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Praxis 5732-Math
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Gravity
Key Concepts:
Terms in this set (90)
Feet to Inches
Multiply by 12
Yards to Feet
Multiply by 3
Yards to Inches
Multiply by 36
Miles to Feet
Multiply by 5280
Miles to Yards
Multiply by 1760
Meters to Centimeters
Multiply by 100
Kilometers to Meters
Multiply by 1000
Inches to Feet
Divide by 12
Feet to Yards
Divide by 3
Inches to Yards
Divide by 36
Feet to miles
Divide by 5280
Yards to miles
Divide by 1760
Centimeters to Meters
Divide by 100
Meters to Kilometers
Divide by 1000
Circumference
2πR
Area of a Circle
A=πr^2 or A=(pi)r(squared)
Area of a Triangle
1/2 bh
Pythagorean Theorem
a^2+b^2=c^2
Volume of a Sphere
V=4/3 πr^3
Surface Area of a Sphere
S=4πr(squared)
Distributive Law
a(b+c)=ab+ac
Volume
L x W x H
8 oz
1 Cup
16 oz
1 lb.
2 cups or 16 oz
1 pint
4 cups or 2 pints or 32 oz
1 quart
4 quarts or 16 cups or 8 pints
1 gallon
Supplementary Angle
Sum of angles equals 180 degrees
Complimentary Angle
Sum of angles equals 90 degrees
Isosceles Triangle
2 equal sides
Equilateral Triangle
All sides equal
Scalene Triangle
No equal sides
Triangles
The sum of all angles equal 180 degrees
Obtuse Angle
Greater than 90, but less than 180 degrees
Acute Angle
Less than 90 degrees
Straight Angle
180 degrees
Right Angle
90 degrees
Opposite Angles
Always equal
Adjacent Angles
The sum equals 180 degrees
Milli
1/1000
Centi
1/100
Deci
1/10
Deca
10
Hecto
100
Kilo
1000
2000 lb
1 ton
FOIL
First Outer Inner last
Quadrilaterals
All internal angles equal 360 degrees
Perimeter of a circle
C/D = X
Diameter
D = 2r
Area of Parallelogram
B x H
Area of Rectangle
L x W
Area of a Square
S squared
Area of a Trapezoid
1/2BH
Volume of Rectangle Solid
BH or LWH
Volume of Cylinder
πr(squared)H
Volume of a Pyramid
1/3BH
Volume of a Cone
1/3πr(squared)H
Inequalities
≤ ≥ =
Equations or Expressions
No = sign
Inequalities <
points left, open circle
Inequalities >
points right, open circle
Inequalities ≤
points left, closed circle
Inequalities ≥
points right, closed circle
Inequality Rule
Flip the arrow around if you divide or multiply by a NEGATIVE
Mean
To find the mean of a set of numbers, add all of the numbers together and divide by the quantity of numbers in the set. (The average)
Median
It is literally the center number if you arrange all the data in ascending or descending order. Find the middle
Mode
The mode of a set of numbers is the number that appears the greatest number of times.
When adding radicals with the same radicands
you just add the coefficients
True or False: You can add radicals with different radicands
false
When multiplying radicals
you multiply the coefficients and radicands
When multiplying radicals the same coefficient and radicands you...
just drop the square root symbol
When dividing radicals you
divide the coefficients and radicands
True or false you can have a negative number under an even root?
False
"King Henry Doesn't Usually Drink Chocolate Milk"
Kilo- *1000
Hecto *100
Deka *10
Original Unit
Deci *1/10
Centi *1/100
Milli *1/1000
Steps to simplifying a single radical
1. Find 2 factors , one with a perfect square 2. Find the square root of the perfect square 3. put the square root and second factor together
Monomials
single terms that are composed of variables and their exponents and a positive or negative coefficient.
i.e. 5x, -6y^3
Binomials
two non-like monomial terms separated by + or - signs
i.e. x+2, 3x^2-5x
Trinomials
three nonlike monomial terms separated by + or - signs.
i.e. x^2+2x-1
Negative Exponents - what's the deal?
A base raised to a negative exponent is equivalent to the reciprocal of the base raised to the positive exponent (absolute value of the exponent).
Ex: 5^-1 = 1/5
7^-2 = (1/7)^2 = 1/49
(2/3)^-2 = (3/2)^2 = 9/4
Exponent Rules (3):
1) When multiplying identical bases, you add the exponents.
Ex: 2^2 x 2^4 x 2^6 = 2^12
2) When dividing identical bases, you subtract the exponents.
Ex: 2^7/2^3 = 2^4
3) If a base raised to a power (in parentheses) is raised to another power, you multiply the exponents altogether.
Ex: (3^2)^7 = 3^14
(g^4)3 = g^12
Integers
-3,-2,-1,0,1,2,3,.... (whole numbers and there opposites
Rational Numbers
all numbers that can be written as fractions, i.e. 2/5, -4/5. The decimal form of these numbers is either terminating decimal, i.e. 3/4 = .75; or repeating decimal, i.e. 1/3 = .333333...
Irrational Numbers
Cannot be expressed as terminating or repeating decimals
Associative Property
If parentheses can be moved to group different numbersin an arithmetic problem without changing the result. ONLY MULTIPLICATION AND ADDITION
Distributive Property
When a value is being multiplied by a sum or difference, multiply that value by each quantity within the parentheses. i.e. 5(a+b)=5a+5b
Multiplying/Dividing Integers
positive x positive = positive
positive x negative = negative
negative x negative = positive
Negative Exponents
negative exponent is equivalent to the reciprocal of the base raised to the positive exponent (absolute value of the exponent)
5^-1=1/5; 7^-2 (1/7)^2= 1/49 ; (2/3)^-2= (3/2)^2=9/4
Square Roots
The square of a number is the product of the number and itself. 9 is the square root of 3. 3x3=9.
The square root may not be whole number. Square roots of nonperfect squares are irrational.
Probability
Probability is the numerical representation of the likelihood of an event occurring. Always represented by a decimal or fraction between 0 and 1, with 0 meaning that the event will never occur, and 1 meaning that the event will always occur. The higher the probability, the more likely the event is to occur.
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