Rational #
Can be expressed as the ratio of two integers, where B is not equal to zero
Integers
Positive and negative whole numbers and zero
Whole numbers
Natural numbers and zero
Natural numbers
Counting numbers not including zero or negative
Irrational numbers
Real numbers that cannot be written as the ratio of two integers - they are infinite, not repeating decimals--- square root of 5 or pi -3.1415927.....
Fraction
An expression of numbers in the form of X/Y where X =the numerator and Y # the denominator 3/4
Mixed number
Has an integer part and fraction part 5 2/3
Percent
Means per 100 written with a percentage sign 10% = 10/100=1/10
Greatest common factor
Largest number that is a factor of all members problem. Can be no larger than the smallest number of the problem - if smallest number in the problem is not a factor, continue increasing smaller until you find a common factor. GCF of 12, 20, 36 -> 4
Least common multiple
Smallest number of a group of numbers that all given numbers will divide into evenly - will always be the largest of the given numbers or a multiple of the largest 20, 30, 40 -> largest is 40, but 30 won't divide into 40 evenly, so 120 is the only number that all will divide evenly
Composite number
Whole numbers that have two or more factors. 9->1,3,9
Prime numbers
Whole numbers greater than 1 that have only 2 factors- 1 and itself
Perimeter
Some of the length of the sides of the polygon
Area
Number of square units covered by a polygon
Rectangle
Area formula - LWPerimeter formula - 2(L + W)
Triangle
Area formula - 1/2 bhPerimeter formula - A+ B+ C
Parallelogram
Area formula - BH Perimeter formula - some of length of sides
Trapezoid
1/2BH (A+ B)
Circumference
The distance between a circle - pi ->3.14 -> 22/7C=2pir or C=pid
Polygon
Simple, closed, two dimensional figure to post a blind statements - named according to the number of sides they have
Quadrilateral
Four Sides - some of angles is 360°
Trapezoid
Quadrilateral with exactly one pair of parallel sides
Isosceles trapezoid
Nonparallel sides are congruent
Parallelogram
Quadrilateral with two pairs of parallel sides - diagonals bisect each other - each diagonal divides parallelogram into two congruent triangles
Rectangle
Parallelogram with the right angle
Rhombus
Parallelogram with all sides equal in length
Square
Rectangle with all sides equal in length
Triangle
Polygon with three sides - classified by links of sides and types of Bengals
Acute triangle
Has exactly 3 acute angles that measure less than 90°
Right triangle
One right angle - one acute angle that measures less than 90°
Obtuse triangle
One angle between 90° and 180°
Equilateral triangle
All three sides are the same length
Isosceles triangle
A triangle in which two sides are the same length
Scalene triangle
The triangle in which no sides are the same length
Acute angle
An angle that measures less than 90°
Right angle
An angle that measures 90°
Obtuse angle
An angle that measures between 90° and 180°
Cylinder
Hey space figure that has two parallel, congruent circular bases
Sphere
Space figure having all its points in the same distance from the center
Cone
A space figure having a circular base and a single vertex
Pyramid
Space figure with a square base and four triangle shaped sides
Tetrahedron
If foresighted space triangle: each face is a triangle
Prism
Is based figure with two congruent, parallel bases that are polygons
Ratio
The comparison of two numbers
Proportion
An equation in which one fraction is set equal to another4/15=x/60 to solve, cross multiply(4)(60)=15x. 16=x
Congruent figures
Figures that have the same size and shape
Similar
Two figures that have the same shape
Pythagorean theorem
Given that any right triangle ABC the square of the hypotenuse is equal to the sum of the square of the other two sides. A squared plus B squared equals C squaredSide a B squared is equal to BC squared plus a C squared
Congruent plane
A plane with a point selected as its origin, some link suggested as a unit of distance, and two perpendicular lines that intersect at the origin, with positive or negative direction selected on each line
Coordinates
Unique ordered pair of numbers that identify a point coordinate plane
Slope
And upward or downward direction of the line
Rise
The top of a fraction; it represents the change in the Y coordinates
Run
The bottom of the fractions; it represents the change in the x-coordinate
Distance
The length of the line segment between two different points, a and B. The length of a line formula is
operations
addend+addend=sumsum-addend=differencefactorXfactor=productdividend ÷ divisor = quotient
division
dividend---------- = quotientdivisor
divide by zero
any number ÷ 0 = can't do it0 ÷ any number = 00 cannot be a divisor
prime number
whole number greater than 1 that is divisible only by itself and 1
composite
whole number greater than 1 that are not prime
prime factors
use factor tree - e.g. 36 = 2∗2∗3∗3
GCF greatest common factor
the greatest number that will divide evenly into the two numbers list factors of each then chose the highest one
LCM least common multiple
the smallest product that is a multiple of each of the counting numbers....factor each/ build a product consisting of each factor used the most number of times it appears as a factor. e.g...24=2∗2∗2∗3 36=2∗2∗3∗3 so LCM (24,36) = 2∗2∗2∗3∗3 =72
1 is neither prime or composite
...
rational numbers
whole numbers, integers, positive and negative fractions, decimals, and percents
whole numbers
counting numbers and 0
integers
numbers that are either negative or positive and 0....o is not positive or negative
rational numbers
all numbers that can be written as positive or negative fractions ...rational numbers can be expressed as fractions, decimals, or percents
80%=.80=.8=
05-Apr
60%=.60=.6=
05-Mar
40%=.40=.4=
05-Feb
20%=.20=.2=
05-Jan
87 1/2% = .875=
08-Jul
62 1/2 %=.625=
08-May
37 12%=.375=
08-Mar
12 1/2% = .125=
08-Jan
66 2/3%=.66 2/3 =
03-Feb
5%=.05=
20-Jan
4%=.04=
25-Jan
1%=.01=1/100
1/100
irrational square roots
irrational square roots do not have a number that they are evenly multiplied by...if given an irrational square root to estimate find the 2 numbers it falls between e.g. square root of 41 is between 6 and 7
rational square roots
nonnegative number that multiplies by itself to get the number e.g...square root of 1=1, square root of 25 is 5
Is 1/0 a real number?
NO...0 cannot be a divisor
exponential notation
eg...3⁴ = 3∗3∗3∗3=81negative exponents eg. 2⁻³=½₃ = 1/8=.125any number with 0 as an exponent is 1 e.g...3⁰=1
-3x ≥ 1 =
x ≤ -1/3 (reverse the inequality because you divided both sides by a negative number)
Pictograph
pictures or symbols are used to represent numbers
Measure of central tendency
a numerical value that describes a data set by providing a "central" or "typical" value of the data set.
Mean
the arithmetic average of the numbers.
Median
the middle number or the average of the two middle numbers in an ordered set of numbers.
Mode
the number or numbers that occur with the greatest frequency in a set of numbers;
measure of dispersion
a value that describes the spread of the data about the central value.
range
the difference between the greatest value and the least value in the data set
standard deviation
a measure of the dispersion of a set of data values about the mean of the data set. The more the data values vary from the mean, the greater the standard deviation.
Probability of event E =
# of outcomes favorable to Event E/# of total outcomes possible
A bag contains 5 tiles, numbered 1, 2, 3, 4, and 5. The tiles are all identical in size and shape. If a person picks out a single tile from the bag without looking, what is the probability that the number on the tile will be even?
05-Feb
How to write in Scientific Notation
1. Move decimal to the right of the first nonzero digit.2. indicate the power of 10 by the number of places moved in step 1.3. Move left= pos. power / move right = neg. power
Write 0.000000975 in Scientific Notation
9.75 × 10 ⁻⁷
Absolute value eg. -|−17| =
−17 Absolute value negatives don't "cancel each other out
Order of Operations hint
Please Excuse My Dear Aunt Sally PE(MD)(AS)
Cross products- On a map, the distance between 2 cities is 10.5 inches. 0.5 inches=20 miles. How many miles between the cities?
x miles/10.5 inches= 20 miles/0.5 inches = 420 miles
Acute Angle
Between 0⁰ and 90⁰
Right angle
90⁰
Obtuse angle
between 90⁰ and 180⁰
Straight angle
180⁰
Complementary angles
Two angles whose sum = 90⁰
Supplementary angles
Two angles whose sum = 180⁰
Adjacent angles
Two angles that have a common vertex and common side
Tangent line
A line that intersects a circle at only 1 point
Congruent
Exactly the same size and shape
equilateral triangle
3 equal sides
Isosceles triangle
At least 2 congruent sides
Scalene triangle
No equal sides
Acute triangle
3 acute angles
Right triangle
one right angle
Obtuse triangle
Exactly 1 obtuse angle
Congruent triangles
Corresponding sides and angles are congruent
parallelogram
Opposite sides are parallel and congruent
Rhombus
parallelogram with with 4 congruent sides
Quadrilateral
4 sides
Pentagon
5 sides
Hexagon
6 sides
Pythagorean Theorem
In a right triangle, a² + b² = c²
whole numbers
the whole numbers and zero
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
exponent form
a shorthand way of writing repeated multiplication.
write 46, 368, 000 in scientific notation
4.6368 x 10^7
write 0.00397 in scientific notation
3.97 x 10^-3
properties
rules that apply for addition, subtraction, multiplication, or division of real numbers
types of properties
commutative, associative, identity, inverse, distributive
commutative
You can change the order of the terms or factors:for addition: a + b= b + afor multiplication: ab=ba
associative
you can regroup the terms as you likefor addition: a + (b + c)= (a +b) + cfor multiplication: a(bc)= (ab)c
Identity
addition: a + 0= amultiplication: a x 1= a
Inverse
finding a number such that when added to the number it results in zero; or when multiplied by the number, it results in 1. addition: a+a=0multiplication: a x (1/a)=1
Distributive
a (b + c)= ab + ac
polygon
a simple, closed, two-dimensional figure composed of line segments
Quadrilateral
a polygon with four sides.the sum of the measures of the angles is 360 degrees.
trapezoid
a polygon with exactly one pair of parallel sides
isosceles trapezoid
a quadrilateral in which the nonparallel sides are congruent
parallelogram
a quadrilateral with two pairs of parallel sides.the diagonals bisect each others, each diagonal divides the parallelogram into two congruent triangles, both pairs of opposite sides are congruent, both pairs of opposite angles are congruent, and two adjacent angles are supplementary.
rectangle
a parallelogram with a right angle
rhombus
a parallelogram with all sides equal in length
a square
a rectangle with all sides equal in length.
True or False: All squares are rhombuses
TRUE
True or False: All parallelograms are rectangles
False-some are rectangles
True or False: All rectangles are parallelograms
TRUE
True or False: Some rhombuses are squares
TRUE
True or False: Some rectangles are trapezoids
False: trapezoids have only one pair of parallel sides
True or False: All quadrilaterals are parallelograms
False: Some quadrilaterals are parallelograms
True or False: Some squares are rectangles
False: All squares are rectangles
True or False: Some parallelograms are rhombuses
TRUE
Triangle
A polygon with three sides
Acute triangle
has exactly 3 acute angles. an acute angle is less than 90 degrees.
Obtuse Triangle
a triangle with one obtuse angle. An obtuse angle measures between 90 degrees and 180 degrees.
isosceles triangle
two sides are the same length
scalene triangle
a triangle in which no sides are the same length
cylinder
a space figure that has two parallel, congruent circular bases
sphere
a space figure having all its points the same distance as the center,
pyramid
a space figure with a square base and four triangle shaped sides
tetrahedron
a four-sided space triangle; each face is a triangle
prism
a space figure with two congruent, parallel bases that are polygons.
perimeter of a rectangle
2 (Length + Width)
area of a rectangle
Length X Width
12 inches equals (in)
1 foot (ft)
3 feet equals (ft)
1 yard (yd)
1760 yards equals (yd)
1 mile (mi)
km equals
1000 meters (m)
hectometer (hm)
100 meters (m)
decameter (dam)
10 meters (m)
decimeter (dm)
1/10 meter (m)
centimeter (cm)
1/100 meter (m)
millimeter (mm)
1/1000 meter (m)
1 in equals
2.54 cm
1 ft equals
30 cm
1 yd equals
0.9 m
1 mi equals
1.6 km
28 grams (g) equals
1 oz
16 oz equals
1 lb
2000 lb equals
1 ton (t) (short ton)
1.1 ton equals
1 ton (t)
kg equals
1000 g
1 milligram equals
1/1000 g
1 oz equals
28 g
1 lb equals
.45 kg454 g
8 fluid oz equals
1 c
2 c equals
1 pt
2 pts equals
1 quart
4 qts equals
1 gal
1 kiloliter (kl) equals
1000 liters (l)
milliliter (ml) equals
1/1000 ml
1 tsp equals
5 ml
1 fluid oz equals
15 ml
1 cup equals
.24 l
1 pint equals
.47 l
1 gal equals
3.8 l
1 sq ft =
144 sq in
1 sq yd =
9 sq ft 1296 sq in
perimeter
the sum of the lengths of the sides of any polygon
area
the number of square units covered by a polygon
area of a triangle
1/2bh
perimeter of a triangle
a + b+ c
area of a parallelogram
bh
perimeter of a parallelogram
sum of lengths of sides
area of a trapezoid
1/2 h(a + b)
perimeter of a trapezoid
sum of lengths of sides
Circumference
the distance around a circle2(3.14)(r)
Area of a circle
(3.14)r^2
lateral area of a pyramid
1/2PI
Total area of a pyramid
1/2PI + B
Volume of a pyramid
1/3Bh
volume of a cylinder
(3.14) (r^2)(h)
total surface area of a cylinder
2(3.14)(rh) + 2(3.14)r^2
volume of a right cone
3.14(r^2)(h)/3
total surface area of a right cone
3.14(r)(square root of r^2 + h^2) + 3.14(r^2)
volume of a sphere
4/3 (3.14)(r^3)
total surface area of a sphere
4(3.14)(r^2)
volume of a rectangular solid
LWH
total surface area of a rectangular solid
2LW + 2WH + 2LH
temperature of boiling water
100 degrees C or 212 degrees F
the y-intercept equation
Y-ya= m(X-xa)
if an inequality solves to x is greater than or equal to any number, then the graph indicates a
vertical line
If an inequality solves to y is less than or equal to any number, then the graph indicates a
horizontal line
solution set of linear equations
all the ordered pairs of real numbers that satisfy both equations
substitution
when an equation is solved for either of two variables, the solution if substituted to find the remaining variable.
linear combinations
when one or both of two equations are replaced with an equivalent equation so that they can be combined and one variable eliminated.
linear relationship
a relationship in which two quantities are proportional to each other
variance
the sum of the squares of a set of terms divided by the number of items in a set
3 techniques to help find the number of elements in one event or a sample space
the counting principlepermutationscombinations
the counting principle
(n)(m)
permutations
nPr= n!/(n-r)!
combinations
an unordered collection of distinct elementsnCr= n!/(n-r)r!
rational
Can be expressed as the ratio of two integers, where B is not equal to zero