Algebra B

Course Description

Algebra B will provide the necessary skills and concepts to build a solid foundation in order to further study mathematics and sciences.  Also, it provides the ability to organize and express thoughts more concisely.  A good working knowledge of Pre–Algebra will strengthen general math skills and provide the background to study Algebra.  Once factoring and solving equations are understood, word problems involving rational expressions can be added.  This makes Algebra even more powerful in real–life applications. 

Credits: 5

University of California A-G Approval

State Standards

High School Exit Exam

Course Content

Unit 6 - Rational Equations

California Mathematics Curriculum Standards

Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable. (Algebra I 1.0)

Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a power. They understand and use the rules of exponents. (Algebra I 2.0)

Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x –5) + 4(x–2) = 12. (Algebra I 4.0)

Students solve multi-step problems, including word problems, involving linear  equations and linear inequalities in one variable and provide justification for each step.  (Algebra I 5.0)

Students simplify fractions with polynomials in the numerator and
denominator by factoring both and reducing them to the lowest terms.
(Algebra I 12.0)

Students add, subtract, multiply, and divide rational expressions and
functions.  Students solve both computationally and conceptually challenging
problems by using these techniques. (Algebra I 13.0)

Students solve a quadratic equation by factoring or completing the square. (Algebra I 14.0)

Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. (Algebra 15.0)

Unit Objectives

Upon completion of this Unit, students will:

• Understand powers and power rules.
• Use and understand scientific notation.
• Simplify rational expressions.
• Solve rational equations.
• Solve word problems including work, investment, and mixture problems.
• Understand writing in mathematics (students are required to write a short essay).

Unit 7 - Systems of Equations

California Mathematics Curriculum Standards

Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). (Algebra I 6.0)

Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations. by using the point-slope formula. (Algebra I 7.0)

Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. (Algebra I 9.0)

Unit Objectives

Upon completion of this Unit, students will:

• Graph and solve inequalities.
• Read and graph ordered pairs of numbers on a coordinate plane.
• Graph an equation of a line.
• Find the slope of a line.
• Write equations of lines from given information.
• Use direct variations in solving problems.

Unit 8 - Graphing and Functions

California Mathematics Curriculum Standards

Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). (Algebra I 6.0)

Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations. by using the point-slope formula. (Algebra I 7.0)

Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. (Algebra I 9.0)

Unit Objectives

Upon completion of this Unit, students will:

• Graph systems of equations.
• Solve systems by the substitution method.
• Solve systems by the addition method.
• Solve motion, mixture, and various other problems using systems.

Unit 9 - Squares, Square Roots, and Quadratic Equations

California Mathematics Curriculum Standards

Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable. (Algebra I 1.0)

Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a power. They understand and use the rules of exponents. (Algebra I 2.0)

Students solve equations and inequalities involving absolute values. (Algebra I 3.0)

Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x –5) + 4(x–2) = 12. (Algebra I 4.0)

Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). (Algebra I 6.0)

Students add, subtract, multiply, and divide monomials and polynomials.  Students solve multi-step problems, including word problems, by using these techniques. (Algebra I 10.0) 

Students add, subtract, multiply, and divide rational expressions and
functions.  Students solve both computationally and conceptually challenging
problems by using these techniques. (Algebra I 13.0)

Students solve a quadratic equation by factoring or completing the square. (Algebra I 14.0)

Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements. (Algebra I 25.0)

Unit Objectives

Upon completion of this Unit, students will:

• Find square roots of a number.
• Use the square root table.
• Simplify square roots.
• Add, subtract, multiply, and divide expressions with radicals.
• Solve quadratic equations by factoring and by completing the square.
• Solve equations using square roots.

Unit 10 - Quadratic Equations and Functions

California Mathematics Curriculum Standards

Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a power. They understand and use the rules of exponents. (Algebra I 2.0)

Students solve multi-step problems, including word problems, involving linear  equations and linear inequalities in one variable and provide justification for each step.  (Algebra I 5.0)

Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). (Algebra I 6.0)

Students add, subtract, multiply, and divide monomials and polynomials.  Students solve multi-step problems, including word problems, by using these techniques. (Algebra I 10.0) 

Students add, subtract, multiply, and divide rational expressions and
functions.  Students solve both computationally and conceptually challenging
problems by using these techniques. (Algebra I 13.0)

Students solve a quadratic equation by factoring or completing the square. (Algebra I 14.0)

Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. (Algebra 15.0)

Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. (Algebra 16.0)

Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements. (Algebra I 25.0)

Unit Objectives

Upon completion of this Unit, students will:

• Use the quadratic formula to solve quadratic equations.
• Use quadratic equations to solve word problems.
• Graph functions, particularly quadratic equations.
• Describe the characteristics of a quadratic equation.
• Find the zeros of a quadratic equation.
• Understand writing in mathematics (students are required to write a short essay).