add and subtract polynomials
  • Multiply polynomials

R.7 Factoring Polynomials
  • Factor polynomials by factoring out a greatest common factor
  • Factor polynomials by grouping
  • Factor trinomials with a leading coefficient equal to one
  • Factor trinomials with a leading coefficient not equal to one
  • Factor using special formulas

R.8 Rational Expressions
  • Simplify rational expressions
  • Multiply and divide rational expressions
  • Add and subtract rational expressions with unlike denominators
  • Simplify complex rational expressions

R.4 and R.6 Radicals and Rational Expressions
  • Use the definition for rational expressions of the form $a^{m/n}$ to rewrite expressions
  • Simplify expressions of the form n$^{th}$ root of $a^{n}$
  • Simplify expressions involving rational exponents
  • Simplify radical expressions using the product rule for radicals
  • Add and subtract radical expressions
  • Multiply radical expressions
  • Rationalize denominators of radical expressions

1.1 Linear and Rational Equations
  • Determine whether equations are linear or non-linear
  • Solve linear equations with integer coefficients
  • Solve linear equations with fractions
  • Solve rational equations that lead to linear equations

1.2 Applications of Equations and Rational Equations
  • Solve applications involving unknown numeric quantities
  • Solve applications involving geometric formulas
  • Solve applications involving decimal equations
  • Solve applications involving uniform motion
  • Solve applications involving rates of work

1.4 Quadratic Equations
  • Solve quadratic equations by factoring
  • Solve quadratic equations using the square root property
  • Solve quadratic equations by completing the square
  • Solve quadratic equations by using the quadratic formula

1.6 Other Types of Equations
  • Solve higher-order polynomial equations
  • Solve equations that are quadratic in form
  • Solve equations involving radicals

1.7 Linear Inequalities in One Variable
  • Convert between set-builder and interval notation and graph sets on number lines
  • Solve linear inequalities in one variable
  • Solve three-part inequalities in one variable
  • Solve compound inequalities in one variable

1.9 Polynomial and Rational Inequalities
  • Solve polynomial inequalities
  • Solve rational inequalities

2.1 Distance and Midpoint Formulas
  • Find midpoints or endpoints of line segments using the midpoint formula
  • Find distances between two points using the distance formula

2.3 Lines
  • Find the slopes of lines that pass through two given points
  • Find the point-slope form of a line
  • Find the slope-intercept form of a line
  • Find equations of lines that pass through two given points
  • Find equations of horizontal and vertical lines
  • Sketch graphs of equations
  • Find the slope and the y-intercept of a lines in standard form

2.4 Parallel and Perpendicular Lines
  • Determine whether two lines are parallel, perpendicular, or neither

3.1 Relations and Functions
  • Find the domain and range of relations, and determine if relations represent functions
  • Evaluate functions at given values
  • Classify functions as polynomials, rational functions, or root functions, and find their domains

5.1a Exponential Functions
  • Evaluate exponential expressions
  • Sketch the graph of exponential functions
  • Solve exponential equations by relating the bases

5.2 Logarithmic Functions
  • Change equations between exponential form and logarithmic form
  • Use properties of logarithms to evaluate expressions

5.3 Properties of Logarithms
  • Expand and evaluate logarithmic expressions using properties of logarithms
  • Condense and evaluate logarithmic expressions using properties of logarithms
  • Use the change of base formula to approximate logarithmic expressions

5.4 Exponential and Logarithmic Equations
  • Solve exponential equations
  • Solve logarithmic equations

5.5 Applications of Exponential and Logarithmic Functions
  • Solve applications involving compound interest
  • Solve applications involving exponential growth and decay

6.1 An Introduction to Angles: Degree and Radian Measure
  • Draw angles in standard position using degree measure
  • Find coterminal angles using degree measure
  • Draw angles in standard position using radian measure
  • Convert between degree measure and radian measure
  • Find coterminal angles using radian measure

6.4 Right Triangle Trigonometry
  • Evaluate trigonometric functions of an acute angle in a right triangle
  • Use special right triangles to evaluate trigonometric expressions
  • Use the fundamental trigonometric identities to evaluate trigonometric expressions
  • Evaluate trigonometric functions

6.5 Trigonometric Functions of General Angles
  • Identify which of the four families of special angles a given angle belongs to
  • Find the six trigonometric functions of an angle given a point lying on its terminal side
  • Find the values of the trigonometric functions of quadrantal angles
  • Determine the quadrants where a trigonometric function is positive or negative
  • Find the trigonometric function values given another function value
  • Determine reference angles
  • Evaluate trigonometric functions of angles belonging to the $\pi \over 3$, $\pi \over 4$, and $\pi \over 6$ families -

9.1 Solving Right Triangles
  • Solve right triangles
  • Solve applied problems using right triangles

9.2 The Law of Sines
  • Determine if the Law of Sines can be used to solve an oblique triangle
  • Use the Law of Sines to solve the SAA case or the ASA case
  • Use the Law of Sines to solve the SSA case

9.3 The Law of Cosines
  • Determine whether Law of Sines or Cosines should be used to solve an oblique triangle
  • Use the Law of Cosines to solve the SAS case
  • Use the Law of Cosines to solve the SSS case
  • Use the Law of Cosines to solve applications involving oblique triangles

9.4 The Area of a Triangle
  • Determine the area of oblique triangles
  • Use Heron’s Formula to determine the area of an SSS triangle
  • Solve applications involving the area of triangles

12.1 Systems of Linear Equations in Two Variables
  • Determine whether ordered pairs are solutions to systems of linear equations in two variables
  • Solve systems of linear equations in two variables using the substitution method
  • Solve systems of linear equations in two variables using the elimination method
  • Solve systems of linear equations in two variables using either substitution or elimination

12.6 Systems of Inequalities
  • Graph linear inequalities in two variables
  • Graph systems of linear inequalities in two variables

Syllabus & Pacing Guide

Math 1015 Basic Math & Applications Syllabus & Pacing Guide
NameLast Modified
F26 Math 1015 DE Syllabus [docx]2026-05-20
F26 Math 1015 DE Pacing Guide [docx]2026-05-20

Class Notes

Math 1015 Basic Math & Applications Class Notes
NameLast Modified
Sec R.2 [docx]2025-05-28
Sec R.3 [docx]2025-05-28
Sec R.5 [docx]2025-05-28
Sec R.7 [docx]2025-05-28
Sec R.8 [docx]2025-05-28
Sec R.4 and R.6 [docx]2025-05-28
Sec 1.1 [docx]2025-05-28
Sec 1.2 [docx]2025-05-28
Sec 1.4 [docx]2025-05-28
Sec 1.6 [docx]2025-05-28
Sec 1.7 [docx]2025-05-28
Sec 1.9 [docx]2025-05-28
Sec 2.1 [docx]2025-05-28
Sec 2.3 [docx]2025-05-28
Sec 2.4 [docx]2025-05-28
Sec 3.1 [docx]2025-05-28
Sec 5.1a [docx]2025-05-28
Sec 5.2 [docx]2025-05-28
Sec 5.3 [docx]2025-05-28
Sec 5.4 [docx]2025-05-28
Sec 5.5 [docx]2025-05-28
Sec 6.1 [docx]2025-05-28
Sec 6.4 [docx]2025-05-28
Sec 6.5 [docx]2025-05-28
Sec 9.1 [docx]2025-05-28
Sec 9.2 [docx]2025-05-28
Sec 9.3 [docx]2025-05-28
Sec 9.4 [docx]2025-05-28
Sec 12.1 [docx]2025-05-28
Sec 12.6 [docx]2025-05-28

Videos

Section R.2: Properties of Real Numbers

Section R.3: Integer Exponents

Section R.4 Part 1: Adding and Subtracting Polynomials

Section R.4 Part 2: Multiplying Polynomials

Section R.4 Part 3: Special Products

Section R.7 Part 1: Greatest Common Factor and Factoring by Grouping

Section R.7 Part 2: Factoring Trinomials of the Form $x^2 + b x + c$

Section R.7 Part 3: Factoring Trinomials of the Form $a x^2 + b x + c$

Section R.7 Part 4: Perfect Square Trinomials

Section R.7 Part 5: Factoring Binomials

Section R.8 Part 3: Rational Exponents

Section R.8 Part 4: Simplifying Radical Expressions

Section R.8 Part 5: Adding, Subtracting, and Multiplying Radical Expressions

Section 1.1: Linear Equations

Section 1.2 Part 1: Introduction to Problem Solving

Section 1.2 Part 3: Mixture and Distance Applications

Section 1.4 Part 1: Solving Quadratic Equations by Factoring, by Square Roots, and by the Quadratic Formula

Section 1.4 Part 2: The Method of Completing the Square

Section 1.6: Other Types of Equations

Section 1.7: Linear Inequalities

Section 2.1: Distance and Midpoint Video

Section 2.3 Part 1: Slope

Section 2.3 Part 2: Equations of Lines

Section 12.1: Solving Systems of Linear Equations in Two Variables

Section 12.6 Part 1: Graphing Linear Inequalities in Two Variables

Section 3.1: Functions

Section 5.1a: Exponential Functions

Section 5.2: Logarithmic Functions

Section 5.3 Part 1: Properties of Logs (Part 1)

Section 5.3 Part 2: Properties of Logs (Part 2)

Section 5.4: Exponential and Logarithmic Equations

Section 5.5: Applications of Exponential and Logarithmic Equations

Section 6.1 Part 1: Angles and Their Measure (Part 1)

Section 6.1 Part 2: Angles and Their Measure (Part 2)

Section 6.4: Right Angle Trigonometry

Section 6.5 Part 1: Trigonometric Functions of General Angles (Part 1)

Section 6.5 Part 2: Trigonometric Functions of General Angles (Part 2)

Section 9.2: The Law of Sines

Section 9.3: The Law of Cosines

Section 9.4: Area of a Triangle