Download ALGEBRA II

ALGEBRA II
MAJOR CONCEPTS OF STUDY
I.
Equations and Inequalities
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Graph rational and irrational numbers on a number line.
Know, explain, and use equivalent representations for real numbers and algebraic expressions
including integers, fractions, decimals, percents, ratios; rational numbers written in scientific
notation; absolute value; time, money.
Evaluate powers and combine similar terms in algebraic expressions.
Model real life problems using algebraic expressions.
Use a general problem-solving plan to solve real life problems.
Solve simple inequalities and compound inequalities.
Solve absolute value equations and inequalities and use them to solve real life problems.
Communicate, orally and written, problem solving techniques.
Linear Equations and Functions
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Identify the domain and the range of a function.
Represent relations and functions, evaluate functions, graph linear equations, and use the vertical
line test.
3. Find slopes of lines and classify parallel and perpendicular lines; and use slope to solve real life
problems.
4. Use the slope intercept form of an equation to graph the equation; and use the standard form of an
equation to graph the equation.
5. Write equations of lines.
6. Graph and make generalizations about direct and indirect variations.
7. Use a scatter plot to identify the correlation shown by a set of data and approximate the best fitting
line for a set of data.
8. Graph linear inequalities in two variables and use them to solve real life problems.
9. Represent piecewise functions, such as absolute value and step functions, and use them to model
real life situations.
10. Apply linear equations to real-world problems.
11. Use the formulas for sums of finite arithmetic and geometric series to find partial sums or the sum
of n terms.
12. Use recursion to generate and describe patterned relationships.
III.
Matrices
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Utilize matrices to store data.
Perform operations (e.g. addition, subtraction, scalar multiplication, multiplication, determinants,
and inverses) on a set of matrices, with or without a graphing calculator.
Find the determinant of a 2x2 or 3x3 matrix.
Represent vectors as matrices in two dimensions.
Describe transformations of geometric figures using matrices.
Determine the inverse of a 2x2 or 3x3 matrix or indicate that no inverse exists.
Solve systems of equations using inverse and augmented matrices.
Apply matrices to real life data
Systems of Linear Equations and Inequalities
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Solve and graph linear inequalities in one variable.
Find the solution for a system of linear equations by using substitution, linear combinations, or
matrices and determine if the equations are consistent/inconsistent or dependent/independent.
3. Graph linear inequalities in two variables.
4. Create a system of inequalities from a problem and solve it using linear programming.
V.
Quadratic Functions
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Expand squares of binomials.
Determine key characteristics of quadratic functions and their graphs.
Solve quadratics by completing the square and write quadratic functions in vertex or standard
form.
4. Interpret the graph of a quadratic function.
5. Use the discriminant to determine the roots of a quadratic.
6. Recognize that complex solutions come in conjugate pairs of the form a + bi and a – bi when the
coefficients of a quadratic equation are real numbers and perform operations with complex
numbers.
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VI.
Polynomial and Polynomial Functions
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Apply quadratic equations to real-life situations.
Estimate vertex and zeros of parabolas.
Graph quadratic inequalities in two variables and solve in one variable.
Write quadratic functions given characteristics of their graphs and use technology to find quadratic
regression equation from data.
Evaluate and graph a polynomial function.
Simplify polynomial expressions by performing operations.
Factor and solve polynomial equations by using the GCF, by recognizing special products, and by
grouping terms.
Divide polynomials and relate the result to the remainder theorem and the factor theorem. Find the
rational zeros of a polynomial function and use polynomial equations in real life problems.
Use the Fundamental Theorem of Algebra to determine the number of zeros of a polynomial
function and use technology to approximate the real zeros of a polynomial function.
Exponential and Logarithmic Functions
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A. Represent exponential functions using tables, graphs, verbal statements, and equations.
Represent exponential equations in multiple forms. Translate among these representations.
2. Apply the properties of exponents in numerical expressions and use exponents and scientific
notation to solve real life problems.
3. Graph exponential growth and decay functions and use to model real life problems.
4. Evaluate and write recursive rules for sequences.
5. Simplify and evaluate expressions with base e.
6. Determine key characteristics of logarithmic functions.
7. Use the properties of logarithms to simplify expressions.
8. Solve exponential and logarithmic equations and use them to solve real life problems.
9. Solve equations that contain radical or rational exponents.
10. Recognize properties of nth roots.
11. Develop an informal notion of limit.
VIII. Inverses and Radicals
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Rational Equations and Functions
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A. Combine functions by addition, subtraction, multiplication, and division.
Find inverses of linear functions and nonlinear functions and draw their graphs.
Perform operations with functions including power functions and apply to real life problems.
Evaluate nth roots of real number using both radical notation and rational exponent notation.
Use properties of rational exponents to evaluate and simplify expressions and apply to real life
situations.
Simplify and perform operations on numerical expressions containing radicals.
Solve equations that contain radicals or rational exponents and use them to solve real life
problems.
Write and apply to real life problems direct, inverse and joint variation models.
Determine key characteristics of simple rational functions and their graphs.
Add and subtract rational expression and simplify complex fractions.
Simplify complex fractions that contain rational expressions in numerator and/or denominator.
Solve rational equations and use them to solve real life problems.
Probability and Statistics
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Use the fundamental counting principle to find the number of ways an event can happen.
Use permutations and combinations to find the number of ways an event can happen.
Use the binomial theorem.
Find experimental, theoretical, geometrical probabilities.
Find probabilities for compound and mutually exclusive events.
Find probabilities of independent and dependent events.
Find binomial probabilities and analyze their distributions.
Identify the principal characteristics of the normal distribution and use them to estimate
probabilities.
9. Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems.
10. Explore strategies for making fair decisions.