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Terms in this set (69)
Integer
positive or negative whole number
rational number
any number that can be expressed as a fraction
factor
an integer that can be multiplied by another integer to get the given number ex. 7 is a factor of 21
order of operations
PEMDAS - Parenthesis, exponents, multiplication, division, addition, subtraction
negative exponent
put the number at the bottom of a fraction ex. 3^-3 = 1/3³= 1/27
multiplying exponents with the same base
keep the base add the exponents
ex. (n⁴)(n²) = n⁶
dividing exponents with the same base
subtract exponents
ex. (n⁵)/(n²)= n³
exponents raised to an exponent
multiply the exponents
ex. (n^3)^6 = n^18
any number with exponent of 0
equal to 1
imaginary number
square root of -1 = i
i² =
-1
complex number
one real number and one imaginary number
ex. 4 + 3i
vertical angles
when 2 lines intersect, the pairs of opposite angles. they are congruent
supplementary angles
2 angles whose measures add to equal 180
angles in a triangle
add up to 180
area of a triangle
1/2bh
angle side relationship in triangles
size of the side is directly related to the size of the opposite angle.
ex. the longest side is opposite the largest angle
equilateral triangle
all sides are the same and all angles measure 60 degrees
isosceles triangle
two sides and their opposite angles are the same
right triangle
one angle is 90 degrees, the two acute angle added equal 90
Pythagorean Theorem
a² + b² = c² in a right triangle only. where a and b are the legs and c is the hypotenuse
similar triangles
all the angles are the same and the same ratio exists between all corresponding sides
length of triangle sides
the length of a side must be less than the sum and greater than the difference of the 2 other sides.
ex. if two sides have length 3 and 5, the third side must be less than 8 and more than 2
parallelogram
two pairs of parallel sides, all angles add to 360, opposite angles are equal, consecutive angles are supplementary.
area of rectangle
length times width
trapezoid
4 sides, one pair of parallel sides, angles add to 360
area of trapezoid
average of the base times height
perimeter
distance around a shape - add the sides
radius
line segment from center of a circle to the edge
1/2 the diameter
diameter
line segment starting on one edge of a circle, passes through the center to the opposite edge
tangent to a circle
line that touches a circle at exactly one point
the line is perpendicular to the radius at this point
perpendicular
creates a 90 degree angle
parallel
two lines that exist on the same plane but will never touch
Arclength
degrees/360 x πd
circumference
the distance around a circle
pi times diameter
area of a circle
pi times r²
translation
transformation of a point or shape sliding from one place to another
rotation
transformation that rotates a shape around a specified point
reflection
transformation that flips a point or shape across a specified line usually the x- or y-axis
Volume of a rectangular prism
V = lwh
volume of a cylinder
area of the circle base times height
pi
r^2
h
volume of a sphere
4/3
π
*r³
distance formula
√(x2 - x1)² + (y2 - y1)²
midpoint formula
(x1 + x2) ÷ 2 , (y1 + y2) ÷ 2
domain
all the x values that exist on a graph
range
all the y values that exist on a graph
slope intercept form of a line
y = mx + b
m = slope
b = y-intercept
slope
rise over run
change in y over the change in x
parallel line equations
same slope different y-intercepts
perpendicular line equations
have opposite reciprocal slopes
ex. 2/3 and -3/2
quadratic function
includes x² as its highest power in simplest form
graphs a parabola
zeros of a quadratic function
points where the graph touched or crosses the x-axis
to solve let f(x) = 0 then solve
sine
opposite/hypotenuse
cosine
adjacent/hypotenuse
tangent
opposite/adjacent
cosecant
reciprocal of since
secant
reciprocal of cosine
cotangent
reciprocal of tangent
Pythagorean Triple
3-4-5 and 5-12-13 right triangles and their multiples
45-45-90 triangles
legs = x, hypotenuse = x√2
30-60-90 triangles
short leg = x, long leg = x√3, and hypotenuse = 2x
Odd function
Symmetric to origin f(-x)=-f(x)
even function
graph is symmetrical with respect to the y-axis; f(x) = f(-x)
arithmetic sequence
an=a1+(n-1)d ; an = number at term n, a1 = first term, n = term number, d = common difference
geometric sequence
an=a1(r)^n-1 ; an = number at term n, a1 = first term, r = common ratio, n = term number
Equation of a circle
(x-h)²+(y-k)²=r²
Tangent
touches at exactly one point
radians to degrees
multiply by 180/π
degrees to radians
multiply by π/180
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