# DEFINING LEARNER OUTCOMES FOR INTERMEDIATE ALGEBRA

The following learner outcomes for Intermediate Algebra are classified into 3
categories.

These core outcomes represent the fundamental concepts of
Intermediate algebra which students should be able to do at the end of this course. Some
of these concepts are new to the students while others have been introduced in
elementary algebra and now require greater depth.

Students should have experience with these outcomes in order to
begin developing familiarity with the ideas and confidence performing related skills.
Indicators for these outcomes would be on midterms but not necessarily on the final
exam.

These outcomes are optional. An instructor may expect these of
students during the course but not in lieu of a C1 or C2 outcome.

Simplifying Expressions

C1 1. Factor an algebraic expression using a combination of greatest common
factor, difference of two squares , sum or difference of two cubes , and/or
trinomial factoring
C1 2. Use factoring procedures to solve equations and problems.
C1 3. Know and apply the rules of integral and fractional exponents.
C2 4. Use scientific notation in application problems.
O 5. Divide polynomials using synthetic division.

Complex Numbers

C1 1. Rewrite a radical expression with a negative radicand in the a + bi form.
C1 2. Combine complex numbers by adding, subtracting , multiplying, or dividing
(by bi only).
C2 3. Use conjugates to divide complex numbers.
O 4. Evaluate powers of i.

Functions

C1 1. Evaluate functions using numerical and algebraic values.
C1 2. Identify domain (inputs) and range (outputs) graphically for basic functions.
C1 3. Interpret functional notation in a variety of application problems.
C2 4. Write the equation of the inverse for linear, exponential, and logarithmic
functions and show their relationship graphically.
C2 5. Determine if a relation is a function by looking at a graph, table, or equation.
C2 6. Combine two functions by adding, subtracting, multiplying, dividing, and
composition.
O 7. Identify which functions are one-to-one by looking at their graphs.

Linear Functions , Equations, and Inequalities

C1 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.
C1 2, Solve compound linear inequalities joined by and or or, and of the form
C<ax + b <d. Express answer algebraically, graphically, and using interval
notation.
C1 3. Write the equation of a linear function given the slope and a point on the l
line.
C1 4. Express the slope as a rate of change using appropriate units.
C2 5. Solve an equation or inequality involving absolute value of the form lax + bl .
C2 6. Graph linear inequalities in two variables
C2 7. Write the equation of a linear function given a point and a line perpendicular
or parallel to it.
C2 8. Isolate a particular variable in a literal equation.

C1 1. Graph a quadratic function by finding the vertex, x- and y-intercepts.
C1 2. Use quadratic formula to find exact values of a quadratic equation with
irrational or imaginary solutions. Approximate the irrational solutions.
C1 3. Given a quadratic model, find and interpret the maximum or minimum
values, and the intercepts.
C1 4. Solve an application problem involving quadratic equations.
C2 5. Solve a quadratic inequality. Write the answer in interval notation.
O 6. Relate the discriminant in the quadratic formula to the graph of a parabola.

Rational Expressions and Equations

C1 2. Simplify a complex fraction.
C1 3. Solve a rational equation and check for extraneous solutions.
C1 4. Solve an application problem that involves rational expressions.
O 5. Solve a rational inequality.

C1 1. Solve a radical equation that produces a second-degree equation. Check for
extraneous solutions.
C1 2. Know the meaning of rational exponents and their relationship to radical
form.
C2 3. Simplify radical expressions with emphasis on cube roots and higher .
C2 4. Rewrite radical expressions by rationalizing numerator or denominator.
C2 6. Solve application problems involving the Pythagorean Theorem.
O 7. State the domain of radical functions.

Exponential and Logarithmic Equations and Expressions

C1 1. Solve basic exponential and logarithmic equations.
C1 2. Evaluate basic logarithmic expressions, and convert between logarithmic and
exponential form.
C1 3. Solve an exponential equation that requires the use of logarithms.
C1 4. Solve a logarithmic equation requiring properties of logarithms to condense.
Be able to use base or base logarithms.
C1 5. Solve for specific values of the independent or dependent variables in
exponential and logarithmic expressions.
C2 6. Graph a basic exponential or logarithmic function.
C2 7. Know the graphical relationship between exponential and logarithmic
functions.
C2 8. Solve an application problem involving a given exponential or logarithmic
model.
O 9. Change the base of logarithmic expressions to other bases.
O 10. Find a model for natural growth and decay problems.

System of Equations

C1 1. Solve linear and nonlinear systems of equations algebraically and graphically.
O 2. Solve an application problem in two variables.

Conic Sections

C1 1. Graph the equation of a circle by plotting the center and using the radius.
C1 2. Graph the parabola given by f (x) = ax2 + bx + c or x = ay2 + by + c by finding the
vertex and another point.
C2 3. Identify the graph of a second-degree equation. (no xy term )
C2 4. Find the distance between two points.
C2 5. Find the midpoint between two points.
O 6. Graph the equation of an ellipse or a hyperbola .

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