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SAT Math
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Terms in this set (76)
(A) Getting started stuff
If I assigned certain cards ("study the Bs, Cs, and Ds" or something) see the letter in parentheses on each card. If not, study all.
*If using the app*
Click the "cards" button
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Turn on "Start with term"
Star it if you didn't know it.
Restudy starred cards until you master them.
(A) smallest prime number
2
(A) which of the following are rational?
i
0
.5
1.285
√2
π
6
0
.5
1.285
6
(A) Give three factors of 12
2,3,4,6, etc
(A) Is 0 positive?
no
not positive
not negative
non-positive
non-negative
(A) which of these are prime?
0
1
3
5
7
9
3
5
7
(A) What's the definition of a rational number?
can be written as a fraction
(A) What does "a set of distinct numbers" mean?
all different numbers, no repeats
(A) Which of these are integers?
-2
0
.5
1
2
345
-2
0
1
2
345
(A) Give three multiples of 12
24, 36, 48, etc (multiply 12 by numbers)
(A) Which of these are even?
-5
-4
0
2
3,145
3,146
-4
0
2
3,146
(A) What do squiggly parentheses mean?
{2,4}
Two correct answers for x (not an x and a y)
(B) What are the steps for answering any math question?
1. underline if the question is long or asking something weird
2. scratchwork & strategies
3. did you answer the underlined question?
(B) What's the single most important thing you can do to be successful on a math section?
Scratchwork. Don't do math in your head.
(B) When do you plug answer choices into the question?
This is the first thing to try when you get stuck on a problem.
Phrasing like "what is the value of x...?" (or any variation, like "how many dogs are in the park?" or "how much does a bottle of juice cost?") is a clue that using answer choices is likely to work.
(B) What's the first thing to try when you're stuck on a math question?
plug in answers
(C) What do you do when you see variables in the answer choices?
make up numbers
(C) What are the steps for making up numbers?
1. make up values and box them
2. get an 'answer' for your values using the QUESTION and circle it
3. put your values into the answer choices
4. pick the one that matches
(C) When do you do make up your own numbers?
1. variables in the answer choices
2. changing fractions (the population of flies increased by 1/5...) or percents (the company marks up the price 10%...) with no starting value given
3. changing an equation (what happens if x is doubled and y is halved?)
4. must be/could be
(C) arsenal of strategies
1. use answer choices
2. plug in your own numbers
3. guess and check
(D) What values should you always test for a must be/ could be problem (unless that value is prohibited by the question)?
-3 (a negative number)
0
.5 (a fraction or decimal)
1
2
100 (a big number)
(D) What do you do if a question has percent changes with no starting value given?
Start with 100 and run it through the question.
(D) What do you do if a question has fraction changes with no starting value given?
Multiply your bottom numbers.
So if the frog population decreases 1/5, then increases 1/3, you would start with 15 frogs and run it through the question.
(E) (x²)³=
x⁶
(E) x²+x³=
NO!!
These do not simplify. 1²+1³≠1⁵
(E) x³/x²=
x¹
(E) x⁻³=
1/x³
(E) How can you rewrite x^½?
√x
(E) x²*x³=
x⁵
(F) percent change formula
(amount of change/original amount)*100
(F) A basket of apples contains red apples and green apples. There are 4 red apples for every 3 green apples. If there are 70 apples all together, how many are red?
40
(G) What is the slope of a line parallel to the line y=3x+4
3
(G) On the SAT, what are the three best ways to solve a system of equations with two variables and no exponents?
1. substitution (solve for one variable, plug what you get in for that variable in the other equation)
2. elimination (line up, add or subtract left sides and right sides to get rid of a variable)
3. use answer choices
(G) What is the slope of a line perpendicular to the line y=-3x+4
1/3
(G) How do you find the equation of a line if you're given two points?
use (y₂-y₁)/(x₂-x₁) to find slope. Plug the slope and one of the points into the equation y=mx+b to find b.
(G) slope of a horizontal line
0
(G) slope-intercept form of a line
y=mx+b
m is the slope and b is the y-intercept
(G) slope formula
(y₂-y₁)/(x₂-x₁)
(G) What does it mean if two equations have infinite solutions?
They're the same line. For example, y=x+1 and 2y=2x+2. The second equation is just the first equation multiplied by 2.
(G) What does it mean if two equations have no solution?
They have the same slope and different y-intercepts. For example, y=x+1 and 2y=2x+8. The second equation is really just y=x+4
(G) Distance formula
a²+b²=c²
a=difference between x values
b= difference between y values
(G) midpoint formula
(avg x₁ & x₂, avg y₁ & y₂)
(G) bisect
split in half
(G) slope of a vertical line
undefined
(H) when you're asked how many solutions a quadratic equation (or system) has, what should you do?
b²-4ac
positive answer= 2 solutions
negative answer= no solutions
0 answer= 1 solution
(H) quadratic formula
-b±√(b²-4ac)
--------------
2a
(H) what does the graph of y=(x+4)²+3 look like?
A parabola opening upward with vertex (-4,3)
(H) What is the vertex of the parabola y=2x²-4x+11?
(1,9)
use x=-b/2a to get the x-value of the vertex, then plug it into the equation to get the y-value.
(H) factor a²-b²
(a+b)(a-b)
(J) if f(x)=x²+2 and f(n)=27, what is n?
5
27=n²+2
put whatever's in parentheses in for x
anything not in parentheses is a y-value
(J) what are the three rules of functions?
1. If it's in parentheses, put it in for x. If it's not, don't.
2. f(x) means y
3. f(x)=3 means "what is x when y=3?"
(J) What is domain?
set of all x-values
(J) What is range?
set of all y-values (can also mean the difference between the highest and lowest value in a data set)
(K) median
middle number
(J) if f(x)=x²+2, what is f(3)?
11
f(3)=3²+2
anything in parentheses is an x value
(K) What trick can you use for hard average problems?
pretend every value is exactly equal to the mean
(K)
In Ms. Smith's class, 5 kids have no pets, 5 kids have 1 pet, and 5 kids have 2 pets.
In Ms. Jones's class, 1 kid has no pets, 13 kids have 1 pet, and 1 kid has 2 pets.
Which class's data set has a larger standard deviation?
Ms Smith's. The data points are spread out. Ms. Jones's class has a small deviation because the points are all clustered around the middle.
(K) mode
most frequently occurring number
(L) complementary
adds up to 90⁰
people compliment you on your posture if your back's at a 90 degree angle
(L) What's the area of a right triangle with side lengths 3, 4, and 5?
6
(L) Pythagorean theorem
a²+b²=c²
c is the hypotenuse
(L) supplementary
adds up to 180⁰
you need vitamin supplements if you're 180 years old
(L) area parallelogram
(L) what do you need to know about similar triangles?
They have the same angles. Set up a proportion and cross multiply.
(L) How do you flip a parabola?
Put a negative in front of the equation
examples: y=-x²+2x+1 and y=-(x+3)²
(L) what does the graph of (x+4)²+(y+3)²=4 look like?
A circle with a center point of (-4,-3) and a radius of 2.
(M) cosine=
adjacent/hypotenuse
(M) tangent=
opposite/adjacent
(M) sine=
opposite/hypotenuse
(M) The sine of 55° is equal to the cosine of what angle?
35°
sin(x)=cos(90-x)
(M) How can you recognize a sine graph?
Goes through (0,0)
(M) Is the tangent of 4π/3 radians positive or negative?
(M) cosine graph
(M) sine graph
(M) How can you recognize a cosine graph?
Goes through (0,1)
(O) What do you do with (x+2i)/(x-3i)?
When i shows up in a fraction, multiply the top and bottom by the bottom but with the sign switched (so x+3i)
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