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Aug 07, 2024
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# 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.

1. Construct a table and graph an equation using a graphing calculator.
2. Solve equations numerically (using a table) to the nearest tenth.
3. Solve equations graphically.
4. Build equations for and solve word problems.
5. Use formulas to solve problems.
6. Solve a formula or equation for one of its variables.
7. Solve percent equations.
8. Solve discount and mark-up problems.
9. Solve percent of increase and decrease problems.
10. Solve mixture problems.
11. Solve problems involving distance.
12. Solve problems involving money.
13. Solve problems involving interest.

Goal 2:  Students will apply function notation and concepts.

1. Identify relations.
2. Identify functions.
3. Identify domains and ranges.
4. Apply the vertical line test.
5. Apply function notation.
6. Graph linear functions.
7. Write an equation of a line using function notation.
8. Find equations of parallel and perpendicular lines.
9. Identify and find equations of arithmetic sequences.
10. Graph nonlinear functions.
11. Shift functions vertically and horizontally.
12. Reflect graphs.
13. Solve direct variation problems.
14. Solve inverse variation problems.
15. Solve problems involving direct or inverse variation.
16. Graph an “eyeballed” line of best fit for real world data.
17. Use a calculator to find a line of best fit for real world data.

Goal 3:  Students will solve systems of equations.

1. Review solving 2x2 systems of equations graphically, by substitutions, and by elimination.
2. Identify a 2x2 system of linear equations as having a single solution, an infinite number of solutions, or two solutions.
3. Determine the most appropriate solution method to use given the characteristics of a particular system.
4. Explain the algebraic results from solving 2x2 systems of equations whose graphs are parallel or coincident.
5. Solve 3x3 systems of equations methodically.
6. Solve applied problems using a 2x2 or 3x3 system of equations.
7. Apply a Quantity-Rate Table to set up appropriate systems of equations.

Goal 4:  Students will solve various types of inequalities.

1. Define linear inequalities in one variable.
2. Graph solution sets on a number line.
3. Use interval notation.
4. Solve linear inequalities.
5. Solve inequality applications.
6. Find the intersection of two sets.
7. Solve compound inequalities containing “and.”
8. Find the union of two sets.
9. Solve compound inequalities containing “or.”
10. Solve absolute value equations.
11. Graph the solutions to linear inequalities in 2 variables.
12. Solve systems of linear inequalities in 2 variables.

Goal 5:  Students will apply exponent properties.

1. Find square roots.
2. Approximate square roots.
3. Find cube roots.
4. Find nth roots.
5. Find m-root of an where a is any real number.
6. Graph square root and cube root functions.
7. Apply a1/n.
8. Apply am/n.
9. Apply a-m/n.
10. Evaluate exponential expressions without a calculator.
11. Use exponent rules to simplify expressions with rational exponents.
12. Use rational exponents to simplify radical expressions.
13. Apply product rule for radical expressions.
14. Apply quotient rule for radical expressions.
15. Simplify radicals.
16. Use distance and midpoint formulas.
17. Add or subtract radical expressions.
18. Multiply radical expressions.
19. Rationalize denominators with one or two terms.
20. Rationalize numerators.
21. Solve radical equations.
22. Use Pythagorean Theorem to model problems.
23. Write square roots of negative numbers in the form bi.
24. Add and subtract complex numbers.
25. Multiply complex numbers.
26. Raise i to various powers.

Goal 6:  Students will operate on rational expressions.

1. Find the domain of a rational function.
2. Use rational functions in applications.
3. Simplify rational expressions.
4. Write equivalent rational expressions.
5. Multiply rational expressions.
6. Divide rational expressions.
7. Convert among units of measurements using unit conversion factors.
8. Add and subtract rational expressions.
9. Solve equations containing rational expressions.

Goal 7:  Students will use the characteristics of quadratic functions to operate on them.

1. Graph quadratic equations.
2. Solve quadratic equations by factoring.
3. Identify the domains and ranges of quadratic functions.
4. Determine characteristics of quadratic graphs, including vertical and horizontal intercepts, vertices, and axes of symmetry.
5. Determine where a quadratic function is increasing and decreasing.
6. Determine the equation of a quadratic function given its table.
7. Determine the equation of a sequence representing a quadratic function.
8. Relate factors of quadratic functions to their zeros.
9. Factor trinomials using the zeros of the related quadratic function.
10. Determine x-intercepts of quadratic functions by factoring.
11. Determine the equation for a quadratic function using x-intercepts and one other point.
12. Describe the effect of “a” in y= ax2+bx+c.
13. Describe the effect of “c” in y= ax2+bx+c.
14. Identify horizontal and vertical shifts of y= ax2.
15. Graph a quadratic function given its vertex form without constructing a table.
16. Determine the equation of a parabola given its vertex and one other point.
17. 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.
18. Solve minimum and maximum application problems.
19. 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.

1. Solve quadratic equations numerically and graphically.
2. Solve quadratic equations by factoring.
3. Use the square root property to solve quadratic equations.
4. Solve quadratic equations by completing the square.
5. Solve quadratic equations using the quadratic formula.
6. Use the discriminant to determine the number and types of solutions for a quadratic equation.
7. Solve problems modeled by quadratic equations.

Goal 9:  Students will apply properties of exponential and logarithmic functions.

1. Identify the base and exponent in an exponential expression.
2. Write geometric sequences.
3. Determine whether or not a function is exponential, using ratios.
4. Determine the first term and common ratio to find the nth term of a geometric sequence.
5. Write regression and function equations for a geometric sequence.
6. Graph exponential functions.
7. Use a calculator to find a curve of best fit for real world data that appears to be exponential.
8. Identify increasing and decreasing exponential functions.
9. Explore how the base and coefficient of an exponential expression affect the graph of an exponential function.
10. Solve equations of the form bx=by.
11. Solve problems modeled by exponential equations.
12. Model exponential growth and decay.

Goal 10:  Students will apply inverse function properties.

1. Determine whether a function is one-to-one.
2. Apply the horizontal line test.
3. Find the inverse of a one-to-one function.
4. Find the equation of the inverse of a one-to-one function.
5. Graph a function and its inverse.
6. Determine whether two functions are inverses of each other.
7. Write exponential equations in logarithmic form and vice versa.
8. Solve logarithmic equations using exponential notation.

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