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Name: ___________________________
Section: _______
Task: Create a study guide for each unit in Algebra I.
These study guides are for you to use to study for the Algebra I Regents exam. Include all information
that you feel is most important and that you think you need to study the most. Your guide does not have
to be as detailed as the first few were.
Due Dates:
Chapter 1 – done
Chapter 2 – April 13, 2015
Chapter 3 – April 13, 2015
Chapter 4 – April 27, 2015
Chapter 5 – May 19, 2015
Chapter 6 – May 26, 2015
Chapters 7 & 8 – June 2, 2015
Chapter 9 – June 9, 2015
Chapter 10 – will be completed for you
Chapter 1 Objectives – Students must be able to…
-translate verbal expressions into algebraic expressions.
-evaluate expressions using the order of operations.
-understand real numbers sets (rational, irrational, etc.).
-identify and give examples of the properties of real numbers.
-add, subtract, multiply & divide real numbers.
-tell whether a number or point is a solution to an equation.
Important Vocabulary: variable, algebraic expression, numerical expression, evaluate, real numbers,
rational, irrational, integer, whole, natural, Properties: Commutative, Associative, Identity, Zero, Inverse,
Distributive, Equation, Solution
Chapter 2 Objectives - Students must be able to…
-solve two-step equations and explain your work.
-solve multi-step equations and explain your work.
-write and solve equations for a real-world situation.
-solve multi-step equations with no solution or infinitely many solutions (all real numbers).
-solve literal equations.
-find rates and unit rates.
-use dimensional analysis to convert rates.
-solve proportions.
-solve proportions with binomials.
-find missing sides of similar figures.
-use proportions to solve word problems.
-work with percents. (Percent of a number, convert fractions to decimals, etc.)
-solve percent word problems.
-calculate percent of change.
Important Vocabulary: Inverse operation, solution, literal equation, formula, rate, dimensional analysis,
conversion factor, proportion, cross products, similar, percent, percent of change
Chapter 3 Objectives – Students must be able to…
-tell whether a number is a solution to an inequality.
-graph single variable inequalities.
-write inequalities to represent real-world situations.
-solve multi-step inequalities.
-solve multi-step inequalities with no solution or where all real numbers are a solution.
-write and solve inequalities to solve word problems.
-represent sets in different ways.
-understand basic vocabulary with sets.
-find intersection and union of two or more sets.
-solve and graph compound inequalities (AND/OR)
-write inequalities using Interval Notation.
-write compound inequalities to represent real-world situations.
-solve absolute value equations.
-solve absolute value inequalities.
Important Vocabulary: solution, set, universal set, complement, null (empty) set, intersection, union,
compound inequality, interval notation.
Chapter 4 Objectives – Students must be able to…
-sketch a graph given a situation.
-identify the independent and dependent variables.
-identify linear & nonlinear functions from a table, graph or equation.
-write a rule (equation) to represent linear & nonlinear functions from a table.
-graph a function from a table.
-write a function rule for a given situation, verbal expression or table.
-tell whether a graph should be continuous or discrete from a given situation.
-determine if a relation is a function from a set of points, table or graph.
-use function notation to evaluate functions.
-tell whether a sequence is arithmetic.
-write a recursive formula to represent an arithmetic sequence.
-write an explicit formula to represent an arithmetic sequence.
Important Vocabulary: independent variable, dependent variable, linear function, nonlinear function,
continuous graph, discrete graph, relation, domain, range, function, sequence, recursive formula,
explicit formula
Chapter 5 Objectives – Students must be able to…
-find the rate of change from a table.
-find the slope of a graph from a graph or two points.
-identify the slope vertical and horizontal lines.
-tell whether an equation represents a direct variation.
-tell whether a graph represents a direct variation.
-find the constant of variation from a table or situation.
-write a direct variation equation from a table or situation.
-identify the parts of an equation in slope-intercept form.
-graph equations in slope-intercept form.
-write the equation of a line in slope-intercept form, given the slope & y-intercept.
-write the equation of a line in slope-intercept form from a graph.
-write the equation of a line in slope-intercept form given a real-world situation.
-write the equation of line given a point and slope. (point-slope form)
-graph a line in point-slope form.
-write the equation of a line given two points.
-graph horizontal and vertical lines.
-graph lines in standard form by changing into slope-intercept form.
-find the x-intercept and y-intercept to graph a line.
-convert lines in slope-intercept form or point-slope form into standard form.
-determine whether two lines are parallel, perpendicular or neither.
-write the equation of parallel and perpendicular lines given a point and the equation of a line.
Important Vocabulary: rate of change, slope, direct variation, constant of variation, slope-intercept
form, point-slope form, standard form, x-intercept, y-intercept, parallel, perpendicular
Chapter 6 Objectives – Students must be able to…
-tell whether a point is a solution to a system of equations.
-determine how many solutions a system will have by looking at the equations. (slope & y-intercept)
-solve systems of equations by graphing.
-solve systems of equations using the substitution method.
-solve systems of equations using the elimination method.
-applications of linear systems.
-solve & graph systems of linear equations with no solution or infinitely many solutions.
-determine if a point is a solution to a linear inequality.
-graph linear inequalities (two variables).
-use linear inequalities to model real-world situations.
-graph a linear inequality with one variable on the coordinate plane.
-graph a system of linear inequalities and identify possible solutions.
Important Vocabulary: system of equations, solution
Chapter 7 Objectives – Students must be able to…
-simplify expressions using the laws of exponents. (Product, Quotient, Power to a power, Zero)
-simplify expressions with negative exponents.
-convert expressions with rational (fraction) exponents to radicals.
-identify and graph exponential functions (from a table).
-write and evaluate exponential growth and decay functions.
-identify & write Geometric Sequences.
-write recursive and explicit formulas to represent Geometric Sequences.
Important Vocabulary: radical, index, radicand, common ratio, recursive formula, explicit formula
Chapter 8 Objectives – Students must be able to…
-add and subtract polynomials.
-multiply/divide a polynomial by a monomial.
-factor out the GCF.
-multiply polynomials.
-factor trinomials when a = 1 (guess & check).
-factor a difference of perfect squares.
-factor trinomials when a > 1 (ac or box method).
-factor expressions using mixed methods.
-write expressions to represent the area of a shaded region.
Important Vocabulary: polynomial (bi, tri), monomial, degree of a monomial, degree of a polynomial,
factors, conjugates or conjugate pairs
Chapter 9 Objectives – Students must be able to…
-label and describe the characteristics and parts of a quadratic function.
-identify the axis of symmetry and vertex of a quadratic function (from a graph & equation).
-graph a quadratic function by finding the axis of symmetry & zeros.
-tell whether the vertex is a maximum or minimum (from a graph & equation).
-solve a quadratic function by factoring.
-solve a quadratic function by isolating x. (ax2 – c = 0)
-solve a quadratic function by completing the square.
-solve a quadratic function using the Quadratic Formula.
-solve a quadratic-linear system of equations graphically.
-solve a quadratic-linear system of equations algebraically.
Important Vocabulary: quadratic function, parabola, axis of symmetry, vertex, minimum & maximum,
roots/zeros
Chapter 10 Objectives – Students must be able to…
-identify the type of function (linear, quadratic, exponential, absolute value) from an equation.
-identify the type of function from a table.
-identify the type of function from a graph.
-graph square root functions (from a table).
-describe what a function will look like when shifted horizontally or vertically (from a graphing
calculator).
-graph a piecewise function.
-identify reliable methods of sampling and surveying.
-determine if a data set if quantitative/qualitative, univariate/bivariate.
-find the mean, median, mode & range for a given data set & determine which best represents the data.
-read and interpret information from a histogram and a line plot.
-create a box and whisker plot given a set of data.
-use a scatterplot to graph a data set and find and graph a line of best fit to model it.
-find the correlation coefficient and determine if there is a strong correlation.
Important Vocabulary: piecewise function, sample, population, survey, bias, univariate, bivariate,
frequency, interval, quartiles, Interquartile Range, outlier, correlation