Algebra 2 NAPT Study Guide

ONE-VARIABLE EQUATION

when solved, will have a single numerical answer

Quadratic Formula

x equals negative b plus or minus the square root of b squared minus 4ac all over 2a

cot and/or tan: Asymptotes

x=(π/2|b|)+(πn/|b|)

y=cosx: Domain

{x|x E R}

y=sinx: Domain

{x|x E R}

y=cosx: Range

{y|-1≤y≤1}

y=sinx: Range

{y|-1≤y≤1}

cos and/or sin: Amplitude

|a|

cot and/or tan: Period

π/|b|

sec and/or csc:

πn/|b|

Sum Identies:tan(A+B)

(tanA+tanB)/(1-tanAtanB)

Difference Identies: tan(A-B)

(tanA-tanB)/(1+tanAtanB)

Negative-Angle Identies: sin(-ø)

-sinø

Negative-Angle Identies: tan(-ø)

-tanø

SYSTEM OF EQUATIONS

A set of equations with more than one unknown or variable

Periodic or not periodic?

Periodic

BOUNDARY POINT

The endpoint of a ray or segment on a number line where an inequality is true, often called a dividing point

Power Property of Logarithms

The logarithm of a power is the product of the logarithm and the exponent.

Product Property of Logarithms

The logarithm of a product is the sum of the logarithms of its factors.

Quotient Property of Logarithms

The logarithm of a quotient is the difference of the logarithms of the numerator and the denominator.

Rate of Decay

The percent decrease r in the equation y=a(1-r)^t.

Rate of Growth

The percent increase r in the equation y=a(1+r)^t.

BOUNDRY CURVE

The visual dividing marker of a non-linear graph representing where true responses are for the function

BOUNDRY LINE

The visual dividing symbol in a linear graph representing where true responses are for the function

Reciprocal Identies: sec

1/cos

Reciprocal Identies: csc

1/sin

Reciprocal Identies: cot

1/tan

cos and/or sin: Period

2π/|b|

sec and/or cdc: Period

2π/|b|

Pythagorean Identies: cos^2+sin^2

=1

Pythagorean Identies: cot^2+1

=csc^2

Pythagorean Identies: 1+tan^2

=sec^2

Amplitude

Always positive =a the highest point on the graph

Natural Base

An exponential function with base e, y=e^x.

Exponential Decay

Exponential decay occurs when a quantity decreases exponentially over time.

Exponential Growth

Exponential growth occurs when a quantity increases exponentially over time.

Change of Base Formula

For all positive numbers a, b, and n, where a does not equal 1, b does not equal 1, and log a(n) = log b(n)/log b(a).

Logarithm

In the function y=b^y, y is called the logarithms, base b, of x. Usually written a y=log b(x) and is read "y equals log base b of x."

Common Logarithm

Logarithms that use 10 as the base.

Natural Logarithm

Logarithms with base e, written ln x.

UNDOING

Using inverse operations and reversing the order of operations to solve an equation in one variable

quadratic function

a function described by the equation f(x) = ax² + bx + c, where c≠ 0

TWO-VARIABLE EQUATION

a function in which the final answer is an ordered pair with a specific relationship to each other

polynomial function

a function that is represented by a polynomial equation

axis of symmetry

a line about which a figure is symmetric

ONE-VARIABLE INEQUALITY

a mathematical sentence in which the final answer will be all values to one side of the single numerical answer

polynomial

a monomial or a sum of monomials.

coefficient

a number multiplied by a variable in an algebraic expression.

SOLUTION

a number or expression that makes the equation or inequality true when substituted for the variable

monomial

a number, a variable, or a product of a number and one or more variables with whole-number exponents

relative minimum

a point when the graph goes form decreasing to increasing

relative maximum

a point when the graph goes from increasing to decreasing

completing the square

a process used to make a quadratic expression into a perfect square trinomial

vertex form

a quadratic function in the form y = a(x-h)² +k, where (h, k) is the vertex for the parabola and x = h is the axis of symmetry

irrational numbers

a real number that is not rational. The decimal form neither terminates nor repeats

solution

a replacement for the variable in an open sentence that results in a true sentence

INTERSECTION

a single ordered pair shared by two or more functions

equation

a statement that 2 expressions are equal

variable

a symbol or letter used to represent one or more numbers.

Pascal's Triangle

a triangular arrangement of numbers in which each row starts and ends with 1, and each other number is the sum of the two numbers above it

real numbers

all numbers used in everyday life; the set of all rational and irrational numbers

algebraic expression

an expression that contains at least one variable.

rational numbers

any number m/n, where m and n are integers and n is not zero. The decimal from is either a terminating or repeating decimal

complex number

any number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit

Difference Identies: cos(A-B)

cosAcosB+sinAsinB

Sum Identies: cos(A+B)

cosAcosB-sinAsinB

Negative-Angle Identies: cos(-ø)

cosø

Cotangent ratio

cot= cos/sin

RE-WRITE

done in order to change expressions or equations into more useful forms or sometimes, just simpler forms.

EXTRANEOUS SOLUTION

expressions, when solved algebraically accurate, involving a variable will lead to a numerical result that does not make the original equation true

square root property

for any real number n, if x squared = n, the x = plus or minus the square root of n

Zero Product Property

for any real numbers a and b, if ab = 0, then either a = 0, b = 0 or both a and b equal zero

TWO-VARIABLE INEQUALITY

functions in which the final answer is all ordered pairs to one side of a number that are related to each other

SYSTEM OF INEQUALITIES

functions in which the final answer results in an infinite amount of correct answers confined to a specific section of the coordinate plane by a boundary line.

discriminant

in the Quadratic Formula, the expression b² - 4ac

quadratic term

in the equation f(x) = ax² + bx + c, ax² is the ___ term

constant term

in the equation f(x) = ax² + bx +c, c is the ___ term

inverse operations

operations that undo each other

INTERCEPTS

points where a graph crosses a coordinate plane exactly on an axis

constant

quantity whose value does not change

Sum Identies: sin(A+B)

sinAcosB+cosAsinB

Difference Identies: sin(A-B)

sinAcosB-sinBcosA

Tangent ratio

tan= sin/cos

SOLUTION REGION

the confined section of the coordinate plane

end behavior

the directions of the graph to the far left or far right

absolute value

the distance of a number from zero on a number line.

multiplicity

the number of times that a variable's associated factor appears in the polynomial

additive inverse

the opposite of a number that when you add = 0

vertex

the point at which the axis of symmetry intersects a parabola

multiplicative inverse

the reciprocal of a number that = 1 when you multiply

parabola

the set of all points in plane that are the same distance from a given point, called the focus, and a given line, called the directrix

degree of a monomial

the sum of the exponents of all variables in the one term

zeros

the x-intercepts of the graph of a quadratic function; the points for which f(x) = 0

maximum value

the y-coordinate of the vertex of the quadratic function f(x) = ax² + bx + c, where a<0

minimum value

the y-coordinate of the vertex of the quadratic function f(x) = ax² + bx +c, where a > 0

MAXIMIZE

to make as large as possible

compound inequality

two or more inequalities joined together by either "and" or "or".

like terms

two or more terms that contain the same variable.

cot and/or tan: Amplitude

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sec and/or csc: Amplitude

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