MAT-094 Objectives

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.

Time Management

  • 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.

Homework/Study Habits

  • SS8 Identify characteristics of a good personal study environment.
  • SS9 Identify and practice good study habits.

Textbook/Notebook

  • SS10 Identify the helpful features of a mathematics textbook.
  • SS11 Take notes in class using an organized note-taking method.

Tests

  • 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.

Math Models

  • 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.

Problem Solving

  • ML6 Identify and apply each step in the problem solving process.
  • ML7 Identify and apply a variety of problem solving strategies.

Math Language

  • ML8 Use math terms and symbols correctly.
  • ML9 Translate math symbols into words.
  • ML10 Understand and apply formulas.
  • ML11 Translate words into mathematical expressions.