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32 Cards in this Set

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  • Back
Variable
a letter or symbol used to represent an unknown number
Constant
a value that does not change
Numerical Expression
contains only constants and/or operations
Algebraic Expression
contains only variables, constants, and/or operations
Evaluate an Expression
to find its value...substitute given numbers for the variables and then simplify the expression using the order of operations
Equation
a mathematical statement that two expressions are equal
Solution of an Equation
a value of the variable that makes the equation true
Properties of Equalities
you can add, subtract, multiply, or divide the same number to both sides of an equation, and the statement will still be true...used to solve equations
Distributive Property
for all real numbers, a, b, and c, a(b+c)=ab+ac
Example: 3(2x+1)=6x+3
Coefficient
a number that is multiplied by a variable...in 3x, 3 is the coefficient (x is the variable)
Like Terms
terms that have the same variables with the same exponents...to collect like terms, you add or subtract their coefficients (variables and exponents stay the same)
Identity
an equation that is always true no matter what value is substituted for the variable...the solution is All Real Numbers
If when solving, the variables cancel and the remaining equation is true, then the equation is an identity
If the remaining equation is false, then the equation has no solutions (but has no special name)
Formula
an equation that states a rule for a relationship among quantities
Literal Equation
an equation with two or more variables...a formula is a type of literal equation
Absolute Value of a Number
its distance from zero on a number line
Steps for Solving an Absolute Value Equation
1. Use inverse operations to isolate the absolute-value expression
2. Rewrite the resulting equation as two cases (one positive answer and the other negative answer) without absolute values
3. Solve the equation in each of the two cases
Ratio
a comparison of two quantities by division (a fraction a/b or a:b)
Proportion
a statement that two ratios are equal
Rate
a ratio with two quantities with different units
Ex: 34 km/ 2 hr
Unit Rate
a rate with a denominator of 1...you can change any rate to a unit rate
Ex: 16 km/1hr or 16 km/hr
dimensional analysis
a process that uses rates to convert measurements from one unit to another
Conversion factor
a rate in which two quantities are equal but have different units...used to convert from one set of units to another
Proportion
a statement that sets two ratios (fractions) equal to each other...The idea of proportions is that a ratio can be written in many ways and still be equal to the same value
Cross Products Property
used to solve proportions...if a/b=c/d, then ad=bc
Scale
a ratio between two sets of measurements such as 1 in: 5 miles
Scale Drawing
uses a scale to represent an object as much smaller or larger than the actual object...a map is an example of a scale drawing
Similar Figures
figures that have exactly the same shape but not necessarily the same size
Corresponding Sides/Angles
sides/angles of two figures that are in the same relative position...Two figures are similar IFF the lengths of the corresponding sides are proportional and the corresponding angles have equal measures
Indirect Measurement
method of measurement that allows you to solve a proportion involving similar triangles to find a length that is not easily measured..Ex: Using shadows
Precision
level of detail in a measurement...determined by the smallest unit or fraction of a unit that you can reasonably measure
Accuracy
the closeness of a measured value to the actual or true value
Tolerence
describes the amount by which a measurement is permitted to vary from a specified value...Usually expressed as a range of values