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COURSE OF STUDY
This course begins with a review of basic concepts and skills studied in previous courses. As the course develops, some of the topics studied include inequalities and proof; linear equations and functions and graphs; products and factors of polynomials; simplifying rational expressions and equations, studying quadratic equations and functions, and studying the conic sections. Applications of these topics are more involved and are dealt with on a more abstract level. Theory is emphasized. SAT problems are included in Chapter Tests.
General Objectives:
At the end of this course, students will be able to:
A. Perform basic operations with real numbers
B. Solve Polynomial Equations and Word Problems
C. Solve inequalities in one variable
D. Analyze and graph linear equations
E. Recognize functions and relations
F. Multiply and factor polynomials, and apply to equations, inequalities, and word problems.
G. Simplify and perform the four arithmetic operations on rational expressions, and apply to the solving of fractional expressions.
H. Simplify radical expressions, and extend into the complex number system.
I. Solve quadratic equations using the quadratic formula and completing the square and analyze the roots of these equations.
J. Recognize and write equations of the conic sections
K. Evaluate real numbers with rational and negative exponents.
L. Realize that setting up and solving algebraic equations is needed in many science and engineering fields.
6. Material Covered Each Quarter:
First Semester: Chapters 1 – 4
First Quarter:
A. Language of Algebra – Simplifying Expressions
B. Operations with Real Numbers
C. Solving Equations and Solving Problems
D. Solving Inequalities
E. Absolute Value
Second Quarter:
A. Linear Equations and their Graphs
B. Linear Systems
C. Functions and Relations
D. Products and Factors of Polynomials
E. Solving Polynomial Equations and Inequalities
Second Semester: Chapters 5 – 7 and 9
Third Quarter:
A. Using the Laws of Exponents
B. Simplifying Rational Expressions
C. Fractional Equations
D. Roots and Radicals
E. Real Numbers and Complex Numbers
Fourth Quarter:
A. Solving Quadratic Equations
B. Roots of Quadratic Equations
B. Real Numbers and Complex Numbers
C. Quadratic Functions and their Graphs
D. Conic Sections: Circles, Parabolas, Ellipses, Hyperbolas
E. Systems of Equations
7. Specific Objectives:
At the end of Chapter 1, the students will be able to:
A. Graph real numbers on a line, compare numbers, and find their absolute value.
B. Simplify numerical expressions and evaluate algebraic expressions.
C. Apply field properties to the real numbers
D. Simplify polynomials through addition and subtraction.
E. Solve certain equations in one variable.
F. Solve word problems by using an equation in one variable.
At the end of Chapter 2 students will be able to:
A. Solve inequalities in one variable and apply to word problems.
B. Solve conjunction and disjunction of inequalities.
C. Solve equations and inequalities involving absolute value.
D. Deduce properties of real numbers from axioms.
E. Prove theorems involving inequalities and absolute value.
F. Practice answering exercises from old SAT tests.
At the end of Chapter 3 students will be able to:
A. Find solutions of open sentences in two variables.
B. Graph a linear equation in two variables
C. Find the slope of a line; to draw a line given its slope and a point on a line.
D. Find an equation of a line given its slope and a point on the line, or two points, or its slope and y-intercept.
E. Solve systems of linear equations and inequalities in two variables, and use this to solve word problems.
F. Find values of functions and linear functions, and to graph these and find their equations.
G. Draw the graph of a relation and to distinguish functions and relations.
At the end of Chapter 4, students will be able to:
A. Simplify expressions containing integral exponents
B. Apply special product methods to multiplying two polynomials.
C. Find the greatest common factor and least common multiple of integers and polynomials
D. Factor polynomials by using the greatest common factor, by recognizing special products, and by grouping terms, or by general factoring methods.
E. Solve polynomial equations and inequalities and apply to word problems.
At the end of Chapter 5 students will be able to:
A. Simplify quotients by use of laws of exponents.
B. Simplify expressions involving the exponent zero and negative exponents
C. Apply scientific notation and significant digits to factors and expressions.
D. Simplify, multiply, divide, add, and subtract rational expressions
E. Simplify complex fractions.
F. Solve equations and inequalities having fractional coefficients, and fractional equations.
At the end of Chapter 6, students will be able to:
A. Identify roots of real numbers.
B. Simplify radicals and expressions involving sums, products, and quotients of radicals.
C. Solve equations containing radicals.
D. Distinguish between a rational and irrational number using characteristics of decimal representations.
E. Use the number 1 to simplify square roots of negative numbers
F. Add, subtract, multiply and divide complex numbers.
At the end of Chapter 7 students will be able to:
A. Solve quadratic equations by completing the square, using the quadratic formula or factoring.
B. Determine the nature of the roots of quadratic equation by using its discriminant.
C. State relationship between the roots and coefficients of a quadratic equation.
D. Recognize and solve equations in quadratic form.
E. Graph parabolas and find their vertices and axes of symmetry.
F. Analyze a quadratic function, draw its graph, and find its minimum or maximum.
At the end of Chapter 8 the students will be able to:
A. Calculate the distance between any two points and the midpoint of the line segment joining them.
B. Distinguish equations for each of the conic sections: Circle, Ellipse, Parabola, and Hyperbola.
C. Write and analyze equations for each of the conic sections and graph these equations.
D. Use algebraic methods to find solutions of quadratic systems.
E. Solve systems of linear equations in three variables.
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