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Gravity
Terms in this set (157)
PSAT Reading strategies
...
Take your time
...
Read passages before answering questions
...
Focus on the overall meaning as you read
...
Literature
1st paragraph more carefully, then the rest normally
Nonfiction
1st paragraph, first sentence, last paragraph carefully
Multiple passages
Pay attention to the overall relationship
Do not hesitate to skip and come back to questions
...
Cover the answers as you read the questions
...
Underline and circle key words as you read
...
Create your own general answer by considering the context
...
Do not hesitate to refer back to the passage
...
Answers are 100% correct or 100% wrong
...
Focus on meaning, not matching
...
Determine word definitions based on context clues
...
Four english passage types
Careers, humanities, social science/history, science
Coordination and Subordination
...
There was a big fire at our house, and we moved into a hotel while the house was being fixed.
INCORRECT
There was a big fire at our house, so we moved into a hotel while the house was being fixed
CORRECT
Logical Comparisons
...
The coach of the football team is stronger than the baseball team
INCORRECT
The coach of the football team is stronger than the coach of the baseball team
CORRECT
Modifier Placement and Clarity
...
The kitten nuzzled up against my leg, purring softly.
INCORRECT
While purring softly, the kitten nuzzled against my leg
CORRECT
Wordiness
Clear descriptions, remove repetitive and irrelevant wording
Parallelism
Consistent, flowing information
The blizzard was snowy, had wind, and icy
INCORRECT
The blizzard was snowy, windy, and icy
...
Verb use
Make sure tense and mood are properly used
Either/or and neither/nor
Singular
Accept vs except
I accept most of his apology, except for his claim that he had good intentions all along
Affect vs effect
Affect - verb
effect - noun
I vs me
I - subject
me - object
Its vs It's
it's = it is
Less vs fewer
less - cannot be easily counted
fewer- countable items
Best vs better
best - more than two
better -comparison between two things
Lie vs lay
lie - to recline
lay- to place
Than vs then
than -comparisons
then - time
Who vs whom
who - subject
whom- object
which vs that
which - if clause is not needed
that - if clause is needed
common prepositions
in moderation
in collaboration
on a regular basis
on behalf
by process
for the good of
of the opinion
Commas
*
When do you separate a phrase (dependent clause?)
When it comes before a complete sentence (independent clause)
Semicolon
Separate two complete, related sentences
Colon
After a complete sentence to set off a list
After complete sentence to set off clarification
Dashes
Indicate interruption or change of thought
Set off parenthetical phrase
Apostrophe's
...
Before s to indicate
a singular entity possesses something
After s to indicate
A plural entity possesses something
12 strategies
...
Take your time
Pace yourself to finish when time is called
Underline and circle key information as you read long questions
Try to hear as you read silently by mouthing things
Think about the meaning
Consider relevant context
Maybe read the passage through once before answering questions
Try and create your own answer before looking at the choices
Do not hesitate to come back to a question
Use similarities among answers to eliminate choices
Grammar rules, not preferences
...
What are the four kinds of math questions?
1. Heart of algebra
2. Problem solving and data analysis
3. Passport to advanced math
4. Additional topics in math
Use substitution to solve equations
Substitute one variable in terms of the other
2x=y and y-3x=-5
(2x)-3x = -5
solve for x
plug back in to find y
Use elimination to solve equtions
When two questions are similar to one another, multiply one of the equations by a number that allows you to add or subtract the equations easily to eliminate one of the variables
Example? 3x+2y=7 and 2x-y=0
1. Multiply the second equation by two
3x+2y=7 + (4x-2y=0) and add to eliminate the y-variable. Plug found x back in to original equation to find y.
Second degree equation containing x, a, b, and c
ax + bx + c = 0
Quadratic formula
Take out common factors
nx+ny = n(x+y)
Be able to factor
2x³+6x/3x = 2x(x²+3)/3x
Simplify to 2/3(x²+3)
FOIL
First, inner, outer, last
Factor x² + x + 12 = 0 type
(x+ something) (x-something) = 0
(a+b)(a+b) =
(x+3)(x+3) =
a²+2ab+b²
x²+6x+9
(a+b)(a-b) =
(m+2)(m-2) =
a²-b²
m²-4
(a-b)(a-b) =
(3-y)(3-y) =
a² - 2ab +b²
9-6y+y²
Sum of cubes!
(a+b)(a²-ab+b²) =
(2+x)(4-2x+x²) =
a³+b³
8+x²
Difference of cubes!
(a-b)(a²+ab+b²) =
(y-4)(y²+4y+16) =
a³-b³
y³-4³
Slope-intercept form
y = mx + b
b =....
y intercept of the line
m...
slope, rise/run
Slope formula
(y₂-y₁)/(x₂-x₁)
Positive correlation
x and y values both increase or both decrease
Negative correlation
One increases, one decreases
Linear relationship
Represented by constant slope
y = x
Quadratic relationship
Between two variables, not constant slope
y = x²
Exponential relationship
y = cb^x
Percentage formula
part/whole * 100 = percent
What is 45% of 300?
0.45 x 300 = 135
Ratios
Set up and cross-multiply, when there is an x
Unit conversion
Cancel out units you do not want, think CHEM
Scientific notation
...
5,348.00
3 to the left, 5.348 x 10³
0.00476
3 to the right, 4.76 x 10⁻³
Inequalities
When multiplying by negative number, change direction of inequality sign!!!
Exponent rules
...
x^ax^b
x^(a+b)
x^a/x^b
x^(a-b)
(x^a)^b
x^ab
x^-a
1/x^a
x^a/b
b√x^a
What is the order?
Power over root
Absolute value
Distance from zero
|x+2| = 4
x + 2 = 4
x + 2 = -4
Probability equation
Probability = number of successes/number of possible outcomes
Independent counting problem
Involves drawing and object and replacing it before drawing it again.
What you pick the first time has no impact on what you pick the second time (coin flip)
Dependent counting problem
Each choice depends on the last (drawing name out of hat)
distance
distance = rate x time
200 miles in 5 hours....
200 miles = x * 5 hours
Measures of center
...
Mean
Sum of items/number of items = mean
AVERAGE
Median
Middle term of a set when set up smallest to larges.
What happens when the set us even?
Take mean of two middle numbers
Mode
Most common number, can have multiple modes
If each appears once?
No mode
Range
The difference between the smallest and largest values in a set of data
Standard deviation
How spread out or varied the data points are in a set.
Standard deviation equation
= √average of squared differences of data points from their mean
Normal distribution
The typical distribution of a large sampling in a bell-curve
Confidence intervals
A range of values defined so that there is a pre-determined probability that the value of an unknown parameter that is under investigation will fall within the range
The higher the level....
The more likely the parameter will fall within the interval.
Suppose a stockbroker has research indicating a 95% confidence interval that a company's stock will have a return between -7.8% and +9.5% during the next year. What does this mean?
Unknown parameter = average stock for the year
95% chance the average return will be in this interval
Margin of error
The maximum expected difference between the actual (unknown) parameter and the estimate for that parameter obtained through a sample
The smaller a margin of error...
The more accurate the survey results
Function solutions
...
Root/zero of a function
The value for which the function has a value of zero
Can it have more than one?
Yes
How do you find?
Determine the equation or look at the graph
How to find?
Put into foils, set equal to zero to find them
Or
Use the quadratic formula
Imaginary numbers
A complex number involves the square root of a negative number, and will be expressed using i
i
√-1
√-64
8i
i¹
i
i²
-1
i³
-i
i⁴
1
i⁵
i
i⁶
-1
Hypotenuse
The longest side, across from the 90 degree angle
Opposite
Directly opposite the angle
Adjacent
Next to the angle being used
sine =
opposite/hypotenuse
cos =
adjacent/hypotenuse
tan = opposite/adjacent
...
Trigonomic identities
sin²x + cos²x = 1
tan x = sin x /cos x
Circle formula
(x-h)²+(y-k)²=r²
radius of a circle
r
area of a circle
A=πr²
circumference of a circle
C=2πr
volume of box
lwh
area of rectangle
lw
volume of cylinder
πr²h
area of triangle
area = (1/2)bh
volume of sphere
4/3πr³
Pythagorean theorem
a²+b²=c² (c=hypotenuse, only true for right triangles)
volume of a cone
V=1/3πr²h
30-60-90 triangle
45-45-90 triangle
Volume of a pyramid
1/3 (lwh)
A circle has ______ degrees
360
There are _______ radians in a circle
2π
There are ________ degrees in a triangle
180
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