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SAT Math
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Terms in this set (199)
Probability
Successes

Attempts
or
Part

Whole
After you read each problem, what should you do?
1 Write down the numbers/variables/equations
2 Find the hidden clues
When a problem says one number is MORE than another, what do you do?
Make a table!
When do you pick new numbers?
when the problem is mostly variables.
How do you calculate a fraction?
Part

Whole
What is a constant and a coefficient in 5x+3?
Coefficient = 5 and constant = 3
What does "of" mean in math?
Like 5% of 200?
"of" means multiply
What does "out of" mean in math?
like "5 out of 20"?
Divide
5/20
What does "per" mean in math?
"per" means divide
i.e. miles per hour = miles divided by hours
How do we tell what goes on the bottom of the probability equation?
1 Whatever is
"SELECTED AT RANDOM"
from all CBA students
2 People
"SELECTED FROM"
all RBC students
3
"OUT OF all Midd South students,"
how many are athletes?
4
"OF ALL" Midd North students,"
how many are in honors classes?
e.g. "if a righthanded student is selected at random, what is the probability that student is female?"
(Female righthanded students)

(All right handed students)
How do you write this as a fraction?
the ratio of b to a
or b:a
b

a
If you know something has an x intercept, you know...
y=0 there
f(x) = 0
X intercepts = "zeros" = "roots" = "solution"
What is the job of a negative sign in the exponent?
like 5x⁻³
5

x³
How can you tell what the slope of an equation is if they tell you it's a "linear equation"?
Linear equation follows y = mx + b
The number that's multiplied by the X.
F(x)=
Y
G(x)=
Y
What is the slope of
y = kx +4
slope = k
What is the slope of
kx
y=  + 4
3
k/3
How to deal with an equation model problem you don't understand?
y = 19.99 + 1.50x
The equation above models the total cost y, in
dollars, that a company charges a customer to rent a
truck for one day and drive the truck x miles. The
total cost consists of a flat fee plus a charge per mile
driven. When the equation is graphed in the
xyplane, what does the yintercept of the graph
represent in terms of the model?
A) A flat fee of $19.99
B) A charge per mile of $1.50
C) A charge per mile of $19.99
D) Total daily charges of $21.49
Make an x y chart and plug in 0 and 1 for x
Slope will always be the rate (per mile, per day, etc.)
Yintercept will always be the INITIAL VALUE (flat fee, original investment, starting location, etc.)
What are the 8 math tactics?
1Write down each number/variable/equation and find its hidden clue.
2 Write Equation in words
3 Test in Answers A B C D (don't skip any)
4 What is the problem asking?
5 Red Arrow Method
6 Pick your own numbers
7 Make a Table
8 At least 30 seconds per problem
How can you calculate a portion?
e.g. "What portion of RBC students take honors classes"
part

whole
How do you calculate a percentage?
e.g. What percent of the pizzas were burned?
Part

Whole
Burned Pizzas

All pizzas
Which steps should you write out (as opposed to doing in your head)?
Every one!
How many terms in 5x²
1
It's a monomial
How many terms in 3x² 48
2
It's a binomial
How many terms in x² + 3x  18
3
It's a trinomial
What separates terms in math?
+ or 
When you multiply or divide, must we do that to
all
terms?
(5x+3)

5
Yes every term gets multiplied or divided. You must
split the terms
5x 3
 + 
5 5
What is the standard form of a trinomial?
ax²+ bx + c
What does it mean when 2 equations are both true for all values of x?
They are the same equation IN DISGUISE
10x²  3x = 15
30x² kx = 45
Solve for k
10x²  3x = 15
30x² kx = 45
k = 9
10x²  3x = 15
30x² 0.25kx = 45
k = 36
Sometimes on the SAT, multiple math questions refer to one diagram.
How can you tell which questions are grouped together with the same diagram?
There is a thin bold arrow with a triangle in the middle that marks the start and end.
Say you have an equation like
7
 = 3
x
What do you do here?
When you see your variable in the denominator, what do you do every time?
Here, you multiply both sides by x.
Every time, you multiply both sides by your
denominator
What does it mean when 2 linear equations have no solution?
They are parallel and you
set the slopes equal to each other
What does it mean when 2 equations intersect?
They have 1 solution there
they have the same x and y
Median
Middle number
e.g. If you are the median height at your school of 1001 kids, that means there are 500 kids taller and 500 kids shorter than you. And you are the one in the middle.
Mean
Average
When do you make a table?
DIFFERENT UNITS
something is
MORE
than something else
e.g. when a relationship between different units is given
1 decagram = 10 grams
e.g. "Martha worked 15 more hours than Jay this week"
"The worked a total of 75 hours" How long did each one work?
When you have a linear equation, a yintercept of 2, and an ordered pair like (5, 3), what can you do ?
Plug the x=5 and y= 3 in for x and y in the equation y = mx +b
What is the graph of a "Direct Relationship" or "Positive Correlation" ?
ex. y = 5x
What does linear mean?
Like a line
What equation do you use when they say "linear equation"
y=mx+b
What is the graph of an "Inverse Correlation" or "Indirect Relationship"
y = 1/x


Range of a set of numbers
e.g. what is the range of 3, 4, 6, and 8?
Max minus the Min
83 =5
What do you write when you see
"Average annual increase"
Write the slope formula and find it
When you see your variable in the denominator, what do you do every time?
e.g.
c + 5
 = 20
c  5
Multiply both sides by the denominator ! :D
(c  5 )(c + 5)
 = 20 (c  5 )
(c  5)
How do we approach reading a graph?
Read the Title
Read the X and Y axes
Read the notes after it
WATCH OUT FOR DIFFERENT SCALES ON X AND Y AXES
What is the slope of
kx
y=  + 5
3
k/3
What is an intercept of 2 lines?
a point where 2 lines cross each other
What do you multiply by to apply an 8% sales tax?
Multiply the price by 1.08
What would you multiply by to apply a 20% off discount?
Multiply the price by 0.80
What is the best way to approach tables with lots of data in boxes?
Circle the boxes you care about
When a problem says
"Get a in terms of x"
What do you do?
Solve for a
Isolate a
Get "a" by itself
100% is equal to what number?
1
What is an interval of time?
(not interval notation, not that complicated)
A period of time
How do you solve the problem x+15 = 8 ?
...
The gymnastics team needs an average of 46 points (out of a total of 50) per gymnastics meet in order to win their conference. There are 8 gymnastics meets over the season.
What is the hidden info here?
46 points per meet * 8 meets = 368
What is a base?
e.g. 5x²
e.g. (6y)²
x
the thing that receives the exponent
What are vertical angles?
Angles directly across from each other
They are equal
In Geometry (when the question has a shape drawn in the book), what is the hint?
Fill in all the info you can.
What is b^(3/4)?
the 4th root of b cubed
Quadratic Formula
How do we get a quadratic equation to have "no real solutions" ?
Equation of a parabola (This is vertex form)
y = a(x  h)² + k Vertex is (h, k)
y = 3(x 2)²  5
Vertex is (+2, 5)
The xcoordinate of the vertex is opposite of the number in parentheses
equation of a circle
(x + h)² + (y + k)² = r² Vertex is (h, k)
Center is the OPPOSITE of the number in parentheses
What does it mean for a system of linear equations to have NO SOLUTION?
They must be parallel
and the slopes must be the same!
What does a "linear equation" look like on a graph?
A line!
What does it mean for a system of linear equations to have "infinite solutions"?
It means they are actually the SAME LINE and SAME EQUATION in disguise
What does it mean for a system of linear equations to have 1 solution?
It means that the same point must exist on both lines.
So they intersect
They have the same x and y values at that point of intersection
What the heck does a factor of g(x) look like?
If g(x)= x^2 + 7x +12
Factored into:
g(x)= (x + 4)(x + 3)
(x+4) and (x+3) are the factors of g(x)
For a problem asking which must be a factor of g(x), what do you do?
Find where g(x) = 0 aka where y = 0
Pick the
opposite
of that x value
They will try to trick you by saying where x = 0. Watch out.


What is linear growth?
Adding the same number every time
e.g. adding $50 per week
Adding a percent of your INITIAL VALUE every time.
e.g. You start with $100, you gain 5% of your initial value each time.
What is exponential growth?
Adding a % of your
CURRENT VALUE
each time.
Multiplying by a number or % every time.
Show an inputoutput chart for
taking out $100,000 in student loans at 9%.
What happens each year for the next 3 years?
How much extra money did you get each year?
...
Say you had a problem where you increased the price of bread by multiplying the price by 1.90.
What is the percent increase in the price?
90%
How do you make something UNDEFINED?
Get it with a Denominator of 0.
What does it mean when the SAT says
x ≠ 5
or a ≠ 2/x
IGNORE this information.
It ONLY means that the fraction cannot be undefined.
It means that the denominator cannot be 0.
What do you do when the question asks:
"Which of the following
must
be true ?"
Try to
PROVE WRONG
answers A, B, C, and D.
If you can prove an answer wrong
once,
then it doesnt need to be true.
What does "parallel" mean?
Same Slope
How to deal with a problem like
The expression (5x2)/(x+3) is equivalent to which of the following expressions?
A) x
B) x+2
C) 3x7
D) 5x5
Pick new numbers
Test A, B, C and D.
Find out "if x = 3, then the expression equals 44/5"
What is the formula for the average of 2 things?
(a + b)/2
Solving inequalities is just like solving equations EXCEPT
When you multiply or divide by 1, you need to flip the direction of the inequality
Area of circle
pi r squared
What is the circumference of a circle?
2π r
What is the volume of a cylinder?
π r² h
(If you don't remember, check the front of either math section)
Surface area of a cylinder
...
How do we find the TOTAL amount of money someone spends?
example:
You buy 4 skirts at $20 per skirt.
Take the price and multiply it by the number of things you bought.
Example 2: You buy x skirts at $20 per skirt .
$20x is the total you spend
Can you split up radicals if they are multiplied by each other?
EG can you split up
√(3*y)
YES
√(3
y) = √3
Whenever you have time in a problem, is it the INPUT (xvalue) or the OUTPUT (yvalue)?
The TIME is the INPUT (X value)
(15√3) ÷ √3
Do BOTH the 15 and the √3 get divided?
NO.
You only need to divide each term 1 TIME!
15√3 is ONE TERM
When you see 2 triangles on the test, what is most likely happening?
They are most likely similar triangles, which means that they have the same angles, and 1 triangle is a mini version of the other one.
what is x^(1/2)
√x
When using algebra to solve an equation, how many operations (add,subtract) should you do for each line?
ONE OPERATION PER LINE
An equation must have how many variables for you to solve it?
ONE VARIABLE
% means per cent. What does that mean mathematically?
÷ 100
Can % stand alone or do the need to be multiplied by a number?
NO
eg. 5% is not meaningful.
5% of what?
5% of CBA students do Model UN. That is meaningful
5% * 1000 students = 50 students
Do % always need to be multiplied by a number?
YES
If you have a solution, or root, of a function, where is that on a graph?
The solutions are where the function hits the xaxis, the xintercepts
How do you find the arc length? (length of a certain part around a cirlce)
Take 2 π r * ( % around the circle you want)
Example: 50% for halfway around the circle
What is the vertex of a parabola
y= (x  3)²  49
(3, 49)
What is an integer?
A whole number with nothing after the decimal place
It can be negative or positive.
2, 1, 0, 1, 2, 3, 4
When a problem gives you a point like (4, 4) or (1, 5), how do you represent it?
With an xy chart
When 2 equations intersect, what does that mean?
They have a solution!
How do we deal with a problem like
(1+10i)

(63i)
Multiply both sides by the CONJUGATE
(1+10i) (6+3i)
 * 
(63i) (6+3i)
How do you deal with a problem that asks about units?
Factor Label Method
aka Dimensional Analysis
How do you get a quadratic to have 1 solution?
1 ⎷0
How do you get a quadratic to have 2 solutions?
b²4ac = positive #
How do you get a quadratic to have 0 solutions?
b²4ac = negative #
In a list of salaries, why would the average salary be much larger than the median salary?
E.g. Average Salary= 3,000, 000
Median Salary = 500,000
A few workers are making a TON of money.
If you move over 3 decimal places in a number, that is equivalent to mulitplying/dividing it by what?
1000
How do you generally deal with problems that ask about percents?
Pick a new number!
When they say "which of the following is an equivalent form that ________"
what can you know?
ALL of the possible answers are equivalent forms!
sin (a) = cos (b) . What can you tell?
sin (a) = cos (b)
a + b = 90
eg. sin(10) = cos(80)
When the problem compares 2 things, like A is 40% bigger than B, how do we represent this?
With a TABLE
Column A Column B
Pick an easy number to use
Average Rate of Change of X
What are they looking for?
The slope
Δy/Δx
In a 4sided figure (quadrilateral), all 4 of the angles add up to what?
360 degrees
Difference of 2 perfect squares
a²b²
(ab)(a+b)
What is the formula for percent change?
% increase
%decrease etc
Change

Original
New  Old

Old
Say we surveyed New Jersey kids under age 25 about how late they stay awake.
For example, they say the average bedtime is 1am.
If they ask "to what other group could these results be applied?"
what are they asking?
What other group would behave SIMILARLY
for example, other kids under age 25 in the USA.
When a problem asks for the minimum or maximum value of a parabola, you can
1 Graph it
2 Get it into Vertex form
How do you get the equation a parabola or circle into Vertex form?
Complete the Square
If a quadratic equation has 1 solution, what can you tell from the quadratic formula?
√(b²4ac) = 0 !!!
If a quadratic equation has 0 solutions, what can you tell from the quadratic formula?
√(b²4ac) = a NEGATIVE number
If a quadratic equation has 2 solutions, what can you tell from the quadratic formula?
√(b²4ac) = a POSITIVE number
Find the vertex and radius for this circle
4x² + 4y²  16x  24y + 51 = 0.
What does it mean when 2 triangles are similar?
They have the same angles
1 is a mini version of the other one!
What is the formula to find the xpoint of the vertex of a parabola?
x = b/2a
When two angles add up to 90, like (a + b) = 90 degrees, what can you tell about their sine or cosine?
The sin(a) = cos(b)
This also works the other way around
For a straight line (a linear equation), must the slope remain the same throughout the whole line?
YES
If an angle is 1/4 of the circle, then its arc length is what % of the circumference?
also 1/4 of the circumference
If an angle is 1/5 of a circle, then the area inscribed by the angle is what % of the whole area?
1/5 of the area of the circle
How do you find the perimeter of a shape?
adding up all the sides
"the value of a function" is the x value or the y value?
Y VALUE
Max value of a function is the biggest y or the biggest x ?
The biggest Y value
For any line, does the slope ever change?
No
When a function has 4 "roots," what does this mean?
The function crosses or touches the x axis 4 times
In math problems asking about surveys or experiments, what should you pay special attention to?
Which population they are asking about!
Where they got the people!
Social Deviant
an abnormal person
to deviate
to be far away from what's normal
Deviation
how far away you are from the normal .
The standard deviation is a measure of what? (in words, not a formula)
Standard Deviation is a measure of how far the numbers are from the mean.
If they are close, the standard deviation is low
If they are far, the standard deviation is high
What is the function for DOUBLING
2ˣ
If something doubles, can it start at 0 ?
NO
What is function for interest rates? (compounded yearly)
What would be the function if you took out a $100,000 student loan with a 7% interest rate each year?
Final = Starting * ( 1 + r)ᵗ
r = interest rate
t = time, in YEARS. Must be in years.
Which of these equations shows an object accelerating upward?
How about downward?
Δy = vt + ½at² and
Δy = vt  ½at²
Accelerating Up (like a hot air balloon)
Δy = vt + ½at²
Accelerating Down (like a ball thrown up that falls to the ground)
Δy = vt  ½at²
How do we solve
ex. Your Calculus grade consists of 10 tests. Each test has 100 points. Through 6 tests, you have an 88 average.
What do you need to average for the rest of the year to finish with a 90 average?
You need a 93 average
Calculate the total number of points you have and the total number of points you need in the end
how to find the range of a set of numbers
biggest number  the smallest number
What do zeroes of a function represent
The solutions when y=0
x intercepts
How to handle a problem like this
ex. Your Calculus grade consists of 10 tests. Through 6 tests, you have an 88 average.
What is the worst grade you can get on your next test and still average a 90 for the year?
Calculate the total number of points you have and the total number of points you need in the end
Worst grade is a 72
How to solve an equation with 3 terms?
Get all 3 terms on one side = 0
How to solve an equation with 2 terms?
e.g. b²48 = 0
Get 1 term on each side
b² = 48
When you have a function on a graph, what does a DOUBLE ROOT (double answer) look like?
It JUST TOUCHES the xaxis, it doesnt go thru
When you have a function on a graph, what does it mean when the line JUST TOUCHES the x axis
It is a DOUBLE ROOT (answer)
When you have a function on a graph, what does it mean when the line GOES THRU the xaxis
It is a REGULAR ROOT (answer)
A is 4 times as big as B
A = 4B
B is smaller
B needs the heels to be as tall as A
Confidence Interval
If you run the experiment 100 times, how many of those times will be a success?
If your device works 95 times out of 100 times, your confidence interval is 95%
4x²
4x²
(4x)²
16x²
(3x²y³)³
27x^6 y^9
What to do when you are faced with a question where a business sells 2 types of items?
e.g. The 7/11 sells hot dogs and slushies. They sell 151 total items in a day and make $434 in that day. Each hot dog costs $2 and the slushies cost $3. How many hot dogs and slushies did they sell that day?
Set x = # of 1st item
y= # of 2nd item
Make 2 equations.
Equation 1: # of 1st item + # of 2nd items = total items
Equation 2: $ from 1st items + $ from 2nd items times = total $
If you have 3 terms, a trinomial, how do you set it up for solving?
Get all 3 terms on the same side = 0
If you have a problem with a 306090 or a 454590 Triangle, what must you do?
Write down the sample triangles!
An angle in the middle of the circle is how much bigger than an angle taken from the EDGE of a circle?
Middle angle is TWICE as big as angle taken from EDGE
How to deal with a problem that has speed, time, and distance?
S * T = D
How to calculate the Average Speed?
Average Speed = TOTAL Distance ÷ TOTAL Time
y is a function of x
y = f(x)
y is the OUTPUT of the function!
"success is a function of hard work"
success(hardwork) = such and such
success is the OUTPUT
x always means input or output?
X is INPUT
Y always means input or output?
Y is OUTPUT


What is the range of a function?
All the possible Y values
What is the domain of a function?
All the possible X values
What is a zero of a function?
Answer, solution, root, or xintercept
What is the root of a function?
Answer, solution, xintercept, or zero.
With a Geometry problem with parallel lines, what is the hint?
This is not "they have the same slope"
Extend all the lines!
copy and paste onto parallel lines
When you get a question that asks "How many solutions are there to this system of equations," what must you do?
Graph them!
See how many times they intersect


When we are confused about what something means, do we give up?
no, keep going with this problem. It may become clear later
When you have like ( a + b ) , replace them with what?
z = ( a + b )
When a question gives a linear equation and asks about the "initial deposit" or "starting value" , what do they mean?
THE Y INTERCEPT
if y = mx +b, they want b
What do you do whenever you have i^2?
Replace it with a 1 in parentheses
A question says:
f(x) = x^2  6x + 3

x1
What is f(1)?
Replace every 'x' with a (1) in parentheses
f(1) = (1)^2  6(1) + 3

(1)1
If you are told that 1, 2, and 3 are real roots of f(x), how do you find factors of f(x)?
x  (root) is always a factor of f(x)
x1, x2, and x+3 are all factors
If you have the equation of a parabola like y= (x+3)(x5) and are asked to find the xcoordinate of the vertex, what do you do?
Find the zeros of the parabola. The xcoordinate of the vertex will be in between the two zeros.


f(x) = 3cx + 7
f(2) = 5
f(5) = what?
What do you do?
1) Plug in 2 for f(x) and 5 for x
5 = 3c(2) + 7
5 = 6c + 7
2) Solve for c
c = 1/3
(x+7)^2 = 25
Solve for x
Take the square root of both sides, leaving:
x+7 = +/5
Solve two separate equations
x + 7 = 5
x = 2
x + 7 = 5
x = 12
What do you do to solve a polynomial with four terms?
x^3  7x^2 + 3x  21 = 0
Factor by grouping


What does "x is at least 5" mean with an inequality?
x ≥ 5
x is at least 5
What does "y is no more than 7"
y ≤ 7
y is no more than 7
What is the difference between the shapes of the graphs of Linear and Exponential Growth?
This is the linear one
This is the shape of Exponential Growth
What does the graph of y = (1/x) look like?
1/x
How can you tell what the height of a cone is?
If you think it might be a 345 triangle, is it?
YES
When it's a 345 triangle, what do you do?
DRAW the 345 triangle
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