Intermediate Algebra Syllabus and Course Competencies Study Guide

Course Overview

Introduction to Intermediate Algebra

This course, MATH 1140 Intermediate Algebra at Central Community College, is designed to build upon foundational algebra concepts and prepare students for further study in mathematics. The syllabus outlines key topics, grading policies, and expectations for academic integrity and participation. The course covers linear and quadratic equations, inequalities, functions, polynomials, rational expressions, radicals, systems, and word problems, aligning closely with standard intermediate algebra curriculum.

Course Structure and Requirements

Prerequisites and Supplies

• Prerequisite: Completion of Elementary Algebra (MATH 1130) or appropriate test score.

• Supplies: Scientific calculator (TI-30XS or TI-30xIIs recommended), web camera, smartphone or scanner, printer (for online exams).

Grading Breakdown

• Exams: 75% of total grade (5 exams, closed book/note, scientific calculator allowed).

• Quizzes: 15% of total grade (completed online, work must be shown).

• Homework: 10% of total grade (completed online, late penalties apply).

Academic Integrity

• Cheating and Plagiarism: Zero tolerance; violations result in a score of zero and possible college sanctions.

• Proper Use of Technology: AI tools may be used for learning, not for simply obtaining answers.

Course Competencies and Learning Objectives

1. Linear Equations and Inequalities in One Variable

Students will apply properties of equations to solve linear equations and inequalities in one variable.

• Key Points:

  • Solve linear equations in one variable.

  • Solve literal equations.

  • Solve application problems using a linear model.

  • Solve linear inequalities in one variable.

• Example: Solve $2x + 5 = 11$ for $x$. $2x + 5 = 11$ $2x = 6$ $x = 3$

2. Absolute Value Equations and Inequalities

Students will solve absolute value equations and inequalities in one variable.

• Key Points:

  • Solve absolute value equations in one variable.

  • Solve absolute value inequalities in one variable.

• Example: Solve $|x - 4| = 7$. $x - 4 = 7$ or $x - 4 = -7$ $x = 11$ or $x = -3$

3. Linear Equations in Two Variables

Students will graph linear equations, determine characteristics, and write equations of lines.

• Key Points:

  • Graph linear equations in two variables.

  • Determine slope and y-intercept.

  • Identify parallel and perpendicular lines.

  • Calculate slope between two points.

  • Write the equation of a line given information.

• Formula: Slope between points $(x_1, y_1)$ and $(x_2, y_2)$: $m = \frac{y_2 - y_1}{x_2 - x_1}$

4. Functions

Students will determine whether a relation or graph is a function, evaluate functions, perform operations, and graph various functions.

• Key Points:

  • Determine if a relation or graph is a function.

  • Evaluate functions at given points.

  • Add, subtract, multiply, and divide functions.

  • Graph linear, quadratic, and absolute value functions.

• Example: If $f(x) = 2x + 1$, find $f(3)$. $f(3) = 2 \times 3 + 1 = 7$

5. Systems of Equations and Inequalities

Students will solve systems of linear equations and inequalities using various methods and apply these to real-world problems.

• Key Points:

  • Solve systems by substitution and addition.

  • Solve application problems using systems.

  • Graph linear inequalities.

  • Solve systems of inequalities in two variables.

• Example: Solve the system: $x + y = 5$ $x - y = 1$ Adding: $2x = 6 \Rightarrow x = 3$, $y = 2$

6. Polynomials

Students will perform operations on polynomials, factor using various techniques, and solve polynomial equations.

• Key Points:

  • Identify polynomials.

  • Add, subtract, multiply, and divide polynomials.

  • Factor using GCF, grouping, trinomials, and special formulas.

  • Solve polynomial equations by factoring.

  • Solve quadratic equations by completing the square or quadratic formula.

• Formula: Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

7. Rational Expressions and Equations

Students will simplify complex fractions, perform operations on rational expressions, and solve rational equations.

• Key Points:

  • Determine domain of rational expressions.

  • Add, subtract, multiply, and divide rational expressions.

  • Simplify complex fractions.

  • Solve rational equations and application problems.

• Example: Simplify $\frac{2}{x} + \frac{3}{x}$. $\frac{2 + 3}{x} = \frac{5}{x}$

8. Radical Expressions and Equations

Students will simplify radical expressions, perform operations, and solve radical equations.

• Key Points:

  • Identify real numbers in radical expressions.

  • Evaluate square and cube roots.

  • Convert between radical and exponential forms.

  • Simplify, add, subtract, multiply, and divide radical expressions.

  • Solve radical equations.

• Formula: $\sqrt[n]{a} = a^{1/n}$

9. Variation

Students will solve application problems involving direct, inverse, and combined variation.

• Key Points:

  • Solve direct variation problems ($y = kx$).

  • Solve inverse variation problems ($y = \frac{k}{x}$).

  • Solve combined variation problems.

• Example: If $y$ varies directly with $x$ and $y = 10$ when $x = 2$, find $k$. $y = kx \Rightarrow 10 = k \times 2 \Rightarrow k = 5$

10. Complex Numbers

Students will determine real and imaginary parts, evaluate powers of $i$, and perform operations on complex numbers.

• Key Points:

  • Write numbers in standard form ($a + bi$).

  • Evaluate powers of $i$ ($i^2 = -1$).

  • Add, subtract, multiply, and divide complex numbers.

• Example: $(3 + 2i) + (1 - 4i) = 4 - 2i$

Additional Course Policies

Attendance and Participation

• Regular attendance and participation are required for academic success.

• Online attendance includes timely submission of assignments and participation in discussions.

Disability Services and Accommodations

• Students with disabilities are encouraged to contact the Director of Disability Services for accommodations.

Academic Integrity and Technology Usage

• All students must adhere to CCC's policies regarding academic honesty and technology usage.

Summary Table: Course Competencies

Competency	Main Topics	Key Skills
Linear Equations & Inequalities	Equations, Inequalities	Solve, Model, Apply
Absolute Value	Equations, Inequalities	Solve, Interpret
Linear Equations (2 Variables)	Graphing, Slope, Line Equations	Graph, Calculate, Write
Functions	Relations, Operations, Graphs	Evaluate, Operate, Graph
Systems	Equations, Inequalities	Solve, Apply, Graph
Polynomials	Operations, Factoring, Equations	Identify, Operate, Factor, Solve
Rational Expressions	Operations, Equations	Simplify, Operate, Solve
Radicals	Operations, Equations	Simplify, Operate, Solve
Variation	Direct, Inverse, Combined	Solve, Apply
Complex Numbers	Operations, Powers of i	Write, Evaluate, Operate