Beginning algebra, similar to a standard first-year high school algebra course. Includes a review of signed numbers and their properties, equations and inequalities in one variable, graphing linear equations, systems in two variables, integer exponents, rational and polynomial expressions, quadratic equations, the quadratic formula and graphing parabolas.
80.000-90.000 Total Hours
0.000 Total Hours
160.000-180.000 Total Hours
80.000-90.000 Total Hours
Prerequisite: MATH 004 or MATH 041 or or equivalent based on SBCC's Assessment Center placement via multiple measures. Prerequisite or Corequisite: None Concurrent Corequisite: None Course Advisories: None Limitation on Enrollment: None
Course Objectives:
Demonstrate skills in addition, subtraction, multiplication, and division of algebraic expressions.
Demonstrate skills in addition, subtraction, and multiplication of polynomials.
Demonstrate skills in applying rules of integer exponents.
Construct equations and graphs of lines.
Demonstrate skills in solving linear, quadratic, and literal equations.
Demonstrate skills in solving systems of linear equations.
Demonstrate skills in solving linear inequalities.
Use the above algebra to analyze word problems and find solutions.
Construct graphs of parabolas.
Student Learning Outcomes
Distinguish between different operations (addition, subtraction, multiplication, division, integer exponents, square roots) of algebraic expressions, and identify and use relevant properties to simplify expressions.
Given an equation (linear, quadratic, rational, literal), identify type of equation and method for solving, and then solve the equation.
Translate algebraic expressions (including ordered pairs) and equations into English phrases and sentences, and vice versa.
Identify the unknown(s) in application problems (what is being asked?), set up equation(s) or inequality, solve, and interpret solution(s).
Construct graphs of lines and parabolas.
Derive equations of lines from descriptive data.
For each topic in the following course outline, a major goal will be to emphasize word problems including dimensional analysis (units) and estimating and checking reasonableness of solutions.
Linear equations and inequalities in one variable
Expressions vs. Equations/Inequalities
Equivalent Equations
Literal Equations
Linear Inequalities
Equations in two variables with emphasis on linear equations in two variables
Coordinate axes and plotting data
Graphing equations (including nonlinear ones) in two variables by constructing tables of values
Graphing Ax + By = C
Slope of a line interpreted geometrically
Slope of a line interpreted as a rate
Slope - intercept form of linear equations
Deriving equations of line from descriptive data
2 x 2 Linear Systems
Graphical methods
Algebraic methods
Systems without unique solutions
Exponents
Properties of Exponents
Negative exponents
Scientific Notation
Operations with polynomials and rational expressions
Definition of polynomials and other terminology including coefficient, degree, and term
Addition, subtraction, and multiplication of polynomials
Division by monomials
Factoring polynomials including common factors, difference of squares, and basic trinomials
Factoring by grouping
Domain of rational expressions
Reduction, multiplication, and division of rational expressions with monomial denominators and linear binomial denominators
Least Common Denominator, adding, and subtracting of rational expressions with monomial denominators and linear binomial denominators
Solving rational equations with monomial and linear binomial denominators
Proportions
Quadratics
Definition of Square roots
Simplifying square roots (optional)
Solving quadratic equations by the square root method
Pythagorean Theorem (as an application of quadratic equations)
Solving quadratic equations using the Quadratic Formula
Solving quadratic equations by factoring
Graphing y = ax2 + bx + c
Relationship between roots of ax2 + bx + c = 0 and x-intercepts of y = ax2 + bx + c
Methods of Instruction
Directed Study
Distance Education
Lecture
Mediated Learning
Lecture and/or guided group work are the methods of instruction to be used, along with student problem-solving. Students are expected to work outside of class on assigned exercises as well as on supplementary reading from the text.
Daily assignments consisting of problems like the ones below.
1) Simplify 4(x +7)-2(x - 4)
2) Solve 4(x + 7) - 2(x - 4) = 7
3) Regular admission tickets to a movie theater are $9.50 a piece, and senior admission tickets are $7 each. A total of 180 tickets were sold on a Saturday, and the total collected was $1597.50. Determine the number of regular admission tickets and the number of senior admission tickets that were sold.
These problems can be found in a textbook or on a web-based assignment.
A. Appropriate Readings: Students are required to read assigned chapters in texts or on computer.
B. Writing Assignments: Students must work assigned mathematical problems requiring the manipulation of abstract symbols.
C. Appropriate Outside Assignments: Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete frequent homework assignments.
D. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills such as equation solving and graphing which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. Critical thinking will also be emphasized through numerous treatments of word problems.
A student's grade will be based on multiple measures of performance in the solving of algebra problems. Such measures will include at least three exams and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student's dexterity with algebra skills and familiarity with mathematical vocabulary.
Instructors are required to provide students, in writing, with a course syllabus in accordance with district policy, which will include the specific procedures by which students will be evaluated. These procedures must be consistent with the objectives and course content stated above.