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Praxis Core (Math)
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Gravity
Terms in this set (116)
Whole Numbers
0 and go on forever: 1, 2, 3 and so on. Each whole number is separated from the next by a quantity of 1
Partial Numbers
Fractions and decimals; not whole numbers
Positive and Negative numbers
a negative number is the opposite of a positive number, and vice versa.
Integers
All the whole numbers and their opposites. The only integer that doesn't have an opposite is 0
Absolute Value
an integer's positive distance from 0. It's value without a negative sign.
Ex: |4| = 4 or |-4| = 4
Working with integers
* Subtracting an integer is the same as adding its opposite, and adding a number is the same as subtracting its opposite.
*If an even number of negative integers are multiplied or divided, the product is positive. If an odd number of negative integers are multiplied or divided, the product is negative.
*To add two integers with the same sign, add their absolute values and give the sum of the sign that both numbers have
* To add two integers with opposite signs, subtract the smaller absolute value from the greater absolute value and give the difference the sign of the number with the greater absolute value.
Factor
a factor of a whole number is the whole number that can be divided into it a whole number of times.
Remember: every whole number has itself and 1 for factors. If those are the only two factors of a number its a prime number.
Prime number
a whole number that only has itself and 1 for factors.
Prime factorization
a representation of the number as a product of all its prime factors.
greatest common factor vs least common multiple
GCF: greatest factor in common (20: 1, 2, 4, 5, 10, 20)
LCM: lowest number in common and is a multiple instead of a factor. (3: 3, 6, 9, 12...)
Exponent
represents how many times a number is a factor. 2 = squared, 3 = cubed
Square root
a way to find what has to be squared to get a number
Numerator and Denominator
N: integer on the top of the fraction
D: integer of the bottom of the fraction
Ratio
A comparison of two quantities
Mixed Number
an integer followed by a fraction
Simplified
it cannot be written with two integers with smaller absolute values. Written in the simplest form possible.
(Find the GCF of the numerator and denominator and divide)
Converting mixed numbers to fractions
*Multiply denominator of the fraction by absolute value of the integer.
*Add the numerator to that product.
*Write the result of the denominator of the fraction
**Put a negative sign before the fraction if the mixed number is negative
Converting fractions to mixed numbers
*Write the highest integral number of times the denominator fits completely into the numerator.
*Write what remains as the numerator of a fraction beside the integer.
*The denominator of the fraction will be the denominator of the fraction you are converting.
Common denominator
same denominator for both fractions
Adding fractions
w/ common denominator: add numerators
Diff denominators: make denominator the same - multiply the numerator and the denominator by the same number which should be the number you have to multiply to get the denominator you want.
Multiplying fractions
multiply the numerators and then multiply the denominators
Dividing fractions
same as multiplying by its reciprocal (switch the numerator and denominator)
Reciprocal
switch the numerator and denominator
Improper Fraction
a fraction in which the numerator is greater than the denominator
Percent
a representation of a number of hundredths (%)
Decimals
represent whole and partial numbers
Converting percents to decimals
drop the % sign and put the number over 100 & simplify or drop the sign and move the decimal two places to the left
Converting decimals to percents
moving the decimal two places to the right and adding % sign.
Multiplying decimals
the total number of digits after the decimal point in the answer equals the number of placeds after the decimal points in the numbers you're multiplying. (ex: 3 numbers after decimal before = 3 decimals after when done)
Number line
illustrate orders of numbers. Arrows indicate that the numbers go on infinitely in both directions.
Coordinates
The numbers represented by points on the number line.
Magnitude
a numbers absolute value or positive distance from 0.
Sequence
a list of numbers in a certain type of order
Arithmetic sequence
the same quantity is added to each number to get the next
Geometric sequence
each number is multiplied by the same quantity to get the next
Order of operations
PEMDAS - parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right)
Metric System Prefixes
Milli - 1/1000
Centi - 1/100
Deci - 1/10
Main unit (meter, liter, gram) - 1
Deca - 10
Hecto - 100
Kilo - 1,000
Distance Conversions
12 inches make up a foot
3 feet make a yard
5,280 feet compose a mile
Volume Conversions
2 cups form a pint
2 pints make a quart
4 quarts make up a gallon
Weight Conversions
16 ounces makes a pound
a ton is 2,000 pounds
Variables
letters that represent numbers
Coefficient
A number that precedes a variable or variables to indicate that it is multiplied by them. Ex: 10xyz, 10 is the coefficient
Term
A variable or group of variables next to a coefficient, or with an understood coefficient of 1. A number followed by no variables is also a term.
Expression
A single term or a group of terms seperated by + or - forms an expression
Like terms
terms that have either exactly the same variable or variables with only one exponent for each variable or no variables. Can be combined.
Multiplying two term expressions
FOIL (first inner outer last)
Proportion
An equation in which one ratio (usually in the form of a fraction) is set equal to another.
Substitution method
Finding the value of one variable in terms of the other in one equation. Then you can substitute that expression for the variable in the second equation.
Elimination
Adding the same value to or subtracting the same value from both sides of a true equation results in another true equation. Usually variable term has a coefficient other than 1.
Inequality
One side is (or may be) greater than or less than the other side.
Reverse Foil
Add
Relation
A set of ordered pairs
Domain and range
The set of x values in a relation is the domain. The set of y values in a relation is the range.
Function
A relation in which each number in the domain is paired with the only one number in the range. Each domain is paired with just one range value (x never repeats)
Direct variation
A relationship pattern in which one quantity increases as another one increases, though they may increase at different rates.
Inverse variation
A relationship pattern in which one quantity decreases as another one increases. The two quantities don't increase together. The greater one quantity is, the smaller the other one is.
Distance formula
D = rt
Distance, rate and time.
Conditional statements
If-then statements
Point
An exact and infinitely small location
Line
A continuous set of an infinite number of points extending infinitely in two directions. Lines are one dimensional.
Segment
Part of a line with two expoints.
Plane
A flat surface that is infinitely thin and goes forever in all directions.
Angle
A shape formed by two sides, with each side being either a line or part of a line.
Vertex
The point at which the two sides of an angle meet.
Congruent
Two segments or angles that have the same measures.
Supplementary
Two angles having measures that add up to 180
Linear pair
Pair of angles that together form a line.
Complementary
Two angles having measures that add up to 90 degrees.
Vertical angles
Opposite of each other. They are always congruent. If you have intersecting lines you always have two pairs of vertical angles.
Polygon
An enclosed figure formed on one plane by segments joined at their end points. The number of sides a polygon has is also the number of interior angles it has.
Convex polygons
Polygons that don't point inward anywhere.
Triangle
3 sided polygon. The sum of all the interior angles of a triangle = 180 degrees. If two sides of a triangle are congruent, the angle opposite (across from) those sides are congruent. Same rule with angles.
Quadrilaterals
4 sided polygons. The sum of their interior angles is always 360 degrees.
Parallelogram
A quadrilateral in which both pairs of opposite sides are parallel. Both pairs of opposite sides are also congruent.
Rectangle and square
Is a quadrilateral in which all four interior angles are right angles and all rectangles are parallelograms so their opposite sides are congruent
Trapezoid
A quadrilateral that had just one pair of parallel sides. The two parallel sides are the bases of the trapezoid.
Similar shapes
Same shape but not necessarily congruent.
Proportional sides
The ratio of the measure of a side in one polygon to the measure of the side that corresponds to it in the other polygon is always the same ratio.
Perimeter
The distance around an object
Perimeter of a rectangle
2l + 2w
Circumference
The perimeter of a circle. C/D=pie
Or C=2pieR
Circumference, diameter, pie (3.14), radius
Area
Amount of plane in it. How much room is inside a two dimensional shape.
Area of a parallelogram
Base x height
Area of a rectangle
Length x width
Area of a square
S^2
Area of a triangle
1/2bh
Base, height
Area of a circle
PieR^2
Area of a trapezoid
1/2h(b1+b2)
Surface area
Applies to 3D figures and is the total amount of the area that is on a figure. (3D figures are made of nothing but faces)
Slant height
The distance from the apex or the top point, to the center of an edge of the base.
Surface area of a rectangular solid
2B + Ph
Base, perimeter, height
Surface area of a cylinder
2pieR^2+2pieRH
Surface area of a pyramid
B+1/2P(slant height)
Surface area of a cone
PieR^2 + pieR(slant height)
Surface area of a sphere
4pieR^2
Volume
The amount of space inside a 3D figure
Volume of rectangle solid
Bh or lwh
Volume of q cylinder
PieR^2h
Volume of a pyramid
1/3Bh
Volume of a cone
1/3PieR^2h
Volume of a sphere
4/3PieR^3
Slope
Y1-y2/X1-x2 or y=mx+b
M= slope b=y intercept
Distance between two points
square root of (X1-x2)^2 + (y1-y2)^2
Midpoint
(X1+x2/2, y1+y2/2)
Transformations
Figures altered by changing the location in their vertices.
Translation
Moving it a number of units horizontally and a number of units vertically
Reflections
Flipping figures over an axis and creating new images that are like mirror relfections
Donations
Changes in sizes of the figure
Rotations
Moving of figures along circular paths while the distance between every point and the center of the circular path stays the same.
Pythagorean theorem
A^2 + b^2 = c^2
Leg, leg, hypotenuse.
45-45-90 triangle
Isosceles, two congruent sides. The two legs are congruent. The hypotonuse is always the square root of 2 times the measure of the leg.
60-60-60 triangle
Equilateral, all three sides are congruent
30-60-90
Hypotenuse measure is twice that of the shorter let (which is opposite the 30 degree angle), and the longer leg is the square root of 3 times the measure of the shorter leg.
Stem and leaf plot
Stem (tens) leaf (ones)
Box and whisker plots
#s organized from least to greatest.
The least value, the lower quartile (the median of the lower half of the data set), the median, the upper quartile, the greatest value.
Graph on a line.
Exponents
Move decimal from Left to right = negative/right to left = positive.
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