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Gravity
Terms in this set (132)
Integer
All positive and negative whole numbers (and zero)
Factor
A number that divides evenly into another integer, including 1 and the number itself
Prime number
A number with only two distinct factors: 1 and itself
Arithmetic Sequence
A sequence formed by adding the same number each time
Geometric Sequence
A sequence formed by multiplying each term by the same number to find the next term
Congruent
Geometrically equal (same angles and side lengths)
Similar
Same shape, but different sizes (equal angles, different side lengths)
Midpoint
The exact middle of a line segment
Bisect
to cut an angle or line segment exactly in half
Median
The middle number of an ordered set. If there are two numbers in the middle, you take the average to find the median.
Mode
The most frequently occurring number. there can be more than one mode.
Range
The difference between the largest and smallest numbers in a set
Tangent
To touch the edge of but not cross
Inscribed
When one shape is inside of another while touching the larger shape's edges
Total degrees in a shape
total degrees = 180(n-2)
n is the number of sides the shape has
Remember that a circle has 360 degrees and a triangle has 180 degrees.
Mean or Average
Sum of Things in the Set
# of Things in the Set
Percent Change Formula
((New Value - Original Value)/Original Value) x 100
if you have a percent change problem without numbers, choose your own. consider choosing 100 as your starting number!
Slope-intercept form
y = mx + b
m is the slope
b is the y intercept
Slope Formula
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Midpoint Formula
((x₁+x₂)/2, (y₁+y₂)/2)
Circle formula
(x-h)²+ (y-k)² = r²
Ellipse formula
(x-h)²/a² + (y-k)²/b² = 1
Hyperbola formula
(x-h)²/a² - (y-k)²/b² = 1
Area of a circle
A=πr²
Circumference formula
C = 2πr
Area of a triangle
A = ½bh or (1/2)(ab)sinC
Pythagorean Theorem
c²=a²+b²
Area of a parallelogram
A = base × height
remember that for a square, A=s². The perimeter is 4s. Those are NOT the same. :)
Perimeter formula
sum of all sides
if you have a perimeter question later in the test, be very careful about labeling ALL sides before you add them up!
Area of a trapezoid
A=½(b₁+b₂) x h
Arc length formula
arc length = (θ/360)(2πr)
Sector Formula
sector area = (θ/360)(πr²)
sinθ
sinθ = opposite/hypotenuse
cosθ
cosθ = adjacent/hypotenuse
tanθ
tanθ = opposite/adjacent
cscθ
cscθ = hypotenuse/opposite
secθ
secθ = hypotenuse/adjacent
cotθ
cotθ = adjacent/opposite
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines
c² = a² + b² - 2abcosC
Surface Area of Rectangular Prism
A = 2LW+2LH+2WH
Volume of Rectangular Prism
V=LWH
Surface Area of Cylinder
A=2πrh+2πr²
Volume of a Cylinder
V = πr²h
30-60-90 Triangle side lengths
x, 2x, x√3
45-45-90 Triangle side lengths
x, x, x√2
Compound interest formula
P(1+r/n)^nt
The probability of both A and B
can also be written P(A and B)
independent events: P(A) x P(B)
dependent events: P(A) x P(B after A)
The probability of A or B
can also be written--P(A or B)
P(A) + P(B)
How to solve for expected value
Multiply each value of x by its own probability, then add up all the products
X⁰
1
√b
b^½
x^(-2)
1/(x²)
x²x³
x⁵
(x²)³
x⁶
how to convert a decimal to a fraction using a TI calculator
once the decimal is typed in, hit the MATH button. FRAC should be highlighted. Hit ENTER.
diagonals formula
(n(n-3))/2
n is the number of sides in the shape
Word Translations: what, is, of, percent
what-variable
is-equals
of-multiply
percent-divide by 100
per-divide
Supplementary Angles
Add to 180 degrees
Complementary Angles
Add to 90 degrees
Quadratic Formula
Permutation Formula
Probability of a given that b
the number of a that is also b/total b
similar triangles vs congruent triangles
similar - same shape, different size, = angles, sides are proportional
congruent - same shape, same size
cardinal directions (north, south, east, west)
Scientific Notation for .002891
2.891 x 10⁻³
if you punch scientific notation questions into your calculator put parentheses around each one. For example, (2.891 x 10⁻³)/(4.2 x 10³)
sin²x + cos²x
1
when can you use SOH CAH TOA and pythagorean theorem
only with right triangles!
x^(2/3)
2 is the exponent
3 is the root
i
i°=1
i¹= i
i²=-1
i³=-i
i⁴=1
Don't forget that I=√-1
What does empty set mean?
If you try to solve an equation, there are no solutions that work.
what does all real numbers mean?
If you try to solve the equation, all real solutions will work.
How many degrees are there in π radians?
180 degrees
sum
difference
quotient
product
Sum means add
Difference means subtract
Quotient means divide
Product means multiply
What does it mean when you have an open hole on a graph versus a closed hole?
open hole-that value is not included.
closed/shaded hole-the value is included.
What is the domain and range on a graph?
domain-all of the x values on a graph
range-all of the y values on a graph
vertical angles
vertical angles are congruent
When is a function undefined?
A function is undefined when the denominator is zero.
Linear standard form
Ax + By = C
In this form, the slope is -A/B.
Finding the perimeter of a parallelogram
You will have two sets of congruent sides. If the problem gives you one side and the perimeter, the correct answer will repeat the given side and then have two other sides that are the same as each other. All four (the one in the problem and the three in the answer) should add to the given perimeter.
Odd vs. even functions
prime factorization
the set of prime numbers that multiply together to result in the original number
discriminant of a quadratic function
What should you do if they ask you about a pie chart or circle graph?
set up a proportion.
part/whole=angle/360
What should you do if a question asks you to add fractions?
You ALWAYS need a common denominator even if the equation has variables.
isosceles vs. scalene vs. equilateral
equilateral-all sides are congruent
scalene-none of the sides are congruent
isosceles-two sides are congruent
obtuse vs. right vs. acute triangles
perpendicular and parallel slopes
parallel slopes are the same.
perpendicular slopes are negative reciprocals (for example, 2/3 and -3/2)
linear
linear means a straight line. (examples: y=1, x=2, y=3x +6). Anything with x² is NOT linear.
dimensional analysis
(consider using it if you need to change from one unit to another)
vectors
x vs. x² vs. x³ (bounce? wiggle? cross?)
What should you do if you see the word equivalent?
If you aren't sure how to solve, you can choose a number to plug into the question and then plug that same number into the answers and choose the one that is the same. This is often slower than solving but it's great if you can't figure out another way.
stem and leaf plot
inversely vs. directly
inversely y=k(1/x)
directly y=kx
Vertical asymptotes
In a triangle, which side is the longest side?
The one across from the largest angle.
standard deviation
Standard deviation is a number used to tell how measurements for a group are spread out from the average. A low standard deviation means that most of the numbers are close to the average, while a high standard deviation means that the numbers are more spread out.
complex plane
shifts to a parabola (x²)
to flip upside down-make it negative
to move left by 1- (x+1)²
to move right by 2- (x-2)²
to move up 1- x² +1
to move down 2- x² -2
if a problem asks you to find the value that is halfway between two numbers...
take the average of those 2 numbers.
consecutive
one after another in the typical order (ie: 1,2,3,4,5)
If they ask for consecutive odd numbers it would be 1,3,5,7 and so on.
positive slope
a line that rises up toward the right
negative slope
a line that slopes down to the right
How many square feet are there in one square yard?
9 square feet in 1 square yard
What should you do if they ask you to order fractions and decimals?
1) Use your calculator to put them all into decimal form.
2) Add a placeholder zero at the end of any shorter decimals to make them all the same length. (for example, change 0.2 to 0.20)
3) Double check whether you are ordering smallest to largest or largest to smallest!
What should you do if you see variables in the exponents of an algebra problem?
Create a common base!
respectively
in the order that they are given (for example, Car A and car B have 2 and 4 doors, respectively. This would mean that Car A has 2 doors and Car B has 4 doors because A and 2 come first and B and 4 both come second)
normal distribution
this is a very rare problem type, but see the picture to memorize if you are aiming for that 36!
The first standard deviation is about 68%
The second standard deviation is about 95%
The third standard deviation is about 99%
amplitude of a function
the height of the wave as measured on the y axis (see picture)
period of a function
the length of a complete wave as measured on the x axis (see image)
greatest common factor (GCF)
the largest number that divides evenly into both numbers (for example, the GCF of 10 and 20 is 10. the GCF of 12 and 16 is 4.)
least common multiple (LCM)
the smallest value that both numbers divide into evenly (for example, the LCM of 20 and 40 is 40. The LCM of 12 and 20 is 60.)
absolute value
Remember:
1) absolute value lines turn the outcome positive.
2) that you do not turn it positive until you have completed all of the operations inside the absolute value.
3) that the inside could be positive or negative so when you are solving an algebraic equation with an absolute value, you need to create two equations (see picture).
classifying numbers (integer, natural, rational/irrational, real/imaginary, complex)
(see image)
How do you find the area of a shaded region?
Find the area of both shapes and subtract!
What do you do if they ask you to figure out how many small boxes fit in a larger box or how many tiles fit on a certain floor?
1) convert everything into the same unit (all inches or all feet...it doesn't matter which unit as long as they are the same!)
2) Find the area or volume of the big and the small.
3) Divide! big/small
Logarithm: convert log base x = y to exponent form
b to the y power equals x
Log rules
What should you do if you see a note beneath the problem?
ALWAYS read the note. Often they are giving you a formula, so don't skip over it even if it's in parentheses!
y= mx + b
What is m? What is b?
m is the slope (rise/run).
b is the y intercept.
How do you add (or subtract matrices)?
Add (or subtract) the top lefts, the top rights, the bottom lefts and the bottom rights.
How do you multiply matrices?
You can plug them into your calculator (see the Matrix button on your TI!) or you can do it by hand (see the image!)
determinant of a matrix
ratio
when you see a ratio, you can divide the first number by the second (see image)
What should you do if they ask you to find the 358th digit of a repeating decimal like .3178 repeating?
First determine the pattern. If the pattern repeats every four digits like in this example, you divide 358 by four.
Then you take the whole number answer (drop the decimal. DON'T round.) and multiply that by four. In this case, 358/4 is 89.5, so you would multiply 89 times 4 to get 356.
That means that the pattern repeats 89 times and gets you all the way to the 356 digit, so you would have 2 more to go to get to the 358th digit.
Therefore you would pick the second digit (in this case 1).
multiplying by the conjugate
multiply by the conjugate if you see a root or an imaginary number (i) in the denominator. If you see i DON'T convert to the square root of -1. Keep it in terms of i.
solving for inequalities
if you multiply or divide by a negative number, always flip the greater than or less than sign.
composite functions f(g(x))
Plug the inside function into the outside function. This is NOT the same as multiplying functions.
multiplying functions
What should you do if a word problem has two items for sale at two different prices and asks you how many of one item are sold, but only gives you the total number sold and total amount made for both items?
Set up a system of equations! Write one equation for how many are sold.
x + y = Total # of items sold
Write a second equation for the cost.
(cost of x) (x) + cost of y (y) = total money earned
Solve the system with elimination or substitution.
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