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Math CRCT Study Notes
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66
Mathematics
8th Grade
04/23/2014

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Term
Integer Rules
ADDITION AND SUVTRACTIKKN
Definition
Same signs add and keep
Different signs subtract and keep the sign of the bigger number
Term
Integer Rules
MULTIPLI ATION AND DIVISION
Definition
Same signs positive
different signs negative
+--
-+-
--+
Term
Tramsformations
DIALATOINS
Definition
Bigger or smaller
Multiply the scale factor
Term
Transformations
ROTATIONS
Definition
Turn
90* counterclockwise-switch x and y, change sign of the new x
90* clockwise-switch x and y, change sign of new y
180*-change sign of x and y
Term
Transformations
TRANSLATIONS
Definition
sLIDE
Add x and y to y
Positive is right and up, negative is left and down
Term
Tramsformations
RECLECTIONS
Definition
X-axis-Change thhe sign of y
Y-axis-change the sign of x
Term
Transformations
RIGID TRANSFORMATIONS
Definition
Change and object's location without changing the dimensions of the object
Term
Transformations
LINE SYMMETRY
Definition
Fold line where the object looks exactly like it did before the turn
Term
Transformations
CONGRUENT
Definition
Same size and shape
Reflactions, rotations, and translations
Term
Transformations
SIMILAR
Definition
Same shape but different size
Dialations
Term
Tranaformations
A-A'
Definition
A is the original point, the - shows the transformation happened, A' is the new point
Term
Transformations
PREIMAGE
Definition
The shape before the transformation
Term
Transformation
IMAGE
Definition
The shape afte the transformation
Term
Transversals
CORRESPONSING
Definition
Same position: angles are congruent
Term
Transversals
TRANSVERSAL
Definition
Line that intersects a set of parallel lines
Term
Tranversals
ADJACENT ANGLES=
Definition
Angles that share a sign
Term
Tranaversals
VERTICAL ANGLES
Definition
Angles that are opposite of each other; congruent
Term
Transversals
SAME SIDE INTERIOR ANGLES
Definition
Two angles on the same side of the transversal and in-between the parallel lines; supplementary
Term
Transversals
SAME SIDE EXTERIOR ANGLES
Definition
Two angles on the same side of the transversal and ountside the parallel lines; supplementary
Term
Transe paversals
ALTERNATE INTERIOR ANGLES
Definition
Two angles that are on opposite sides of the transversal and in-between the parallel lines; congruent
Term
Transversals
ALTERNATE EXTERIOR ANGLES
Definition
Two angles that are on opposite sides of the transversal and outside of the parallel lines; congruent
Term
Exponents
Anything raised to the zero power equals
Definition
ON
Term
Exponenmts
Anything to the first power is
Definition
ITSELF
Term
Exponencts
{-3}2
-3{2}
Definition
A negative number in parenthases raised to an EVEN power is positive, however, a negetive number NOT in the parenthases raised to any power stays the same
Term
Exponents
{-4}3=-64
-4{3=-64
Definition
A negative number raised to an ODD power is negative
Term
Exponents
BASE
Definition
BIG number
Term
Exponents
EXPONENTS
Definition
Little number
Term
Exponents
MULTIPLYING NUMBERS
Definition
Add exponents on like bases
Term
Exponents
DIVIDING NUMBERS
Definition
Subtract exponents on like bases
Term
Rational amd Irratiomal Numbers
RATIONAL NUMBERS
Definition
Whole numbers, fractions, repeating, and terminating decimals
Positive or negative integers
Term
Rational amd Irratiomal Numbers
IRRATIONAL NUMBERS
Definition
Numbers that do NOT terminate or repeat
Term
Rational amd Irratiomal Numbers
EXAMPLES
Definition
Pi
Square roots of numbers that are not perfect squares
When a number ends in an ellipse {...}
Term
Rational amd Irratiomal Numbers
SQUARE ROOTS
Definition
Ask "what number times itself equsls the number under the radical symbol"
Term
Rational amd Irratiomal Numbers
ESTIMATING A SQUARE ROOT
Definition
Find the closest perfect squares
Guess and check
Term
Rational amd Irratiomal Numbers
CUBE ROOTS
Definition
Ask "what number goes into itself three times equals the number under the cubed root symbol"
Term
Scientific Notation
MULTIPLICATION
Definition
Multiply the numbers and add the exponents
Term
Scientific Notation
DIVISION
Definition
Divide the numbers and subtract the exponents
Term
Scientific Notation
ADDITION
Definition
Match the exponents, add, and keep the matched exponent
Term
Scientific Notation
SUBTRACTION
Definition
Match the exponents, subtract, and keep the matched exponent
Term
Equations
TO SOLVE
Definition
Use the oorder of operations in reverse to isolate the variable
Term
Equations
ONE SOLUTION
Definition
Variavle equals a number
Term
Equations
NO SOLUTION
Definition
Two diifferent numbers are on each side of the equal sign
Term
Equations
INFINITE SOLUTIONS
Definition
Numbers equal on either side of the equal sign
Term
Pythagorean Theorem
A2+B2=C2
Definition
A and b are the legs and c is the hypotenuse
Term
Pythagorean Theorem
DISTANCE FORMULA
Definition
Distance={x2-x1}2+{y2-y1}2
Term
Volume
SPHERE
Definition
V=4/3{pi}r3
Term
Volume
CONE
Definition
V=1/3{pi}r2h
Term
Functions
FUNCTION VS. RELATION
Definition
A function is a relation in which each number of the domain is paired with only one number of the range
Term
Functions
HORIZONTAL AND VERTICAL LINES
Definition
Horixantol lines are functions
Vertical lines are not functions
Term
Functions
VETICAL LINE TEST
Definition
If a vertical line crosses a graph more than once, the graph is NOT a function
Term
Functions
LINEAR FUNCTIONS
Definition
Straight line
Equation can bbe written in y=mx+b form
Term
Functions
Y=MX+B FORM
Definition
x and y have exponents of 1
x and y are not multiplied together
x and y do not appear in denominators, exponents, or under radical signs
Term
Functions
RATE
Definition
The ratio of two numbers in whitch the second term is 1
Term
Functions
SLOPE
Definition
Constant rate of change
Rise over run
Difference in the y over the difference over the x
Term
Functions
DIRECT PROPORTION
Definition
Graph is a straight line that goes through the origin
Y-intercept is zero
Term
Functions
SIMILAR TRIANGLES AND SLOPE
Definition
Similar triangles-the ratio of the height of the triangle to the base forms a constant ratio no matter how close or far apart the points are from the line. This slope remains the same as long as the points are located on the same line.
Term
Linear Functions
SLOPE INTERCEPT FORM
Definition
y=mx+b
{x,y} is the ordered pair
m is the slope
b is the i-intercept
Term
Linear Functions
GRAPHING IN SLOPE-INTERCEPT FORM
Definition
Put the y-intercept in
Use rise over run
Term
Linear Functions
STANDARD FROM
Definition
Ax+By=C
To graphy a line in standard form find the intercepts, the plot, and connect the two points
Term
Linear Functions
X AND Y INTERCEPTS
Definition
X-intercept-put in 0 for y and solve for x
Y-intercept-put in 0 for x and solver for y
Term
Systems of Equations
INCONSISTENT
Definition
No solution
Two different numbers on each side of the equal sign
Term
Systems of Equations
CONSISTENT DEPENDENT
Definition
Infinite solutions
each sides of the equa. signs match
Term
Systems of Equations
CONSISTENT DEPENDENT
Definition
One solution
A variable equal a number
Term
Systems of Equations
PARALLEL LINES
Definition
Same slope
Different y-intercepts
No solution
Term
Systems of Equations
CONGRUENT LINES
Definition
Same line, y-intercept, and slope
Infinite solutions
Term
Systems of Equations
SOLVING SYSTEMS
Definition
Graphing: graph each line, intercestion=solution
Substitution: solve for one variable and plug it into an equation
Elimination: get rid of a variable term
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