Praxis Core (Math)
Terms in this set (116)
0 and go on forever: 1, 2, 3 and so on. Each whole number is separated from the next by a quantity of 1
Fractions and decimals; not whole numbers
Positive and Negative numbers
a negative number is the opposite of a positive number, and vice versa.
All the whole numbers and their opposites. The only integer that doesn't have an opposite is 0
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.
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.
a whole number that only has itself and 1 for factors.
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...)
represents how many times a number is a factor. 2 = squared, 3 = cubed
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
A comparison of two quantities
an integer followed by a fraction
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.
same denominator for both 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.
multiply the numerators and then multiply the denominators
same as multiplying by its reciprocal (switch the numerator and denominator)
switch the numerator and denominator
a fraction in which the numerator is greater than the denominator
a representation of a number of hundredths (%)
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.
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)
illustrate orders of numbers. Arrows indicate that the numbers go on infinitely in both directions.
The numbers represented by points on the number line.
a numbers absolute value or positive distance from 0.
a list of numbers in a certain type of order
the same quantity is added to each number to get the next
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
12 inches make up a foot
3 feet make a yard
5,280 feet compose a mile
2 cups form a pint
2 pints make a quart
4 quarts make up a gallon
16 ounces makes a pound
a ton is 2,000 pounds
letters that represent numbers
A number that precedes a variable or variables to indicate that it is multiplied by them. Ex: 10xyz, 10 is the coefficient
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.
A single term or a group of terms seperated by + or - forms an expression
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)
An equation in which one ratio (usually in the form of a fraction) is set equal to another.
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.
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.
One side is (or may be) greater than or less than the other side.
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.
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)
A relationship pattern in which one quantity increases as another one increases, though they may increase at different rates.
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.
D = rt
Distance, rate and time.
An exact and infinitely small location
A continuous set of an infinite number of points extending infinitely in two directions. Lines are one dimensional.
Part of a line with two expoints.
A flat surface that is infinitely thin and goes forever in all directions.
A shape formed by two sides, with each side being either a line or part of a line.
The point at which the two sides of an angle meet.
Two segments or angles that have the same measures.
Two angles having measures that add up to 180
Pair of angles that together form a line.
Two angles having measures that add up to 90 degrees.
Opposite of each other. They are always congruent. If you have intersecting lines you always have two pairs of vertical angles.
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.
Polygons that don't point inward anywhere.
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.
4 sided polygons. The sum of their interior angles is always 360 degrees.
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
A quadrilateral that had just one pair of parallel sides. The two parallel sides are the bases of the trapezoid.
Same shape but not necessarily congruent.
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.
The distance around an object
Perimeter of a rectangle
2l + 2w
The perimeter of a circle. C/D=pie
Circumference, diameter, pie (3.14), radius
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
Area of a triangle
Area of a circle
Area of a trapezoid
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)
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
Surface area of a pyramid
Surface area of a cone
PieR^2 + pieR(slant height)
Surface area of a sphere
The amount of space inside a 3D figure
Volume of rectangle solid
Bh or lwh
Volume of q cylinder
Volume of a pyramid
Volume of a cone
Volume of a sphere
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
Figures altered by changing the location in their vertices.
Moving it a number of units horizontally and a number of units vertically
Flipping figures over an axis and creating new images that are like mirror relfections
Changes in sizes of the figure
Moving of figures along circular paths while the distance between every point and the center of the circular path stays the same.
A^2 + b^2 = c^2
Leg, leg, hypotenuse.
Isosceles, two congruent sides. The two legs are congruent. The hypotonuse is always the square root of 2 times the measure of the leg.
Equilateral, all three sides are congruent
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.
Move decimal from Left to right = negative/right to left = positive.