Algebra I Chapter 1 - 5 Study Set
What are the next two terms of 2, 6, 18, ...
54 and 162 Multiply previous term by 3
Terminating Decimal
A decimal number that ends.
Repeating Decimal
A decimal number that has digits that repeat forever.
set-builder notation
A notation used to describe the elements of a set
Perfect Square
A number made by squaring a whole number.
Irrational Numbers
A number that can NOT be expressed as a ratio of two integers or as a repeating or terminating decimal. Examples include: PI or any square root that is not a perfect square number.
Rational Numbers
A number that can be expressed as a ratio (fraction) examples include-terminating and repeating decimals
Base of an Exponent
A number that is raised to a power.
Squared Number
A number with an exponent 2.
Cubed Number
A number with an exponent 3.
rate of change
A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.
inequality
A statement that compares two quantities using <, >, ≤,≥, or ≠
vertical line test
A test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation
Real Numbers
All the numbers on the number line ( including fractions, decimals, rational and irrational )
Integers
Positive or Negative whole numbers
Combine Like Terms
To simplify an expression by adding and subtracting terms with the same variable(s) and exponent(s).
compound inequality
Two inequalities that are combined into one statement by the word "and" or "or"
inverse operations
Two operations that undo each other
arithmetic sequence
a sequence in which each term is found by adding, subtracting, multiplying, or dividing to find the next term
term
a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs.
constant
a term that has no variable factor
independent variable
a variable (often denoted by x ) whose variation does not depend on that of another.
dependent variable
a variable (often denoted by y ) whose value depends on that of another.
y = |x|
absolute value function
Subtraction Inverse
addition
equivalent expression
algebraic expressions that have the same value
function notation
an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x
function rule
an equation that describes a function
Proportion
an equation that states 2 ratios are equal
solution of an inequality
any value that makes the inequality true
Multi - Step Equation
get the variable by itself by undoing the problem, reverse the order of operations, get the variables on one side of equal sign and numbers on the opposite side
at least
greater than or equal to
Solve: 5x + 2 = 1/2 (10x + 4)
identity
Similar Figures
same shape but not the same size, help you measure real-world distances indirectly
graph of a linear function
straight line
Addition Inverse
subtraction
like terms
terms with the same variable(s) that are raised to the same power
absolute value
the distance a number is from zero on the number line
Range of a function
Complete set of all dependent variables (y-values)
function
a relation in which each element of the domain is paired with exactly one element of the range
Perfect Cube
The result of using a whole number in a multiplication three times.
2 step Equation
get the variable by itself by undoing the problem, reverse the order of operations
What are the next two terms of 0.5, 0.25, 0.125, ...
0.0625 and 0.03125 Divide by two
Division Property of Inequalities
If each side of a true inequality is divided by the same positive number, the resulting inequality is also true. a < b a/c < b/c watch out if you divide by a negative, you must flip the inequality sign the opposite direction
Addition Property of Equality
If you add the same number to each side of an equation, the two sides remain equal. a = b a+c = b+c
addition property of inequality
If you add the same number to each side of an inequality, the inequality remains true. a < b a+c < b+c
Division Property of Equality
If you divide each side of an equation by the same nonzero number, the two sides remain equal. a = b a/c = b/c
Multiplication Property of Equality
If you multiply each side of an equation by the same nonzero number, the two sides remain equal. a = b a*c = b*c
Subtraction Property of Equality
If you subtract the same number from each side of an equation, the two sides remain equal. a = b a-c = b-c
subtraction property of inequality
If you subtract the same number from each side of an inequality, the inequality remains true. a < b a-c < b-c
Round a Number
Means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use.
Square Root
One of two equal factors of a number
Relative Error
Ratio of the absolute vale of the difference of a measured (estimated) value and an actual value compared to the actual value
slope
Rise over run
Exponent
Tells you how many times the base number is multiplied to itself.
intersection
The overlapping of two graphs of a compound inequality
table, graph, chart
Visual or graphic that shows lots of information using lines, labels and numbers
multiplication property of inequality
When you multiply each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true. a < b a*c < b*c watch out if you multiply by a negative, you must flip the inequality sign the opposite direction
linear function
a function in which the graph of the solutions forms a line
nonlinear function
a function with a graph that is not a straight line
variable
a letter that represents an unknown number
algebraic expression
a mathematical phrase that includes one or more variables.
inequality
a mathematical sentence that compares the values of two expressions
equation
a mathematical sentence that uses an equal sign
Identity
both sides of equal sign are same
Ratio
compares two numbers by division
Domain
complete set of all independent variables (x-values)
recursive formula
defines the terms in a sequence by relating each term to the ones before it
output
dependent variable
explicit formula
expresses the nth term of a sequence in terms of n
1 step Equation
get the variable by itself by undoing the problem - addition - you subtract - subtraction - you add - multiplication - you divide - division - you multiply
Input
independent variable
A linear function is a function that _____________ a line
is
Solve: 2(x - 4) = 4x - (2x + 4)
no solution
No Solution
no solution works
y = x^2
parabola
Percent Change
ratio of the amount of change to the original amount - amount of increase - new amount is greater than original amount - amount of decrease - new amount is less than the original amount
whole number
the nonnegative integers
coefficient
the number in front of the variable that the variable is multiplied by
multiplication inverse
the number that, when multiplied by a given number, results in a product of one; reciprocal
distributive property
this allows you to multiply a number outside of a grouping symbol by all numbers that are inside of the grouping symbol; Example: 3(x+2) = 3x + 6
simplify
to reduce an expression to its simplest form.
evaluate
to substitute a given number for each variable and then solve.
Solve: - 14 = -5 + 3x
x = - 3
Solve: -7x = 28
x = - 4
Solve: 27 + x = 46
x = 19
Solve: x + 5(x-1) = 7
x = 2
Solve: 3(x-5) = 2(x+5)
x = 25
Solve: - 5 + x = 21
x = 26
Solve: 5(2x - 3) = 15
x = 3
Solve: 3x - 4 = 11
x = 5
Solve: x/7 = 12
x = 84
slope-intercept form
y=mx+b, where m is the slope and b is the y-intercept of the line.
Percent Proportions
you can represent "a is p percent of b" using the percent proportion
What is the domain of {(2,3), (4,5), (5, 6), (6,6)}?
{2, 4, 5, 6}
What is the range of {(2,3), (4,5), (5, 6), (6,6)}?
{3, 5, 6}
no more than
≤ less than or equal to