Download Algebra 2 Learning Targets

Algebra 2 Learning Targets
Benton Community High School
Jeremy Cue
Foundations for Functions
1. Order real numbers from least to greatest.
2. Classify numbers to subsets (irrational, rational, integer, whole, natural) of the real numbers.
3. Find the additive and multiplicative inverse of a number.
4. Identify the commutative, associative, and distributive properties of real numbers.
5. Simplify square-root expressions.
6. Rationalize the denominator of a square-root expression.
7. Add and subtract square-root expressions.
8. Evaluate algebraic expressions for given values of variables.
9. Simplify algebraic expressions by using the distributive property and by combining like-terms.
10. Simplify expressions by using the properties of exponents.
11. Simplify scientific notation expressions by using the properties of exponents.
12. Determine whether a relation is a function.
13. Identify the domain and range of relations and functions.
14. Evaluate functions by using function notation.
15. Evaluate a function that represents a real world problem, and interpret both the input and output
values of the function within the context of the problem.
Linear Functions
1. Solve linear equations.
2. Solve linear inequalities and graph the solution set on the real number line.
3. Solve proportions.
4. Model and solve real world percent problems with proportions.
5. Model and solve indirect measurement problems with proportions.
6. Write linear functions in slope-intercept form.
7. Graph linear functions by using the slope and y-intercept.
8. Find the slope of the line through two points.
9. Write the equation of a linear function by using point-slope form.
10. Model and solve real world linear relationship problems by using linear functions.
11. Graph linear inequalities.
12. Solve compound inequalities and graph the solution set on the real number line.
13. Solve absolute-value equations.
14. Solve absolute-value inequalities and graph the solution set on the real number line.
15. Graph absolute-value functions and find the domain and range.
Systems of Equations
1. Identify the number of solutions for a system of equations.
2. Solve a system of equations by graphing.
3. Solve a system of equations by substitution.
4. Solve a system of equations by elimination.
5. Model and solve real world systems of equations problems by using substitution and elimination.
6. Solve a system of inequalities by graphing.
7. Solve a system of three linear equations by substitution and elimination.
Matrices
1. Add and subtract two matrices.
2. Find scalar multiples of matrices.
3. Multiply two matrices.
4. Find the determinant of 2x2 and 3x3 matrices.
5. Find the inverse of a 2x2 matrix.
6. Solve a system of equations by using a matrix equation and matrix inverses.
Quadratic Functions
1. Graph quadratic functions in vertex form and find the domain and range.
2. Graph quadratic functions in standard form and find the domain and range.
3. Factor quadratic expressions.
4. Solve quadratic equations and find the zeros of quadratic functions by factoring.
5. Solve quadratic equations and find the zeros of quadratic functions by completing the square.
6. Solve quadratic equations and find the zeros of quadratic functions by using the quadratic formula.
7. Simplify expressions by using i, the imaginary unit.
8. Model and solve real world projectile motion problems by using quadratic functions.
9. Solve quadratic inequalities and express the solution in set notation and interval notation.
Polynomial Functions
1. Simplify addition, subtraction, multiplication, and exponent expressions involving imaginary numbers.
2. Write polynomials in standard form and identify the degree, leading coefficient, and name.
3. Add, subtract, and multiply polynomials.
4. Divide polynomials by using both long division and synthetic division.
5. Analyze the graph of a polynomial function and determine if the function has a positive or negative
leading coefficient, an even or odd degree, the number of turning points, the number of local maxima,
the number of local minima, and the number of real zeros.
6. Solve polynomial equations and find the zeros of polynomial functions by factoring and identify the
multiplicity of each zero.
7. Graph polynomial functions based on their leading coefficient, degree, zeros, and multiplicity of each
zero.
8. Analyze polynomial functions with regards to the Fundamental Theorem of Algebra, the Irrational
Zero Theorem, the Complex Zero Theorem, and the Factor Theorem.
9. Write the equation of a polynomial function given its zeros.
Rational and Radical Functions
1. Simplify, multiply, and divide rational expressions.
2. Add and subtract rational expressions.
3. Analyze the graph of a rational function and identify the vertical and horizontal asymptotes.
4. Find the domain, zeros, vertical asymptotes, and horizontal asymptotes of rational functions.
5. Solve rational equations.
6. Simplify radical and rational expressions.
7. Graph square-root functions and identify the domain and range.
8. Solve radical equations.
Exponential and Logarithmic Functions
1. Graph exponential functions and find the domain and range.
2. Model and solve real world exponential growth and decay problems by using exponentials and
logarithms.
3. Find the value of logarithmic expressions with and without a calculator.
4. Convert exponential equations to logarithmic form, and convert logarithmic equations to exponential
form.
5. Model and solve real world pH problems by using logarithms.
6. Simplify logarithmic expressions by using the properties of logarithms.
7. Graph logarithmic functions and find the domain and range.
8. Solve exponential and logarithmic equations by using the properties of logarithms.
9. Simplify expressions involving e (the natural base) and ln (the natural logarithm) by using the
properties of logarithms.
10. Model and solve real world interest compounded continuously problems by using exponentials and
logarithms.
Conic Sections
1. Write the equation of a circle.
2. Graph circles and identify the center and radius.
3. Write the equation of an ellipse.
4. Graph ellipses and identify the center, vertices, and co-vertices.
5. Write the equation of a hyperbola.
6. Graph hyperbolas and identify the center, vertices, and co-vertices.
7. Write the equation of a parabola.
8. Graph parabolas and identify the vertex, focus, and directrix.
9. Write the equation of a conic section (circle, ellipse, hyperbola, or parabola) in standard form by
completing the square.
10. Solve a nonlinear system of equations by substitution.
11. Solve a nonlinear system of equations by elimination.
Properties and Attributes of Functions
1. Evaluate piecewise functions by using function notation.
2. Graph piecewise functions.
3. Add, subtract, multiply, and divide two functions.
4. Evaluate a composition of functions by using function notation.
5. Simplify a composition of functions.
6. Find the domain of a function.
Probability and Statistics
1. Model and solve real world counting problems by using the fundamental counting principle.
2. Model and solve real world counting problems by using permutations.
3. Model and solve real world counting problems by using combinations.
4. Model and solve real world probability problems by finding the theoretical probability of an event.
5. Model and solve real world probability problems by finding the experimental probability of an event.
6. Model and solve real world probability problems by finding the probability of two or more
independent events.
7. Model and solve real world probability problems by finding the probability of two or more dependent
events.
8. Model and solve real world probability problems by finding the probability of two mutually exclusive
events.
9. Model and solve real world probability problems by finding the probability of two inclusive events.
10. Model and solve real world probability problems by finding the binomial probability of an event.
11. Find the mean, median, and mode of a data set.
12. Create a box-and-whisker plot, find the interquartile range, and identify the outliers of a data set.