COMPETENCIES AND SKILLS:
UNIT I: Real Numbers and their Basic Properties
Section 1.1
• Graph subsets of the real numbers on the number line.
• Recognize and use the following and inequality notation:
• Recognize and use the following binary operation notation: +, -, ×, (a)(b), ab,
÷, /, a/b.
• Recognize absolute value notation.
• Simplify expressions involving absolute value.
• Identify opposites of real numbers.
Section 1.3
• Identify base and exponent and evaluate exponential expressions.
• Use order of operations to simplify expressions.
• Use geometric formulas to calculate perimeter and area of: square, rectangle,
triangle,
trapezoid, and circle.
• Use geometric formulas to calculate volumes of rectangular solid, cylinder,
pyramid,
cone, and sphere.
Section 1.4
• Add real numbers.
• Subtract real numbers.
• Solve applications involving addition and subtraction of real numbers.
Section 1.5
• Multiply real numbers.
• Divide real numbers.
• Solve applications involving multiplication and division of Real Numbers.
Section 1.6
• Translate written information to algebraic expression.
• Evaluate algebraic expressions.
• Identify: constant, variable, factor, term, ( numerical ) coefficient.
Section 1.7
• Recognize and use the following properties of Real numbers: Closure Property,
Commutative Property, Associative Property, Distributive Property, Property of
Identity,
Property of Inverses.
UNIT II: Equations - Inequalities
Students will solve linear equations and inequalities and
applications involving linear equations
and inequalities.
Section 2.1
• Use the addition property to solve a linear equation.
• Use the subtraction property to solve a linear equation.
• Use the multiplication property to solve a linear equation.
• Use the division property to solve a linear equation.
• Translate an application involving percent to an equation and solve.
Section 2.2
• Solve an equation that involves the use of two or more properties .
• Use the Least Common Denominator (LCD) to "clear an equation of fractions ."
• Solve application problems.
Section 2.3
• Use the distributive property to remove parentheses .
• Recognize and combine like terms.
• Use strategies for simplifying in solving linear equations.
• Identify identities and contradictions.
Section 2.4
• Solve an application by writing and solving an equation.
• Solve an integer application.
• Solve a geometry application.
• Solve an investment application. (Optional)
Section 2.5
• Solve liquid and dry-measure applications.
• Solve a uniform motion application.
Section 2.6
• Solve a literal equation /formula for a specified variable.
• Solve an application involving a formula.
Section 2.7
• Use properties of inequalities to solve a simple linear inequality.
• Use properties of inequalities to solve a double inequality.
• Solve applications involving linear inequalities.
UNIT III: Polynomials and Factoring
Section 4.1
• Identify the base and exponent in an exponential expression.
• Evaluate an exponential expression.
• Use the properties of exponents to simplify exponential expressions.
Section 4.2
• Simplify expressions involving zero exponents
• Simplify expressions involving negative exponents .
Section 4.3
• Write standard numbers in scientific notation.
• Convert from scientific notation to standard form.
• Multiply and divide using scientific notation.
Section 4.4
• Classify a polynomial according to the number of terms.
• Identify the degree of a polynomial.
• Evaluate a polynomial when expressed in f(x) form.
Section 4.5
• Add polynomials.
• Subtract polynomials.
Section 4.6
• Multiply polynomials.
• Find special products by using the special product formulas.
• Solve application problems involving multiplication of polynomials.
Section 4.7
• Divide a polynomial by a monomial.
Section 4.8
• Divide a polynomial by a polynomial.
Section 5.1
• Factor out a common factor.
• Factor out a negative factor.
• Define a quadratic equation .
• Define/Utilize the zero factor property for real numbers.
• Solve a quadratic equation by factoring.
• Factor by grouping .
Section 5.2
• Factor the difference of two squares.
• Define/identify an irreducible/prime polynomial.
• Solve quadratic equations by factoring.
Section 5.3
• Recognize/factor a perfect square trinomial.
• Factor a general trinomial with lead coefficient = 1.
• Define/identify a prime trinomial.
• Solve quadratic equations by factoring.
Section 5.4
• Factor a trinomial with lead coefficient ≠ 1.
• Solve quadratic equations by factoring.
Section 5.5
• Factor the sum and difference of cubes .
Section 5.6
• Define/use the steps for factoring a polynomial.
Section 5.7
• Use the Zero-Factor Property to solve equations.
• Solve quadratic equations by factoring.
Section 5.8
• Solve applications involving factoring.
UNIT IV: Graphing Linear Equations
Section 3.1
• Identify the following elements of the rectangular coordinate system: origin,
x-axis
(abscissa), y-axis (ordinate), quadrant I, quadrant II, quadrant III, quadrant
IV.
• Graph an ordered pair on the rectangular coordinate system.
• Identify the coordinates of a point on the rectangular coordinate system.
Section 3.2
• Graph a linear equation in two variables by plotting ordered pairs.
• Find x- and y-intercepts for a linear equation in two variables.
• Use x- and y-intercepts to graph a linear equation in two variables.
• Recognize the equation of a line parallel to the x- or y-axis.
Section 8.2
• Find the slope of a non-vertical line.
• Identify the slope of a horizontal or vertical line.
• Identify the relationships between the slopes of parallel lines.
• Identify the relationship between the slopes of perpendicular lines.
Section 8.3
• Define the slope-intercept form of the equation of a line.
• *Define function; domain of a function; range of a function; independent
variable;
dependent variable.
• *Determine if a graph in two variables represents a function.
• *Identify the domain and range of a function.
• *Interpret functional notation "y = f(x)."
STUDENT LEARNING OUTCOMES for MAT 101
The student should be able to:
* Understand the Real Number System and the various
subsets of the Real Number
System.
* Solve linear equations in one variable and more than one
variable (i.e., formulas).
* Solve linear inequalities.
* Understand and use the properties of integer exponents.
* Operate (add, subtract, multiply & divide) on polynomial
expressions.
* Factor polynomial expressions or identify as prime.
* Graph linear equations in two variables.
* Use simple problem solving techniques to solve word
problems.
