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Middle School Math Praxis
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Gravity
Middle School Math Praxis terms
Terms in this set (86)
right prism volume
V=bh
sphere surface area
A=4πr^2
sphere volume
V=4/3πr^3
right prism surface area
A=2B+3(lw) (sum of areas of rectangular sides)
rectangular prism volume
V=lwh
rectangular surface area
A=2hl+2hw+2lw
cube volume
V=s^3
cube surface area
A=6s^2
cylinder volume
V=πr^2h
cylinder surface area
A=2πrh
cylinder total surface area
A=2πrh+2πr^2
pyramid volume
V=1/3Bh
pyramid surface area
A=B +4(½bh) (sum of areas of 4 triangle sides)
cone volume
V=1/3πr^2h
cone surface area
A=πr sqroot r^2+h^2
cone total surface area
A=πrs+πr^2
Absolute value equation
A V-shaped graph that points upward of downward
Area of a circle
Πr²
Area of a sector
x°/360 times (∏r²), where x is the degrees in the angle
Area of a square
s², where s = length of a side
Area of a trapezoid
½(b₁ +b₂) x h
[or (b₁ +b₂) x h÷2]
Area of a triangle
½(base x height) [or (base x height)÷2]
Area of Circles
A=∏r^2
Area of rectangle, square, parallelogram
A=bh
a³-b³
(a-b)(a²+ab+b²)
Circumference Formula
C =∏d
Circumference of a circle
∏d OR 2∏r
Direct Variation
y=kx
k represents the constant of variation
Examples: "F varies as x" means F=kx
"F varies jointly as x and y" means F=kxy
"F varies as x + y" means F=k(x+y)
"F varies inversely as x" means F= (k/x)
Equation of a circle
(x-h)²+(y-k)²=r² where (h,k) are coordinates for the center of the circle
Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
Perimeter of a square
4s (where s = length of a side)
Point-Slope form
y-y₁=m(x-x₁)
Quadratic Formula
-b±[√b²-4ac]/2a
Slope
(y₂-y₁)/(x₂-x₁)
Slope intercept form
y=mx+b
one to one correspondance
link a single number name with one object, and only one object
rational numbers
can be expressed as the ratio of two integers, a/b, where b does not equal 0
integers
positive and negative whole numbers and zero
whole numbers
natural numbers and zero 0,1,2,3,4,5,6
natural numbers
the counting numbers 1,2,3,4,5,6...
irrational numbers
real numbers that cannot be written as the ratio of two integers (infinite non-repeating decimals example 7 divided by 10
cardinal numbers
also known as counting numbers because they indicate quantity
ordinal numbers
indicate the order of things in a set
commutative property
you can change the order of the terms or factors and you will still get same answer, only applies to addition and multiplication examples: a+b=b+a, or ab=ba
associative property
you can regroup the terms as you like, does not apply to division or subtraction, example: a+(b+c)=(a+b)+c, or a(bc)=(ab)c
identity property
finding a number so that when added to a term results in that number examples: 17+0=17, 34x1=34
inverse property
finding a number such that when added to the number it results in zero or when multiplied results in 1 examples: 25-25=0, 5x1/5=1
distributive property
allows us to operate on terms within parentheses without first performing operations within the parentheses example: 6 x (4+9)=(6 x 4) + (6 x 9)
greatest common factor
the largest number that is a factor of all the numbers in a a problem
least common multiple
the smallest number of a group of numbers that all the given numbers will divide into evenly example 20, 30, 40 lcm is 120
linear relationship
a relationship in which quantities are proportional to each other
nonlinear relationship
a relationship in which change in one quantity does not affect the other quantity to the same extent
solids
the union of all points on a simple closed surface and all points in its interior
polyhedron
a simple closed surface formed from planar polygonal regions
face
each polygonal region
translation
a transformation that slides an object a fixed distance in a given direction
rotation
a transformation that turns a figure about a fixed point called the center of rotation
reflection
objects have the same shape and size but the figures face in opposite directions
line of reflection
the line where a mirror may be placed; the distance from a point to this line is the same as the distance from the point's image to this line
glide reflection
a combination of a reflection and a translation
dilation
a transformation that shrinks an object
tessellation
an arrangement of closed shapes that completely covers the plane without overlapping or leaving gaps
nets
a two-dimensional figure that can be cut out and folded up to make a three dimensional solid
volume
the number of cubic units in a solid v=bh
area
the number of square units covered by a polygon a=1/2bh
surface area
the total area of all the faces including the bases S= 2(lw+hw+lh)
acute angle
greater than 0 and less than 90 degrees
right angle
exactly 90 degrees
obtuse angle
greater than 90 and less than 180 degrees
straight angle
exactly 180 degrees
adjacent angle
have a common vertex and one common side but no interior points in common
complementary angle
add up to 90 degrees
supplementary angle
adds up to 180 degrees
vertical angle
have sides that form two pairs of opposite rays
corresponding angles
same corresponding position on two parallel lines cut by transversal
alternate interior angle
diagonal angle on the inside of two parallel lines cut by a transversal
mean
the sum of the numbers given, divided by the number of items being averaged
median
the middle number of a set
mode
the number taht occurs with the greatest frequency in a set of numbers
range
a measure of varaiblity the largest number minus the smallest number of a set
Additive/Multiplicative Identity
The value that, when added/multiplied to a number, does not change the number.
Additive/Multiplicative Inverse
Process carried out by adding/multiplying a number to another to equal 0. -3+3=0.
multiplying a number, the number you get to multiply it to 1
Trapazoid
a 4 sided shape with exactly one set of parallel lines.
Isosceles triangles
equal angles are opposite equal sides
Equilateral Triangle
all sides and angles are equal
distance formula
d=√(x2-x1)²+y2-y1)²
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