Course Objectives

Algebra 1B Objectives

Unit 1:  Linear Equations

Lesson 1:  Functions and Relations

• Identify the domain and range of a relation.
• Determine whether or not a relation is a function by using the vertical line test.
• Understand and use function notation.
• Find the output of a function for a given input both by using mapping diagrams and by using the equation of the function.

Lesson 2:  Graphs of Linear Equations

• Rewrite linear equations with two variables in slope intercept form.
• Find ordered pairs that are solutions of linear equations with two variables.
• Graph linear equations by finding ordered pairs that are solutions to the equation.
• Graph equations of the form y = c (horizontal lines).
• Graph equations of the form x = c (vertical lines).
• Translate a sentence or phrase into an algebraic equation.
• Graph linear equations.
• Find the value of a function, graph linear equations, perform operations on functions, graph linear inequalities, and solve systems of equations using a graphing calculator.
• Solve distance, rate, and time problems using the graphs of linear equations.
• Write linear equations to model real life situations involving fixed and variable costs.
• Solve problems involving fixed and variable costs using linear equations.

Lesson 3:  Other Forms of Linear Equations

• Understand the meaning of slope as an indicator of a line's slant and steepness.
• Calculate the slope of a line given two points on the line.
• Find the slope of horizontal and vertical lines.
• Graph linear equations by finding the x- and y-intercepts.
• Find the slope and y-intercept of an equation by rewriting the equation in slope intercept form.
• Graph linear equations using the slope and y-intercept of the graph.
• Write the equation of a line in slope-intercept form given two points on the line, the slope of the line and a point on the line, or the slope and y-intercept of the line.
• Determine if the graphs of two linear equations are parallel or perpendicular by examining the slopes of the graphs of the equations.
• Identify and understand, using y = x and y = -x as parent functions, the effect of changes to the slope or y-intercept of a linear equation; specifically that changes to the slope affect the direction and steepness of the line, and that changes in the y-intercept cause the graph to be translated vertically.

Unit 2:  Systems of Equations and Inequalities

Lesson 1:  Solutions by Graphing

• Solve systems of two linear equations by graphing.
• Determine the number of solutions a system of two linear equations has by looking at the slopes of the graphs of the equations.
• Solve a system of two linear inequalities by graphing.
• Graph the solutions to a system of two linear inequalities.

Lesson 2:  Solving Systems of Equations

• Write and graph linear equations that represent real world relationships.
• Solve real world problems using linear equations.
• Solve systems of two linear equations using the substitution method.
• Solve application problems that involve systems of two linear equations using the substitution method.
• Solve systems of two linear equations using the addition method.
• Solve systems of two linear equations using multiplication and addition (the linear combination method).

Lesson 3:  Problem Solving

• Solve problems that deal with geometric concepts by solving systems of two linear equations. Geometric concepts include supplementary and complementary angles, isosceles triangles, sum of the measures of the angles of a triangle, perimeter of a rectangle, etc.

Unit 3:  Rational Expressions and Radicals

Lesson 1:  Working with Rational Expressions

• Simplify rational expressions by factoring and canceling.
• Multiply rational expressions.
• Divide rational expressions

Lesson 2:  Rational and Irrational Numbers

• Understand and apply the definitions and characteristics of rational and irrational numbers.
• Find the square root of a perfect square.
• Write radical numbers in simplest radical form.
• Perform multiplication with radical numbers.
• Solve application problems involving square roots.

Lesson 3:  Radicals and Right Triangles

• Use the Pythagorean Theorem to find the missing side of a right triangle.
• Use the Pythagorean Theorem to determine if a triangle is a right triangle.
• Solve application problems with right triangles using the Pythagorean Theorem.
• Write radical expressions including variables raised to a power in simplest radical form.

Unit 5:  Quadratic Equations

Lesson 1:  Solving Quadratic Equations

• Solve quadratic equations using the square root property, including equations with perfect square trinomials.
• Solve quadratic equations by factoring and using the Zero Product Rule.
• Solve quadratic equations by completing the square.
• Determine the nature of the solutions of a quadratic formula using the discriminant.
• Solve quadratic equations with the quadratic formula.
• Solve quadratic equations with the most appropriate method.

Lesson 2:  Quadratic Equations and Problem Solving

• Solve geometric problems using quadratic equations.
• Graph quadratic functions by hand and with a graphing utility.
• Find the vertex, axis of symmetry, and maximum or minimum values of the graph of a quadratic function.
• Solve application problems using quadratic functions.
• Determine the number of real solutions of a quadratic function by finding the discriminant.

Unit 6:  Statistical Analysis

Lesson 1:  Measures of Variability

• Find the range of a set of data displayed in a table.
• Create a box-and-whiskers plot from a set of data.
• Read, interpret, and analyze data displayed in a box-and-whisker plot.

Lesson 2:  Probability

• Calculate the probability of an event as a ratio or percentage, including certain events and impossible events.
• Calculate the probability of compound, dependent events.
• Calculate the probability of compound, independent events.