Algebra 2

This course furthers the study of Algebra I, linear and quadratic equations, and also includes, irrational numbers, rational and radical expressions, equations and polynomials; there is also a possibility of getting back into right angle trig before taking the ACT test again. This course is beneficial for ACT Math prep and prepares students for entry level college courses.

Prerequisites: Algebra I, Geometry
1 credit

STANDARD REFERENCE NUMBER

N-RN.2

N-CN.2

A-SSE.3

A-APR.3

A-APR.6

A-REI.2

A-REI.4

A-REI.7

F-IF.2

DOMAIN

Number and Quantity

Algebra

Function

R.E.A.L. CRITERIA

REA

REAL

REA

REAL

FULL STANDARD

Rewrite expressions involving radicals and rational exponents using the properties of exponents. (6)

Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. (4 &5)

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. (1&4)

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (1,2,4&5,8)

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. (8)

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (6&8)

Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. (4)

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3. (3)

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (1,2, and the rest)

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior (for each family as we go 1-8) project in end.