Departmental Course Outline for Algebra 1B

Algebra 1B (course 222) completes coverage of the Algebra 1 curriculum begun in 8th grade. It also includes topics in statistics, data analysis, counting, and probability.

Note: This working document describes our coverage plans, but may be revised somewhat during the year. We hope you will find it useful as an overview of the course and as an approximation of what topics will be covered.

Minimum Topic Coverage

• Function concept and representations
  • Definition of function: unique output for each input
  • Function formulas and evaluation, including f(x) notation
  • Table and graph representations
  • Writing functions representing real-world situations
  • Domain and range
• Linear functions and equations
• Solving one-variable linear equations algebraically and graphically
• Slope of a line
• Two-variable linear equations in slope-intercept, point-slope, and general forms
• Writing a linear function given the slope and a point, or given two points
• Graphing linear functions (slope-intercept, point-slope, and two-intercept methods)
• Parallel and perpendicular slopes
• Vertical and horizontal lines
• Application problems involving a rate and an initial value
• Solving and graphing linear inequalities
• Solving one-step linear inequalities
• Solving multi-step linear inequalities
• Solving compound inequalities
• Solving absolute-value equations and inequalities
• (Optional) Graphing the absolute-value function
• (Optional) Graphing linear inequalities in two variables
• Systems of linear equations and inequalities
• Solving linear systems by graphing
• Solving linear systems by substitution
• Solving linear systems by linear combinations
• Applications of linear systems
• Special types of linear systems
• Exponents and exponential functions
• Multiplication properties of integer exponents
• Zero and negative integer exponents
• Division properties of integer exponents
• Scientific notation
• Exponential growth and decay functions
• Quadratic equations and functions
• Square roots and their basic properties
• Solving quadratic equations using square root
• Graphs of quadratic functions
• Solving quadratic equations by graphing
• Solving quadratic equations by factoring ax^2+bx+c=0
• Applications to real situations
• (Optional) Solving quadratic inequalities by graphing
• Polynomials and factoring
• Adding and subtracting polynomials
• Multiplying polynomials
• (Optional) Dividing polynomials
• Solving polynomial equations in factored form
• Factoring x^2+bx+c and ax^2+bx+c
• Factoring out a common factor
• (Optional) Rational functions and expressions
• ("") Simplifying rational expressions
• ("") Multiplying and dividing rational expressions
• ("") Adding and subtracting rational expressions
• ("") Ratios and proportions
• Statistics
• Data analysis
• Mean, median, and mode
• Range, extremes, and quartiles
• (Optional) Standard deviation
• Comparisons between data sets using the above concepts
• Data representations
• Tables, scatterplots, and line graphs
• Frequency displays (histograms, line plots, circle graphs)
• Stem-and-leaf plots
• Box-and-whisker plots
• Modeling
• Linear regression (line of best fit)
• (Optional) Quadratic regression
• (Optional) Exponential regression
• Using models to make predictions
• Sampling and predictions
• Design of surveys and polls; random sampling
• Effect of sample size on validity of predictions
• Combinatorics and probability
• Counting methods
• Multiplication principle
• Arrangements, permutations, and combinations (n!, nCr, nPr)
• Probability concepts and methods
• Probabilities when all outcomes are equally likely
• Probabilities for compound events and repeated experiments
• Representations of outcomes and their probabilities, such as tree diagrams and organized lists
• Probability simulations, compared to theoretical probabilities

Calculator Skills

• Enter algebraic expressions (using parentheses, negative key, carat key)
• Graph functions and set appropriate graph window
• Analyze functions (values, tables, x and y intercepts)
• Enter a data table and create a scatterplot
• Perform linear regression and graph the regression line
• Use combinatorics functions (n!, nCr, nPr)
• Use of one-variable statistical features: mean, median, extremes, quartiles (Optional: standard deviation)
• Use of exact answers in subsequent calculations (for accuracy)

Textbook Usage