MATH 105 - Intermediate Algebra with Support
4 Credit: (5 lecture, 1 lab, 0 clinical) 6 Contact Hours:
This course explores algebraic concepts including linear, quadratic, exponential and logarithmic functions using numerical, graphical, and symbolic representations; sequences; and systems of equations. Students experience these concepts using a problem solving approach with appropriate technology. This course includes co-requisite support.
OFFERED: every semester
Course Goals/ Objectives/ Competencies:
Goal 1: Students will operate with three representation of function: numerically, graphically, and algebraically, using appropriate technology when applicable.
- Construct a table and graph an equation using a graphing calculator.
- Solve equations numerically (using a table) to the nearest tenth.
- Solve equations graphically.
- Build equations for and solve word problems.
- Use formulas to solve problems.
- Solve a formula or equation for one of its variables.
- Solve percent equations.
- Solve discount and mark-up problems.
- Solve percent of increase and decrease problems.
- Solve mixture problems.
- Solve problems involving distance.
- Solve problems involving money.
- Solve problems involving interest.
Goal 2: Students will apply function notation and concepts.
- Identify relations.
- Identify functions.
- Identify domains and ranges.
- Apply the vertical line test.
- Apply function notation.
- Graph linear functions.
- Write an equation of a line using function notation.
- Find equations of parallel and perpendicular lines.
- Identify and find equations of arithmetic sequences.
- Graph nonlinear functions.
- Shift functions vertically and horizontally.
- Reflect graphs.
- Solve direct variation problems.
- Solve inverse variation problems.
- Solve problems involving direct or inverse variation.
- Graph an “eyeballed” line of best fit for real world data.
- Use a calculator to find a line of best fit for real world data.
Goal 3: Students will solve systems of equations.
- Review solving 2x2 systems of equations graphically, by substitutions, and by elimination.
- Identify a 2x2 system of linear equations as having a single solution, an infinite number of solutions, or two solutions.
- Determine the most appropriate solution method to use given the characteristics of a particular system.
- Explain the algebraic results from solving 2x2 systems of equations whose graphs are parallel or coincident.
- Solve 3x3 systems of equations methodically.
- Solve applied problems using a 2x2 or 3x3 system of equations.
- Apply a Quantity-Rate Table to set up appropriate systems of equations.
Goal 4: Students will solve various types of inequalities.
- Define linear inequalities in one variable.
- Graph solution sets on a number line.
- Use interval notation.
- Solve linear inequalities.
- Solve inequality applications.
- Find the intersection of two sets.
- Solve compound inequalities containing “and.”
- Find the union of two sets.
- Solve compound inequalities containing “or.”
- Solve absolute value equations.
- Graph the solutions to linear inequalities in 2 variables.
- Solve systems of linear inequalities in 2 variables.
Goal 5: Students will apply exponent properties.
- Find square roots.
- Approximate square roots.
- Find cube roots.
- Find nth roots.
- Find m-root of an where a is any real number.
- Graph square root and cube root functions.
- Apply a1/n.
- Apply am/n.
- Apply a-m/n.
- Evaluate exponential expressions without a calculator.
- Use exponent rules to simplify expressions with rational exponents.
- Use rational exponents to simplify radical expressions.
- Apply product rule for radical expressions.
- Apply quotient rule for radical expressions.
- Simplify radicals.
- Use distance and midpoint formulas.
- Add or subtract radical expressions.
- Multiply radical expressions.
- Rationalize denominators with one or two terms.
- Rationalize numerators.
- Solve radical equations.
- Use Pythagorean Theorem to model problems.
- Write square roots of negative numbers in the form bi.
- Add and subtract complex numbers.
- Multiply complex numbers.
- Raise i to various powers.
Goal 6: Students will operate on rational expressions.
- Find the domain of a rational function.
- Use rational functions in applications.
- Simplify rational expressions.
- Write equivalent rational expressions.
- Multiply rational expressions.
- Divide rational expressions.
- Convert among units of measurements using unit conversion factors.
- Add and subtract rational expressions.
- Solve equations containing rational expressions.
Goal 7: Students will use the characteristics of quadratic functions to operate on them.
- Graph quadratic equations.
- Solve quadratic equations by factoring.
- Identify the domains and ranges of quadratic functions.
- Determine characteristics of quadratic graphs, including vertical and horizontal intercepts, vertices, and axes of symmetry.
- Determine where a quadratic function is increasing and decreasing.
- Determine the equation of a quadratic function given its table.
- Determine the equation of a sequence representing a quadratic function.
- Relate factors of quadratic functions to their zeros.
- Factor trinomials using the zeros of the related quadratic function.
- Determine x-intercepts of quadratic functions by factoring.
- Determine the equation for a quadratic function using x-intercepts and one other point.
- Describe the effect of “a” in y= ax2+bx+c.
- Describe the effect of “c” in y= ax2+bx+c.
- Identify horizontal and vertical shifts of y= ax2.
- Graph a quadratic function given its vertex form without constructing a table.
- Determine the equation of a parabola given its vertex and one other point.
- Change an equation from standard form to vertex form by setting it equal to “c” and averaging the x-values of the symmetrical points found.
- Solve minimum and maximum application problems.
- Use a calculator to determine a parabola of best fit for real world data that appears to be quadratic.
Goal 8: Students will solve quadratic equations using various methods.
- Solve quadratic equations numerically and graphically.
- Solve quadratic equations by factoring.
- Use the square root property to solve quadratic equations.
- Solve quadratic equations by completing the square.
- Solve quadratic equations using the quadratic formula.
- Use the discriminant to determine the number and types of solutions for a quadratic equation.
- Solve problems modeled by quadratic equations.
Goal 9: Students will apply properties of exponential and logarithmic functions.
- Identify the base and exponent in an exponential expression.
- Write geometric sequences.
- Determine whether or not a function is exponential, using ratios.
- Determine the first term and common ratio to find the nth term of a geometric sequence.
- Write regression and function equations for a geometric sequence.
- Graph exponential functions.
- Use a calculator to find a curve of best fit for real world data that appears to be exponential.
- Identify increasing and decreasing exponential functions.
- Explore how the base and coefficient of an exponential expression affect the graph of an exponential function.
- Solve equations of the form bx=by.
- Solve problems modeled by exponential equations.
- Model exponential growth and decay.
Goal 10: Students will apply inverse function properties.
- Determine whether a function is one-to-one.
- Apply the horizontal line test.
- Find the inverse of a one-to-one function.
- Find the equation of the inverse of a one-to-one function.
- Graph a function and its inverse.
- Determine whether two functions are inverses of each other.
- Write exponential equations in logarithmic form and vice versa.
- Solve logarithmic equations using exponential notation.
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