Beginning Algebra 095: Weekly Agenda and Topic Overview

Course Overview

This syllabus outlines the weekly agenda for a Beginning Algebra course (095), including the sequence of topics, assessment deadlines, and class meeting schedule. The course covers foundational concepts in algebra, focusing on real numbers, equations, polynomials, and graphing.

Weekly Topics and Key Concepts

Symbols and Sets of Numbers

• Symbols: Introduction to algebraic notation and the use of variables.

• Sets of Numbers: Understanding different types of numbers such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

• Example: The set of integers includes {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Exponents, Order of Operations, and Variable Expressions

• Exponents: Notation and meaning (e.g., $2^3 = 8$).

• Order of Operations: The sequence for evaluating expressions (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

• Variable Expressions: Expressions containing variables, such as $3x + 2$.

• Example: Simplify $2 + 3 \times 4^2$ using order of operations.

Adding and Subtracting Real Numbers

• Real Numbers: All rational and irrational numbers.

• Adding/Subtracting: Rules for combining positive and negative numbers.

• Example: $-5 + 7 = 2$; $8 - 12 = -4$.

Multiplying and Dividing Real Numbers

• Multiplication: Product of real numbers, including sign rules.

• Division: Quotient of real numbers, with attention to division by zero.

• Example: $(-3) \times 4 = -12$; $12 \div (-3) = -4$.

Properties of Real Numbers

• Commutative, Associative, Distributive Properties: Fundamental properties used to simplify expressions.

• Example: Distributive property: $a(b + c) = ab + ac$.

Simplifying Expressions

• Combining Like Terms: Adding or subtracting terms with the same variable part.

• Example: $2x + 3x = 5x$.

Solving Linear Equations and Properties of Equality

• Addition Property of Equality: If $a = b$, then $a + c = b + c$.

• Multiplication Property of Equality: If $a = b$, then $ac = bc$.

• Solving Linear Equations: Steps to isolate the variable and find solutions.

• Example: Solve $2x + 3 = 7$.

Formulas and Problem Solving

• Formulas: Equations that express relationships between variables (e.g., area, perimeter).

• Problem Solving: Applying algebraic methods to real-world problems.

Linear Inequalities and Problem Solving

• Linear Inequalities: Expressions involving $<$, $>$, $\leq$, or $\geq$.

• Solving: Similar to equations, but reverse the inequality when multiplying/dividing by a negative.

• Example: Solve $-2x > 6$.

Exponents and Scientific Notation

• Negative Exponents: $a^{-n} = \frac{1}{a^n}$.

• Scientific Notation: Expressing numbers as $a \times 10^n$.

• Example: $0.00045 = 4.5 \times 10^{-4}$.

Polynomials

• Definition: An expression consisting of variables and coefficients, using only addition, subtraction, and multiplication.

• Adding/Subtracting: Combine like terms.

• Multiplying: Use distributive property or FOIL for binomials.

• Special Products: Recognize patterns such as $(a + b)^2 = a^2 + 2ab + b^2$.

• Dividing: Divide polynomials by monomials or use long division.

• Example: $(x + 2)(x + 3) = x^2 + 5x + 6$.

Rectangular Coordinate System and Graphing

• Coordinate System: The plane defined by the x-axis and y-axis.

• Graphing Linear Equations: Plotting solutions to equations of the form $y = mx + b$.

• Intercepts: Points where the graph crosses the axes.

• Example: The y-intercept of $y = 2x + 3$ is $(0, 3)$.

Slope and Rate of Change

• Slope: Measures the steepness of a line; $m = \frac{y_2 - y_1}{x_2 - x_1}$.

• Rate of Change: How one quantity changes in relation to another.

• Equations of Lines: Slope-intercept form: $y = mx + b$.

• Example: Find the slope between $(1,2)$ and $(3,6)$: $m = \frac{6-2}{3-1} = 2$.

Metric Conversions

• Metric System: Units such as meters, liters, and grams.

• Conversions: Use conversion factors to change units (e.g., $1\,\text{km} = 1000\,\text{m}$).

Assessment Schedule

• Quizzes and Tests: Regular quizzes and chapter tests are scheduled throughout the semester.

• Homework: Assignments are due at the end of each chapter.

• Final Exam: The final exam window is specified at the end of the course.

Important Notes

• Attendance: Required and part of the course grade.

• Deadlines: All late work and assessments must be completed by the specified final deadline.

Additional info: This agenda provides a logical progression through foundational algebra topics, preparing students for further study in mathematics.