College Prep Algebra 12

River Valley School District Curriculum Template
Course name: College Prep Algebra- 0243		Credit(s) or Grade Level: 121th
Academic Standards: Attached Link		Prerequisite(s): Math 1 or Geometry, Algebra 1
Course Description: This course offers traditional algebra topics with applications. Learners develop algebraic problem solving techniques needed for technical problem solving and for more advanced algebraic studies. Topics include linear equations, exponents, polynomials, rational expressions, and roots and radicals. Successful completion of this course prepares learners to succeed in technical mathematics courses.

Units:	Duration:	Essential Learning/Outcomes:
1: Review of Real Numbers 1: Review of Real Numbers (continued…)	3 Weeks	Students will understand some general tips for success, get help as soon as you need it, and learn how to prepare for and take an exam. Students will be able to use a number line to order numbers, translate sentences into mathematical statements, identify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers, and find the absolute value of a real number. Students will be able to write fractions in simplest form, multiply and divide fractions, add and subtract fractions, and perform operations on mixed numbers. Students will be able to define and use exponents and the order of operations, evaluate algebraic expressions, given replacement values for variables, determine whether a number is a solution given equation, and translate phrases into expressions and sentences into statements. Students will be able to add real numbers, solve applications that involve addition of real numbers, and find the opposite of a number. Students will be able to subtract real numbers, add and subtract real numbers, evaluate algebraic expressions using real numbers, solve applications that involve subtraction of real numbers, and find complementary and supplementary angles. Students will be able to multiply real numbers, find the reciprocal of a real number, divide real numbers, evaluate expressions using real numbers, and solve applications that involve multiplication or division of real numbers. Students will be able to use the commutative and associative properties, use the distributive property, and use the identity and inverse properties.
2: Equations, Inequalities, and Problem Solving 2: Equations, Inequalities, and Problem Solving (continued…)	4 Weeks	Students will be able to identify terms, like terms, and unlike terms, combine like terms, use the distributive property to remove parentheses, and write word phrases as algebraic expressions. Students will be able to define linear equations and use the addition property of equality to solve linear equations, use the multiplication property of equality to solve linear equations, use both properties of equality to solve linear equations, and write word phrases as algebraic expressions. Students will be able to apply a general strategy for solving a linear equation, solve equations containing fractions, solve equations containing decimals, and recognize identities and equations with no solution. Students will be able to solve problems involving direct translations, solve problems involving relationships among unknown quantities, and solve problems involving consecutive integers. Students will be able to use formulas to solve problems and solve a formula or equation for one of its variables. Students will be able to solve percent equations, solve discount and mark-up problems, solve percent of increase and percent of decrease problems, and solve mixture problems. Students will be able to solve problems involving distance, solve problems involving money, and solve problems involving interest. Students will be able to define linear inequality in one variable, graph solution sets on a number line, and use interval notation, solve linear inequalities, solve compound inequalities, and solve inequality applications.
3: Graphing 3: Graphing (continued…)	3 Weeks	Student will be able to read bar and line graphs, define the Rectangular Coordinate System and plot ordered pairs of numbers, graph paired data to create a scatter diagram, determine whether an ordered pair is a solution of an equation in two variables, and find the missing coordinate of an ordered pair solution, given one coordinate of the pair. Students will be able to identify linear equations and graph a linear equation by finding and plotting ordered pair solutions. Students will be able to identify intercepts of a graph, graph a linear equation by finding and plotting intercepts, and identify and graph vertical and horizontal lines. Students will be able to find the slope of a line given two points of the line, find the slope of a line given its equation, find the slopes of horizontal and vertical lines, compare the slopes of parallel and perpendicular lines, and interpret slope as a rate of change. Students will be able to use the slope-intercept form to graph a linear equation, use the slope-intercept form to write an equation of a line, use the point-slope form to find an equation of a line given its slope and a point on the line, use the point-slope form to find an equation of a line given two points on a line, find equations of vertical and horizontal lines, and use the point-slope form to solve problems. Students will be able to identify relations, domains, and ranges, identify functions, use the vertical line test, and use function notation.
4: Solving Systems of Linear Equations	4 Weeks	Students will be able to determine if an ordered pair is a solution of a system of equations in two variables, solve a system of linear equations by graphing, and without graphing, determine the number of solutions in a system. Students will be able to use the substitution method to solve a system of linear equations. Students will be able to use the addition method to solve a system of linear equations. Students will be able to solve a system of three linear equations in three variables. Students will be able to solve problems that can be modeled by a system of two linear equations, solve problems with cost and revenue functions, and solve problems that can be modeled by a system of three linear equations.
5: Exponents and Polynomials 5: Exponents and Polynomials (continued…)	7 Weeks	Student will be able to evaluate exponential expressions, use the product rule for exponents, use the power rule for exponents, use the power rule for products and quotients, use the quotient rule for exponents, and define a number raised to the 0 power, and decided which rule(s) to use to simplify an expression. Students will be able to define a polynomial, monomial, binomial, trinomial, and degree, define polynomial functions, simplify a polynomial by combining like terms, and add and subtract polynomials. Students will be able to multiply monomials, use the distributive property to multiply polynomials, and multiply polynomials vertically. Students will be able to multiply two binomials using the FOIL method, square a binomial, multiple the sum and difference of two terms, and use special products to multiply binomials. Students will be able to simplify expressions containing negative exponents, use all the rules and definitions for exponents to simplify exponential expressions, write numbers in scientific notation, convert numbers from scientific notation to standard form, and perform operations on numbers written in scientific notation. Students will be able to divide a polynomial by a monomial and use long division to divide a polynomial by another polynomial. Students will be able to use synthetic division to divide a polynomial by a binomial and use the Remainder Theorem to evaluate polynomials.
6: Factoring Polynomials 6: Factoring Polynomials (continued…)	5 Weeks	Students will be able to find the greatest common factor of a list of integers, find the greatest common factor of a list of terms, factor out the greatest common factor from a polynomial and factor a polynomial by grouping. Students will be able to factor trinomials of the form x^2 + bx + c and factor out the greatest common factor and then factor trinomials of the form x^2 + bx + c. Students will be able to factor trinomials of the form ax^2 + bx + c, where a does not equal 1, factor out the GCF before factoring a trinomial of the form ax^2 + bx + c, and factor perfect square trinomials. Students will be able to use the grouping method to factor trinomials of the form ax^2 + bx + c. Students will be able to factor the difference of two squares and factor the sum or difference of two cubes. Students will be able to solve quadratic equations by factoring, solve equations with degree greater than 2 by factoring, and find the x-intercepts of the graph of a quadratic equation in two variables. Students will be able to solve problems that can be modeled by quadratic equations.
7: Rational Expressions	Not yet taught	Students will be able to find the domain of a rational function, simplify or write rational expressions in lowest terms, write equivalent rational expressions of the form -(a/b) = (-a/b) = (a/-b), and use rational functions in applications. Students will be able to multiply rational expressions, divide rational expressions, multiply or divide rational expressions, and convert between units of measure. Students will be able to add and subtract rational expressions with the same denominator, find the least common denominator of a list of rational expressions, and write a rational expression as an equivalent expression whose denominator is given. Students will be able to add and subtract rational expressions with unlike denominators. Students will be able to solve equations containing rational expressions and solve equations containing rational expressions for a specified variable. Students will be able to solve proportions, use proportions to solve problems, solve problems about numbers, solve problems about work, and solve problems about distance. Students will be able to simplify complex fractions by simplifying the numerator and denominator and then dividing, simplifying complex fractions by multiplying by a common denominator, and simplifying expressions with negative exponents.
8: More on Functions and Graphs 8: More on Functions and Graphs (continued…)	Not yet taught	Students will be able to graph linear functions, write an equation of a line using function notation, and find equations of parallel and perpendicular lines. Students will be able to review function notation, find square roots of numbers, and graph nonlinear functions. Students will be able to graph piecewise-defined functions, vertical and horizontal shifts, and reflect graphs. Students will be able to solve problems involving direct variation, solve problems involving inverse variation, solve problems involving joint variation, and solve problems involving combined variation.
9: Inequalities and Absolute value	Not yet taught	Students will be able to find the intersection of two sets, solve compound inequalities containing and, find the union of two sets, and solve compound inequalities containing or. Students will be able to solve absolute value equations. Students will be able to solve absolute value inequalities of the form absolute value of X < a and solve absolute value inequalities of the form absolute value of X > a. Students will be able to graph a linear inequality in two variables and solve a system of linear inequalities.
10: Rational Exponents, Radicals, and Complex Numbers 10: Rational Exponents, Radicals, and Complex Numbers (continued…)	Not yet taught	Students will be able to find square roots, approximate roots, find cube roots, find nth roots, and graph square and cube root functions. Students will be able to understand the meaning of a^(1/n), a^(m/n), a^(-m/n), use rules for exponents to simplify expressions that contain rational exponents, and use rational exponents to simplify radical expressions. Students will be able to use the product rule for radicals, use the quotient rule for radicals, simplify radicals, and use the distance and midpoint formulas. Students will be able to add or subtract radical expressions and multiply radical expressions. Students will be able to rationalize denominators, rationalize denominators having two terms, and rationalize numerators. Students will be able to solve equations that contain radical expressions and use the Pythagorean Theorem to model problems. Students will be able to write square roots of negative numbers in the form bi, add or subtract complex numbers, multiply complex numbers, divide complex numbers and raise it to powers.
11: Quadratic Equations and Functions	Not yet taught	Students will be able to use the square root property to solve quadratic equations, solve quadratic equations by completing the square, and use quadratic equations to solve problems. Students will be able to solve quadratic equations by using the quadratic formula, determine the number and type of solutions of a quadratic equation by using the discriminant, and solve problems modeled by quadratic equations. Students will be able to solve various equations that are quadratic in form and solve problems that lead to quadratic equations. Students will be able to solve polynomial inequalities of degree 2 or greater and solve inequalities that contain rational expression with variables in the denominator. Student will be able to graph quadratic functions of the form f(x) = x^2 + k, f(x) = (x - h)^2, f(x) = (x - h)^2 + k, f(x) = ax^2, f(x) = a(x - h)^2 + k. Students will be able to write quadratic functions in the form y = a(x - h)^2 + k, derive a formula for finding the vertex of a parabola, and find the minimum or maximum value of a quadratic function.
12: Exponential and Logarithmic Functions 12: Exponential and Logarithmic Functions (continued…)	Not yet taught	Students will be able to add, subtract, multiply, and divide functions and construct composite functions. Student will be able to determine whether a function is a one-to-one function, use the horizontal line test to decide whether a function is a one-to-one function, find the inverse of a function, find the equation of the inverse of a function, graph functions and their inverses, and determine whether two functions are inverses of each other. Students will be able to graph exponential functions, solve equations of the form b^x = b^y, and solve problems modeled by exponential equations. Students will be able to model exponential growth and model exponential decay. Students will be able to write exponential equations with logarithmic notation and write logarithmic equations with exponential notation, solve logarithmic equations by using exponential notation, and identify and graph logarithmic functions. Students will be able to use the product property of logarithms, use the quotient property of logarithms, use the power property of logarithms, and use the properties of logarithms together. Students will be able to identify common logarithms and approximate them by calculator, evaluate common logarithms of powers of 10, identify natural logarithms and approximate them by calculator, evaluate natural logarithms of powers of e, and use the change of base formula. Students will be able to solve exponential equations, solve logarithmic equations, and solve problems that can be modeled by exponential and logarithmic equations.
13: Conic Sections 13: Conic Sections (continued…)	Not yet taught	Student will be able to graph parabolas of the form x = a(y - k)^2 + h and y = a(x - h)^2 + k, graph circles of the form (x - h)^2 + (y - k)^2 = r^2, find the center and the radius of a circle, given is equation, and write an equation of the circle, given its center and radius. Students will be able to define and graph an ellipse and define and graph a hyperbola. Students will be able to solve a nonlinear system by substitution and solve a nonlinear system by elimination. Students will be able to graph a nonlinear inequality and graph a system of nonlinear inequalities.
14: Sequences, Series and Binomial Theorem	Not yet taught	Students will be able to write the terms of a sequence given its general term, find the general term of a sequence, and solve applications that involve sequences. Students will be able to identify arithmetic sequences and their common differences and identify geometric sequences and their common ratios. Students will be able to identify finite and infinite series and use summation notation and find partial sums. Students will be able to find the partial sum of an arithmetic sequence, find the partial sum of a geometric sequence, and find the sum of the terms of an infinite geometric sequence. Students will be able to use Pascal's Triangle to expand binomials, evalue factorials, use the Binomial Theorem to expand binomials, and find the nth term in the expansion of a binomial raised to a positive power.