Course Outline Seattle Central Community College

Transcription

1 Course Prefix & No.: MATH 080 Division: Science & Math Maximum Class Size: 30 Course Outline Seattle Central Community College Title: Preparatory Mathematics Course length: 11 weeks Program/Department: Mathematics Prerequisite(s): Eligibility for Math 081, 084, or 085 Credits: 5 Total Contact Hours: 55 Lecture: 55 Lab: Clinical: Other: Course Description Learning Outcomes (11 h. = 1 cr.) Mode(s) of Delivery: On campus self-contained Math 080 is taught using ALEKS, a mastery based, computerized instructional application. ALEKS will assess your current math knowledge and create a custom plan for your learning. ALEKS provides the opportunity to complete more than one level of developmental math in one quarter. ALEKS students must be eligible to take MATH 081, 084, 085, 087, or 096. Online textbook required. ALEKS courses may be taken one time only Course Competencies (Evidence of Learning): Depending on the course level they complete, students will be able to: Math 081 Perform arithmetic (add, subtract, multiply, divide, round) on fractions, decimals, and signed numbers [Connect] Describe and properly use the order of operations with fractions, decimals, and signed numbers [Connect] Identify and use the properties of arithmetic and algebra (commutative, associative, distributive, properties with zero and one, addition and multiplication properties of equality) [Connect] Compare fractions, decimals, and percents and use inequalities [Connect] Set up and solve problems involving fractions and decimals and their applications [Connect] Set up and solve proportions and their applications [Connect] Set up and solve percent problems and their applications [Connect] Evaluate and simplify algebraic expressions and formulas [Connect] Solve simple linear equations [Connect] Identify and apply formulas of perimeter, area and volume to simple geometric shapes [Connect] Convert among different units of measurement (Metric and U.S.) [Connect]

2 Math 084: Simplify and evaluate algebraic expressions [Connect] Solve linear equations and implicit equations, including clearing fractions [Connect] Solve and graph linear inequalities (if time permits) [Connect] Write equations of lines using slope-intercept form, and point-slope form [Connect] Given the equation of a line, students should be able to produce a graph, identify all intercepts and the slope and explain the meaning of the slope and intercepts in the context of the problem, with appropriate units [Connect] Solve systems of linear equations in two variables by graphing, by substitution method and addition method [Connect] Use formulas for perimeter, area, and volume to solve geometry problems [Connect] Solve a variety of applications, using variables and algebraic expressions to clearly represent all unknowns, and attaching units where appropriate [Connect] Communicate with proper use of correct mathematical terminology and notation Math 085: Simplify polynomial expressions [Connect] Factor polynomial expressions [Connect] Solve quadratic equations using factoring, by completing the square, by extraction of roots and using the quadratic formula [Connect] Graph a parabola [Connect] Simplify rational expressions [Connect] Solve equations with rational expressions and identify extraneous solutions [Connect] Simplify radical expressions [Connect] Solve equations with radical expressions and identify extraneous solutions [Connect] Solve a variety of applications, displaying proper identification of the variables introduced, and attaching units where appropriate [Connect] Communicate with proper use of correct mathematical terminology and notation Math 098: Linear Functions: determine the equation of a line and line of best fit, explain rate of change and intercepts in context, graph the function, express the solution sets in appropriate notation and explain the solutions in context [Connect] Quadratic Functions: solve quadratic functions algebraically and graphically, determine max/min points, and explain the significance of intercepts and max/min points in context [Connect]

3 Exponential & Logarithmic Functions: graph exponential functions and interpret them in context; convert between exponential and logarithmic forms of an equation and explain their relationship; solve exponential and logarithmic equations and explain them in context [Connect] Mathematical Modeling: (using graphing calculator) find regression lines based on data provided in a problem, use regression line to make predictions, create appropriate graph (window), identify whether a data set is linear, quadratic, exponential, or logarithmic form and use their knowledge of the type of data set to an application setting. [Connect] Systems of Equations: solve systems of equations and explain the significance of the solutions [Connect] Evaluate functions: determine domain and range, use vertical line test, interpret the graph of functions [Connect] Radical Expressions: simplify radical expressions, rationalize denominators, and convert to exponential form [Connect] Optional - Rational Equations and Functions: simplify complex fractions and rational expressions, solve rational equations, recognize extraneous roots, explain their significance in context [Connect] Program/Degree Outcomes Topical Outline and/or Major Divisions This course addresses the following program or degree outcomes: Have knowledge and skills in critical thinking and quantitative analysis Have effective skills for in-person interactions with individuals and within groups. Understand methods and modes of inquiry specific to mathematics Demonstrate effective oral and written communication, teamwork and collaboration in mathematical settings Demonstrate academic honesty and ethical behavior This course covers the following topics: Order of operations with fractions, decimals, and signed numbers Properties of arithmetic (commutative, associative, distributive, properties with zero and one) Arithmetic (add, subtract, multiply, divide) with fractions and mixed numbers Prime factorizations and least common denominators Arithmetic (add, subtract, multiply, divide, place value, round) with decimals Ratio, rate, and proportion Setting up and solving proportions; applications Converting between fractions, percents, and decimals and comparing these quantities using inequalities

4 Setting up and solving percent problems; applications Arithmetic (add, subtract, multiply, divide, order) with signed numbers Algebraic expressions and formulas (evaluating and simplifying) Properties of algebra (commutative, associative, distributive, addition and multiplication properties of equality) Simple linear equations (solving, checking, applications) Formulas of perimeter, area and volume for geometric shapes Units of Measurement (English, metric, length, liquid, weight, converting) Introduction to the language of algebra Brief review of number skills, including manipulation of fractions and integers, and order of operations Simplify algebraic expressions, using commutative, associative, distributive properties, etc. Solve linear equations, using addition and multiplication properties of equality Applications of linear equations,which may include: investment, mixture, uniform motion, ratio and proportion, angles - complement, supplement problems, and geometric problems Equations and graphs of lines: rectangular coordinate system, intercepts, slopes, slope intercept form, point slope form, linear models, meaning of slope and y-intercept. Systems of linear equations: solve by graphing, by substitution method, by addition method, and application of systems. Introduction to polynomial expressions, including arithmetic operations and factoring Rules for integer exponents Solving polynomial equations by factoring Simplify expressions and solve equations involving rational expressions Simplify expressions and solve equations involving square roots Solve quadratic equations using factoring, extraction of roots, completing the square and the quadratic formula Graphs of quadratic equations: vertex, axis of symmetry, intercepts Solve applications and word problems in a variety of contexts Exponents: integer and rational. Scientific notation. Polynomial arithmetic: addition, subtraction and multiplication of single variable polynomials. Linear functions: graphs; equations; slope; slope-intercept form of equations; writing equations for lines; (optional: inequalities) solving graphically and algebraically. Linear systems of equations (2 2) and their applications. Quadratic functions: solving quadratic equations by factoring, completing the square, the quadratic formula, graphing; vertex:

5 maximum, minimum values of quadratic functions; applications of quadratic functions. Radicals and rational exponents: rules for radicals; simplifying radical expressions; operations with rational exponents confined to one variable case. Exponential functions of form f(x) = ab x, graphing the effect of the values of a, b and x on the graph of the function; logs and the use of the log key on the calculator to solve exponential equations. Applications will be emphasized along with the algebra skills necessary to treat the included applications. Distribution Area Additional Information Students are required to pay a fee for access to online computer software (ALEKS). Students will pay that fee directly to the vendor or purchase an access code from the bookstore. CAC Use Only None Special Designation (s) Outline updated by: Maryann Firpo Date: April 2015 SCCC Math Dept Approval: XXX SCCD District Approval: XXX