Math Department

High School Resources

High School Math Performance Standards

Algebra 2

Each ASD mathematics course reflects the program statement and incorporates the general program goals. In addition, each course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what a student should be able to do after successfully completing the course. After satisfactorily completing the ASD Algebra II curriculum, a student will be proficient in the six strands of mathematics which comprise the Algebra II Math Content Standards. As evidence of proficiency, the student will be able to:

A2:1 Number Sense

.1 Use estimation to check reasonableness of answers.
.2 Select appropriate scales when graphing application problems.
.3 Set an appropriate window when graphing with a graphing calculator.
.4 Estimate an equation for a line or curve that models the scatter plot for a given set of data.
.5 Identify and classify subsets of the complex number system as natural, whole, integer, rational, irrational, real, or imaginary.
.6 Determine appropriate domain and range for application problems.
.7 Determine restrictions for variables appearing in rational and radical expressions so that the statement will be meaningful.
.8 Use appropriate units to label solutions of application problems.

A2:2 Geometry

.1 Graph linear functions accurately with pencil and paper given slope- intercept form.
.2 Graph quadratic functions accurately with pencil and paper given vertex form.
.3 Label a geometric figure using algebraic expressions and write a valid relationship involving the expressions.
.4 Identify and graph parent functions including constant, linear, quadratic, cubic, absolute value, exponential, logarithmic, and reciprocal.
.5 Transform parent functions using translation, reflection, stretching and/or shrinking.
.6 Graph equations having discontinuities such as asymptotes and/or holes.
.7 Identify and explain types of symmetry.
.8 Sketch the graphs of circles, ellipses, hyperbolas, and parabolas given in standard form.
.9 Use the formulas of coordinate geometry including slope, midpoint, distance, and equations of lines from memory.
.10 Explain the geometric interpretation of real zeros of a function.

A2:3 Statistics

.1 Read and interpret data displayed in a table, chart or graph.
.2 Organize and display data using stem-and-leaf plots, box-and-whisker plots, histograms, and scatter plots.
.3 Determine a line or curve of best fit for a given set of data.
.4 Use a regression equation that models a set of data to make predictions.
.5 Determine the mean, median, mode, and range for a set of data.
.6 Determine the percentile rank of a data point.
.7 Explain the difference between percentile and percentage.
.8 Calculate the standard deviation for a set of data that is normally distributed.
.9 Determine the reasonableness of statistical conclusions applied to real-world situations.

A2:4 Probability

.1 Explain the difference between combinations and permutations.
.2 Select and use appropriate formulas to solve problems involving combinations and permutations.
.3 List all possible outcomes for a particular event.
.4 Explain the differences among independent, dependent, and mutually exclusive events.
.5 Compute probabilities for simple and compound events.
.6 Solve problems involving conditional probability.
.7 Explain the difference between experimental probability and theoretical probability.

A2:5 Patterns

.1 Develop a rule for a sequence and represent that rule recursively, explicitly, or verbally.
.2 Identify a sequence as arithmetic, geometric, or neither.
.3 Factor polynomial expressions using a variety of patterns including difference of two squares, sum or difference of two cubes, perfect square trinomials, and grouping.
.4 Use Pascal's triangle to find the coefficients for a binomial expansion.
.5 Use the Binomial theorem to find a particular term of a binomial expansion.
.6 Determine if two variables vary directly or inversely and, if applicable, find the constant of variation.

A2:6 Algebra

.1 Determine whether a given relation is a function.
.2 Identify the domain and range of a function.
.3 Find the inverse of a function if it exists and describe it graphically.
.4 Add, subtract, multiply, divide, and compose functions, and identify the domain and range of the new function.
.5 Graph a piece-wise function.
.6 Add, subtract, multiply, and use scalar multiplication on matrices.
.7 Simplify rational expressions and radicals.
.8 Solve problems that contain radicals and rational expressions.
.9 Simplify expressions involving fractional exponents.
.10 Add, subtract, multiply, and divide complex numbers, and simplify the results.
.11 Solve quadratic equations by factoring, using the quadratic formula, and graphing.
.12 Solve quadratic equations that have complex roots.
.13 Identify the conic sections and use completing the square to rewrite them in standard form.
.14 Solve problems involving "and" and "or" statements.
.15 Solve literal equations and formulas for a given variable.
.16 Solve a system of three equations in three unknowns using the substitution method and/or addition method.
.17 Use matrices and a graphing calculator to solve systems of linear equations.
.18 Solve systems of non-linear equations.
.19 Use the rational root theorem and the factor theorem to find rational roots of equations of degree three or more.
.20 Use synthetic division to divide a polynomial by a binomial of the form x-a.
.21 Solve inequalities using number lines and coordinate planes.
.22 Represent a series using sigma notation.
.23 Find partial sums of arithmetic and geometric series.
.24 Calculate the sum of an infinite geometric series with |r| < 1.
.25 Identify, solve, and graph exponential and logarithmic functions.
.26 Simplify expressions involving logarithms.
.27 Solve equations by applying the properties of logarithms.
.28 Solve for an unknown exponent using logarithms.
.29 Apply algebra concepts and skills to solve real world problems.
.30 Solve application problems using appropriate technology.