Download McDougal Algebra 2 Test Ticket - Chapter 1

McDougal Algebra 2 Test Ticket - Chapter 1
Definitions
Term/Concept
Absolute Value
Description
The distance a number is from zero on a number line without regard to direction. The
absolute value of x is written as
Additive Inverse
Algebraic Expression
Coefficient
Division
x.
The opposite of a number. The result of multiplying by –1. The additive inverse of a is a(-1)
or –a. If a was positive, the additive inverse is negative. If a was negative, the additive
inverse is positive.
An expression that includes variables. The elements of an are called terms. Terms are added
together to form an expression. (3x + 2 is an algebraic expression)
The constant part of a variable term. The 3 in 3x is a coefficient.
Multiplying by the reciprocal.
1

b
a  b = a
Equivalent Equation
Equation
Equation, Linear
Extraneous Solution
Formula
Inequality
Integers
Irrational Numbers
Natural Numbers
(Counting Numbers)
Numerical Expression
Power
Rational Numbers
Real Numbers
Reciprocal
(multiplicative inverse)
Solution
Equations that have the same solution.
A statement that sets two expressions equal to each other.
An equation where the highest power of any variable is 1.
A solution of an absolute value equation that does not satisfy the original equation.
An equation that relates two or more quantities that are usually represented by variables.
An expression in which terms are separated by logical operators like <, >, etc.
Positive and negative whole numbers from - to +.
Numbers that can not be represented by the ratio of two integers. Numbers whose decimal
portion neither repeats or terminates
Numbers with out decimals in the range from 1 to +.
Consists of numbers, operations, and grouping symbols.
An expression formed by repeated mulplication of the same factor.
Numbers that can be generated by the ratio of two integers. Numbers whose decimal portion
either repeats and does not terminate, or terminates.
All numbers including rational and irrational numbers.
If a is any nonzero number then the reciprocal of a is
1
.
a
A number is a solution of an equation with one variable if substitution of that number for the
variable in the equation results in a true statement.
Subtraction
Term
Term, Constant
Term, Variable
Variable
Whole Numbers
Adding the opposite or additive inverse. a – b = a + -(b)
Part of an expression that contains variables and/or numbers.
A term that has only a number. The 2 in the following expression is a constant term 3x + 2.
A term that has a variable or a variable multiplied by a constant. x and 3x are variable terms.
A letter used to represent one or more numbers.
Natural Numbers plus zero.
McDougal Algebra 2 Test Ticket - Chapter 1
Rational

Integers
9
2
-1
Whole
Irrational
32.1818181818…
1
= 0.333
3

-2
0
2
Natural
6.5
1, 2, 3, …
-3
-4
1
2
Properties of Addition and Multiplication
If a, b, and c are real numbers, then:
Property
Closure
Addition
a + b is also a real number.
Multiplication
ab is also a real number.
Commutative
a+b=b+a
ab = ba
Associative
(a + b) + c = a + (b + c)
(ab)c = a(bc)
Identity
a + 0 = a, 0 + a = a
a  1 = a, 1  a = a
Inverse
a + (-a) = 0
The following property involves both addition and multiplication.
Distributive
a(b + c) = ab + ac
a
1
= 1, where a  0
a
McDougal Algebra 2 Test Ticket - Chapter 1
Properties of Equality
Reflexive Property
Symmetric Property
Transitive Property
Addition and Subtraction Properties
Multiplication and Division
Properties
For every number a, a = a
For all numbers a and b, if a = b, then b = a
For all numbers a, b, and c, if a = b and b = c, then a = c
For all numbers a, b, and c, if a = b, then a + c = b + c and a – c = b – c
Substitution Property
For all numbers a and b, if a = b, then a may be replaced by b in any equation or
expression.
For all numbers a, b, and c, a + (b + c) = (a + b) + c and (a•b)•c = a•(b•c)
For all numbers a and b, a + b = b +a and a•b = b•a
For all numbers a, b, and c, a(b + c) = ab + ac.
Associative Property
Commutative Property
Distributive Property
For all numbers, a, b, and c, if a = b, then a • c = b • c, and if c  0,
a b

c c
Formulas
Term/Concept
Description
Area of a Circle
Circumference of a Circle
Distance
Temperature
A = r2 Where A=Area, r=radius.
C = 2r Where C=Circumference and r=radius.
d=rt
Where d= distance, r = rate, t = time.
Area of a Triangle
Area of a Trapezoid
Area of a Rectangle
Perimeter of a Rectangle
Interest, Simple
Distance Formula
A = ½ b h Where A=Area, b=length of the base, h=height
A = ½ h(b1 + b2) Where A=Area, b1=base 1, b2=base 2, h=height
A=l•w
P = 2l + 2w
I = P • r • t (I = Interest dollars, P = Principal dollars, r = interest rate, t = time in years)
The distance between any two points with coordinates (x1,y1) and (x2,y2) is given by the
9
F  C  32 Where F=degrees Fahrenheit, C=degrees Celsius.
5
formula d 
Midpoint Formula
( x 2  x1 ) 2  ( y 2  y1 ) 2
On a number line, the coordinate of the midpoint of a segment whose end points have
coordinates a and b is
ab
.
2
In a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have
coordinates (x1,y1) and (x2,y2) are
(
x1  x2 y1  y 2
,
)
2
2