PRAXIS: CORE 5752

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.

Midpoint

(X1+x2/2, y1+y2/2)

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.

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.

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

Area of a triangle

1/2bh Base, height

Area of a trapezoid

1/2h(b1+b2)

Volume of a pyramid

1/3Bh

Volume of a cone

1/3PieR^2h

Distance Conversions

12 inches make up a foot 3 feet make a yard 5,280 feet compose a mile

Weight Conversions

16 ounces makes a pound a ton is 2,000 pounds

Volume Conversions

2 cups form a pint 2 pints make a quart 4 quarts make up a gallon

Surface area of a rectangular solid

2B + Ph Base, perimeter, height

Perimeter of a rectangle

2l + 2w

Surface area of a cylinder

2pieR^2+2pieRH

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.

Volume of a sphere

4/3PieR^3

Surface area of a sphere

4pieR^2

Ratio

A comparison of two quantities

Line

A continuous set of an infinite number of points extending infinitely in two directions. Lines are one dimensional.

Plane

A flat surface that is infinitely thin and goes forever in all directions.

Coefficient

A number that precedes a variable or variables to indicate that it is multiplied by them. Ex: 10xyz, 10 is the coefficient

Parallelogram

A quadrilateral in which both pairs of opposite sides are parallel. Both pairs of opposite sides are also congruent.

Trapezoid

A quadrilateral that had just one pair of parallel sides. The two parallel sides are the bases of the trapezoid.

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)

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.

Direct variation

A relationship pattern in which one quantity increases as another one increases, though they may increase at different rates.

Relation

A set of ordered pairs

Angle

A shape formed by two sides, with each side being either a line or part of a line.

Expression

A single term or a group of terms seperated by + or - forms an expression

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.

Pythagorean theorem

A^2 + b^2 = c^2 Leg, leg, hypotenuse.

Reverse Foil

Add

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.

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

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.

Area of a rectangle

Length x width

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

Exponents

Move decimal from Left to right = negative/right to left = positive.

Translation

Moving it a number of units horizontally and a number of units vertically

Rotations

Moving of figures along circular paths while the distance between every point and the center of the circular path stays the same.

Numerator and Denominator

N: integer on the top of the fraction D: integer of the bottom of the fraction

Inequality

One side is (or may be) greater than or less than the other side.

Vertical angles

Opposite of each other. They are always congruent. If you have intersecting lines you always have two pairs of vertical angles.

Order of operations

PEMDAS - parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right)

Linear pair

Pair of angles that together form a line.

Segment

Part of a line with two expoints.

Area of a circle

PieR^2

Surface area of a cone

PieR^2 + pieR(slant height)

Volume of q cylinder

PieR^2h

Convex polygons

Polygons that don't point inward anywhere.

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

Geometric sequence

each number is multiplied by the same quantity to get the next

Number line

illustrate orders of numbers. Arrows indicate that the numbers go on infinitely in both directions.

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)

Variables

letters that represent numbers

Converting decimals to percents

moving the decimal two places to the right and adding % sign.

Multiplying fractions

multiply the numerators and then multiply the denominators

Decimals

represent whole and partial numbers

Exponent

represents how many times a number is a factor. 2 = squared, 3 = cubed

Dividing fractions

same as multiplying by its reciprocal (switch the numerator and denominator)

Common denominator

same denominator for both fractions

Distance between two points

square root of (X1-x2)^2 + (y1-y2)^2

Reciprocal

switch the numerator and denominator

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.

Arithmetic sequence

the same quantity is added to each number to get the next

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)

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.

Donations

Changes in sizes of the figure

Distance formula

D = rt Distance, rate and time.

60-60-60 triangle

Equilateral, all three sides are congruent

Stem and leaf plot

Stem (tens) leaf (ones)

Volume

The amount of space inside a 3D figure

Perimeter

The distance around an object

Slant height

The distance from the apex or the top point, to the center of an edge of the base.

Coordinates

The numbers represented by points on the number line.

Circumference

The perimeter of a circle. C/D=pie Or C=2pieR Circumference, diameter, pie (3.14), radius

Vertex

The point at which the two sides of an angle meet.

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.

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.

Supplementary

Two angles having measures that add up to 180

Complementary

Two angles having measures that add up to 90 degrees.

Congruent

Two segments or angles that have the same measures.

Slope

Y1-y2/X1-x2 or y=mx+b M= slope b=y intercept

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.

Improper Fraction

a fraction in which the numerator is greater than the denominator

Sequence

a list of numbers in a certain type of order

Positive and Negative numbers

a negative number is the opposite of a positive number, and vice versa.

Magnitude

a numbers absolute value or positive distance from 0.

Percent

a representation of a number of hundredths (%)

Prime factorization

a representation of the number as a product of all its prime factors.

Square root

a way to find what has to be squared to get a number

Prime number

a whole number that only has itself and 1 for factors.

Mixed Number

an integer followed by a fraction

Absolute Value

an integer's positive distance from 0. It's value without a negative sign. Ex: |4| = 4 or |-4| = 4

Integers

All the whole numbers and their opposites. The only integer that doesn't have an opposite is 0

Area

Amount of plane in it. How much room is inside a two dimensional shape.

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.

Proportion

An equation in which one ratio (usually in the form of a fraction) is set equal to another.

Point

An exact and infinitely small location

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)

Surface area of a pyramid

B+1/2P(slant height)

Area of a parallelogram

Base x height

Volume of rectangle solid

Bh or lwh

Multiplying two term expressions

FOIL (first inner outer last)

Transformations

Figures altered by changing the location in their vertices.

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.

Reflections

Flipping figures over an axis and creating new images that are like mirror relfections

Partial Numbers

Fractions and decimals; not whole numbers

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...)

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.

Conditional statements

If-then statements

Area of a square

S^2

Similar shapes

Same shape but not necessarily congruent.