MAT-094 Fundamentals of Algebra
Upon completion the student will be able to:
- Evaluate expressions involving sums, differences, products, and quotients of signed numbers according to the agreement on order of operations.
- Apply the associative, commutative, inverse and identity properties for addition and for multiplication.
- Apply the distributive property.
- Simplify a general linear expression using addition, subtraction and multiplication by a constant.
- Solve linear equations having one solution, no solution or an infinite number of solutions.
- Solve linear equations by simplifying one or both of the linear expressions.
- Solve linear equations with expressions including constant denominators.
- Translate a verbal statement into a mathematical equation, and use the equations to solve a number problem.
- Use an equation of the form ax = b to solve percent, uniform motion, and unit price problems.
- Solve problems involving angle measures of a triangle, and perimeters of triangles and rectangles.
- Solve problems involving values and mixtures.
- Solve problems involving ratio and proportions.
- Evaluate a formula given numerical values for the variables.
- Solve a formula for a given variable.
- Solve linear inequalities in one variable and graph the solutions on the number line.
- Identify and interpret: coordinate system, number plane, origin, axis, quadrant, ordered pair, coordinate.
- Plot points with given coordinates in the number plane.
- Identify the coordinates of the ordered pair represented by a point in the number plane.
- Given a linear equation, construct a table of ordered pairs and draw the graph of the line.
- Define and interpret: slope, x-intercept, y-intercept.
- Find the y and x-intercepts of a line and use them to draw the graph.
- Use the slope formula to compute the slope of a line through two given points.
- Identify and interpret: the equation of a line in slope-intercept form, in point-slope form and in standard form.
- Determine the equation of a line when given: two points, a point and y-intercept, or a point and slope.
- Draw graphs of linear inequalities in two variables.
- Solve systems of two linear equations in two variables by graphing.
- Solve linear systems which have one solution, no solution and multiple solutions.
- Solve systems of two linear equations in two variables algebraically by the addition method.
- Solve systems of two linear equations in two variables algebraically by the substitution method.
- Solve applied problems using systems of two linear equations in two variables.
- State and apply the rules for exponents.
- Evaluate numerical expressions having integer exponents.
- Simplify expressions with variables having integer exponents.
- Express a number given in scientific notation in decimal notation.
- Write numbers in scientific notation.
- Perform operations on numbers in scientific notation and express the answers in scientific notation.
- Define and identify: monomial, binomial, polynomial.
- State the degree of a term, the degree of a polynomial, and write a polynomial in descending powers of a variable.
- Find the sum and difference of two polynomials.
- Multiply a polynomial by a monomial or a binomial.
- Divide a polynomial by a monomial.
- Use long division to divide a polynomial by a binomial.
- Define and identify: factor, common factor, greatest common factor.
- Factor out a common factor from a polynomial.
- Factor by grouping.
- Factor the difference of two squares as a sum and difference of binomials.
- Factor a perfect trinomial square as the square of a binomial.
- Factor a trinomial into two binomial factors.
- Factor a binomial or trinomial completely.
- Solve quadratic equations by factoring.
- Solve problems involving areas using quadratic equations which can be solved by factoring.
- Solve problems involving the Pythagorean Theorem.
STUDY SKILLS AND SUCCESSFUL STUDENT OBJECTIVES
Classroom Policy, Procedures, Resources
- SS1 Describe mathematics course attendance policy, classroom expectations and instructor contact information.
- SS2 Explain mathematics course requirements including materials, assignments, quiz/test/exam schedule,
- grading policy, exit requirements and prerequisite requirements.
- SS3 Work collaboratively with fellow students, tutors and instructor.
- SS4 Identify personal needs and use appropriate strategies and resources to meet those needs.
- SS5 Construct and follow a weekly schedule which allows sufficient time for school and study obligations.
Learning Styles and Learning Strategies
- SS6 Identify personal learning styles; plan study strategies and choose study materials which match personal learning styles.
- SS7 Identify and use active learning strategies which involve multiple learning channels.
- SS8 Identify characteristics of a good personal study environment.
- SS9 Identify and practice good study habits.
- SS10 Identify the helpful features of a mathematics textbook.
- SS11 Take notes in class using an organized note-taking method.
- SS12 Describe and use good test-taking practices.
- SS13 Use strategies to minimize test anxiety and develop a positive attitude.
- SS14 Use test results to identify math errors and test-taking errors.
- ML1 Use concrete models to understand and explain math concepts, relationships and problem situations.
- ML2 Construct number lines and other visual models.
- ML3 Read and understand information given in tables, diagrams and graphs.
- ML4 Show numerical information and relationships using tables, diagrams and graphs.
- ML5 Use calculators and computers appropriately as tools in learning mathematics.
- ML6 Identify and apply each step in the problem solving process.
- ML7 Identify and apply a variety of problem solving strategies.
- ML8 Use math terms and symbols correctly.
- ML9 Translate math symbols into words.
- ML10 Understand and apply formulas.
- ML11 Translate words into mathematical expressions.