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**Math 154 Learner Outcomes**

(Approved 12-14-01)

In an Elementary Algebra course students are introduced to algebra skills which include arithmetic of polynomials. Students are expected to solve linear equations, to graph linear equations in two variables, to solve linear 2x2 systems, to solve second-degree equations by factoring and by using the quadratic formula. Students begin to develop critical thinking skills in using algebra to solve application problems.

*Algebraic Expressions*

**Required Core Outcomes**

1. Simplify algebraic expressions using distributive property, order of operations, and combining like terms.

2.Evaluate algebraic expressions by substituting rational numbers for the variable.

3.Simplify expressions involving whole number exponents using properties for multiplying and dividing powers with like bases, raising a power to a power, and raising a product or quotient to a power.

4.Translate a phrase to an algebraic expression.

*Optional*

5.Interpret negative exponents and simplify expressions by rewriting expression without the negative exponents.

*Linear Equations and Inequalities*

**Required Core Outcomes**

1.Solve a linear equation in one variable using algebraic properties to isolate the variable.

2.Solve a linear inequality in one variable and graph its solution on the number line.

3.Determine whether an ordered pair is a solution to a linear equation in two variables.

4.Solve an application problem by setting up a linear equation or inequality in one variable, solving it, and interpreting your answer. Examples may include simple interest, distance/rate/time, discount, perimeter, area, and car rentals.

5.Solve a given formula (with first degree variables) for a designated variable.

*Optional *

6.Solve a linear equation by inspection and/or a table.

*Linear Relationships*

**Required Core Outcomes**

1.Plot ordered pairs on the Cartesian plane.

2.Graph a linear equation in two variables by finding ordered pairs that satisfy the equation and plotting the corresponding points.

3.Given a linear equation in two variables, locate and label the intercepts of the corresponding line by using graphing and algebraic techniques.

4.Given a linear equation in two variables, find the slope and the y-intercept and use these values to graph the line.

5.Find the slope of the line determined by two given points in the plane using the graph and also by using the slope formula.

6.Given a linear equation representing an application problem find the slope and interpret it as a rate of change using appropriate units. Also find and interpret the y-intercept and the x-intercept.

7.Determine the slope of a horizontal line and recognize that a vertical line has undefined slope.

8.Given the graph of a horizontal or vertical line, write the equation of the line.

9.Sketch lines with positive slopes, negative slopes, undefined slope, and zero slope.

10.Given a linear equation in two variables that represents an application, graph the line, appropriately labeling the axes. Use the graph to estimate or predict information.

11.Given the slope and y-intercept of a line or given the graph of a line, write the linear equation of the line using _{}

*Optional*

12.Given the coordinates of a point on a line, and its slope, write an equation of the line using the point-slope form: _{}

13.Given two points on a line, write the equation of the line.

*Polynomials*

**Required Core Outcomes**

1. Given a polynomial in one variable identify the terms, the degrees of the terms, the coefficients, the constant, and the degree of the polynomial.

2.Identify monomials, binomials, and trinomials.

3.Evaluate polynomial expressions for specified values of the variable.

4.Add and subtract polynomials in one variable.

5.Multiply and square monomials, binomials, and trinomials in one variable.

6.Divide a polynomial by a monomial.

7.Divide a trinomial by a binomial.

8.In a polynomial expression identify the greatest common factor and factor the expression.

9.Factor polynomials, if possible, using greatest common factor, difference of squares, and trinomial factoring methods.

10.Factor 1 out of polynomial and compare the results with original polynomial

*Optional*

11.Factor a four term polynomial expression by grouping.

*Quadratic Equations*

**Required Core Outcomes**

1. Solve quadratic equations by using factoring techniques.

2.Find real solutions to quadratic equations by using the square root method.

3.Find real solutions to quadratic equations by using the quadratic formula.

4.Solve application problems that involve the Pythagorean theorem.

*Strongly Recommended Outcomes*

5.Solve other application problems that result in a quadratic equation requiring the quadratic formula.

*Optional*

6.Complete the square to solve a quadratic equation.

*Systems of Equations*

**Required Core Outcomes**

1.Know the graphical relationship between a 2x2 system of linear equations and the solution to the system.

2.Find the solutions to 2x2 systems using the substitution method and the elimination method.

3.Solve an application problem by setting up a system of two linear equations and solving the system. Interpret your answer. Examples may include comparing car rental prices, total value, and mixture problems.

*Optional: *

4.Identify dependent and inconsistent 2x2 linear systems.

*Square Roots and Radical Expressions*

**Required Core Outcomes**

1.Find square roots of perfect squares

2.Know how the processes of squaring a number and taking the square root are related to each other.

3.Find square roots using a calculator and know the difference between approximate and exact answers.

4.Simplify square root expressions. (Example: _{})

5.Multiply square roots and simplify the answer.

6.Add radicals and leave answers in exact form.

7.Solve simple radical equations. (ex. _{})

*Rational Expressions and Equations*

**Required Core Outcomes**

1.Reduce rational expressions by factoring.

2.Multiply and divide rational expressions by factoring.

3.Add and subtract rational expressions with the same denominators.

4.Find the lowest common denominator of two rational expressions with unlike denominators and add or subtract the expressions.

5.Solve rational equations, including proportions.

6.Solve application problems using rational equations. Examples may include work, distance/rate/time, similar triangles, and applied models.

*Optional*

7. Find the restrictions on the values used to evaluate a rational expression.