(Approved 11-30-01)
Intermediate Algebra is the course in which students further develop their algebra skills acquired in elementary algebra. The characteristics and properties of linear and quadratic functions are studied in detail. Students are introduced to exponential and logarithmic functions, conic sections, and non-linear systems. Students analyze problems using graphical, numerical, and algebraic approaches. They should be able to identify linear, quadratic, exponential relationships in these three different environments. Problem-solving skills are developed to encourage students to use their basic knowledge of algebra to explore problems.Simplifying Expressions
Required Core Outcomes
1. Factor an algebraic expression using a combination of greatest common factor, difference of two squares, sum or difference of two cubes, trinomial factoring, and grouping.
2. Use factoring procedures to solve equations and problems.
3. Know and apply the rules of integral and fractional exponents.
Strongly Recommended Outcomes
4. Use scientific notation in application problems.
Optional
5. Divide polynomials using synthetic division.
Functions
Required Core Outcomes
1. Evaluate functions using numerical and algebraic values.
2. Identify domain (inputs) and range (outputs) graphically for basic functions.
3. Interpret functional notation in a variety of application problems.
Strongly Recommended Outcomes
4. Write the equation of the inverse for linear, exponential, and logarithmic functions and show their relationship graphically.
5. Determine if a relation is a function by looking at a graph, table, or equation.
6. Combine two functions by adding, subtracting, multiplying, dividing, and composition.
Optional
7. Identify which functions are one-to-one by looking at their graphs.
Complex Numbers
Required Core Outcomes
1. Rewrite a radical expression with a negative radicand in the
form.
2. Combine complex numbers by adding, subtracting, multiplying, or dividing (by
only).
Strongly Recommended Outcomes
3. Use conjugates to divide complex numbers.
Optional
4. Evaluate powers of i.
Linear Functions, Equations, and Inequalities
Required Core Outcomes
1. Write the equation of a linear function if given two ordered pairs, two data points, or a linear graph. Use functional notation in the answer.
2. Solve compound linear inequalities joined by and or or, and of the form
. Express the answer algebraically, graphically, and using interval notation.
3. Write the equation of a linear function given the slope and a point on the line.
4. Express the slope as a rate of change using appropriate units.
5. Graph linear inequalities in two variables.
Strongly Recommended Outcomes
6. Solve an equation or inequality involving absolute value of the form
. Express answer in interval notation.
7. Write the equation of a linear function given a point and a line perpendicular or parallel to it.
8. Isolate a particular variable in a literal equation.
Quadratic Functions
Required Core Outcomes
1. Graph a quadratic function by finding the vertex, x- and y-intercepts.
2. Use quadratic formula to find exact values of a quadratic equation with irrational or imaginary solutions. Approximate the irrational solutions.
3. Given a quadratic model, find and interpret the maximum or minimum values, and the intercepts.
4. Solve an application problem involving quadratic equations.
Strongly Recommended Outcomes
5. Solve a quadratic inequality. Write the answer in interval notation.
Optional
6. Relate the discriminant in the quadratic formula to the graph of a parabola.
Rational Expressions and Equations
Required Core Outcomes
1. Add, subtract, multiply, divide rational expressions. Reduce the answers.
2. Simplify a complex fraction.
3. Solve a rational equation and check for extraneous solutions.
4. Solve an application problem that involves rational expressions.
Optional
5. Solve a rational inequality.
Radical Equations and Expressions
Required Core Outcomes
1. Solve a radical equation that produces a second-degree equation. Check for extraneous solutions.
2. Know the meaning of rational exponents and their relationship to radical form.
Strongly Recommended Outcomes
3. Simplify radical expressions with emphasis on cube roots and higher.
4. Rewrite radical expressions by rationalizing numerator or denominator.
5. Add, subtract, multiply, and divide radical expressions.
6. Solve application problems involving the Pythagorean Theorem.
Exponential and Logarithmic Equations and Expressions
Required Core Outcomes
1. Solve basic exponential and logarithmic equations. (
)
2. Evaluate basic logarithmic expressions, and convert between logarithmic and exponential form.
3. Solve an exponential equation that requires the use of logarithms.
4. Solve a logarithmic equation requiring properties of logarithms to condense. Be able to use base e (
) or base 10 (
) logarithms.
5. Solve for specific values of the independent or dependent variables in exponential and logarithmic expressions.
Strongly Recommended Outcomes
6. Graph a basic exponential or logarithmic function.
7. Know the graphical relationship between exponential and logarithmic functions.
8. Solve an application problem involving a given exponential or logarithmic model.
Optional
9. Change the base of logarithmic expressions to other bases.
10. Find a model for natural growth and decay problems.
System of Equations and Inequalities
Required Core Outcomes
1. Solve linear and nonlinear systems of equations algebraically and graphically.
Strongly Recommended
2. Solve a 3x3 system of equations.
3. Graph a 2x2 system of linear inequalities.
Optional
4. Solve an application problem in two variables.
Conic Sections
Required Core Outcomes
1. Graph the equation of a circle by plotting the center and using the radius.
2. Graph the parabola given by
or
by finding the vertex and another point.
Strongly Recommended Outcomes
3. Identify the graph of a second-degree equation. (no xy term)
4. Find the distance between two points.
5. Find the midpoint between two points.
Optional
6. Graph the equation of an ellipse or a hyperbola.