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SAT Math Basics


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Techniques to Remember:
Joe Bloggs
Bite-sized Pieces
To cut directly in half
Two facts about a parallelogram
1. Opposite sides are parallel and equal.
2. Area= b*h
In any triangle the longest side is opposite the?
largest angle
Right Triangles?
Special Right Triangles
Sides of 30-60-90
across 30 - x
across 60 - x sqroot 3
across 90 2x
Special Right Triangles
Sides of isos?
x, x, xsqroot 2
Rules of angles when a line crosses two parallel lines
big=big, small=small, any big + any small= 180
A line tangent to a circle is...
perpendicular to the radius of the circle
Plugging In?
1. Plug in your own numbers for each variable
2. Solve the problem using your chosen numbers= TARGET answer
3. Plug your chosen numbers into the answer choices= Find your TARGET
Steps to PITA
Plugging in the ANSWERS
1. Label your answers
2. Starting with answer choice C, work the steps
3. Arranged in descending/ascending order
4. When you find the correct answer, STOP
When do you PITA?
If the question asks for a specific amount
If there are no variables in the asnwer choices
Look fo "How many?" or "How much? or "What is the value of?"
% Change?
Difference/Original * 100
What does 2A mean?
The capitalized letter refers to the missing number.. 1 to make 21
What do you do on a question dealing with averages?
Fred the Plumber's Butt!
Make your circle with the total on top and then 3 of things next to the average on the bottom
Arrange the numbers from lest to greatest. the middle number is the median. if there ar two, then the average of those two.
The mode is the number that appears the greatest number of times
English to Math Equivalents..
Percent.. x/100
what... variable
is, are.. equals
The Ratio Box?
p. 103
Vary Directly or Directly Proportional means?
x/y =x/y
(xsub2 and ysub2)
Inverse variation or inverse proportion..vary indirectly or vary inversely.. means? formula?
as one gets smaller the other gets bigger
(xsub2 and ysub2)
# of outcomes fulfilling the requirements/ total # of possible outcomes
Geometric Probability?
area of the region fulfilling the requirements/ total area
Questions that ask you to count how many diff ways... Four Chefs are avaiable to cook four diff meals. If each chef is to cook one of the meals, in how many diff ways could the four chefs be assigned to the four meals?
once you use 4 then the next one must be 3 because you lost a chef int he first slot
1,2,3..1000 Question
Karen is choosing DVDs to bring over to her friend's house for a movie night. She has 8 comedies, 6 dramas, and 4 musicals in her collection. if she chooses one of each type, how many diff selections of DVDs can she make?
set up __ ___ ___, then fill in 8, 6, 4
8*6*4 = 192
1,2,3..1000 Questions
passangers on an airplane must choose one breakfast snack and one midmorning snack from the following options: apple, cookies, granola, yogruty, and pretzels. Hos many diff snack combos are possbile? (can choos an apple then a
Set up __ ___, then 5*5
If you see two fractions that equal each other.. don't forget to ?
Cross Multiply!
3/4x^2 =3x First step?
Get rid of fraction- mulitply by 4
Funky Roots and Exponents
Funky Roots and Exponents
square root of x cubed
x^2 - y^2
x^2 +2xy + y^2
x^2 -2xy +y^2
Rational Equations
What do you do?
1. Collect like terms.
2. Whatever you do to one side of an equation, you need to do to the other side.
3. Look for ways to factor.
4. x^n = number? Take the nth root of both sides but remember that you can't take an even root of a negative number.
5. Don't forget to PITA!
Rational Inequalities
If you mulitply or divide by a neg number?
Flip the sign
Radical Equations
If an equation looks like
4th root of x = 25, what do you do?
Raise both sides to the power of n (4) to get rid of the root
domain of a function is all of the values that you can put into the function for x
the range of a function is all the answers taht you can get our of the function
To find the domain of a function, plug in values from the answer choices. Eliminate answers if:
1. The bottom of a fraction becomes zero
2. You'd have to take an even root of a negative number
For Directly Proportional and Indirectly Proportional: if you plug in two diff numbers that decrease .. what should the result be?
Directly - decreases also
Indirectly- increases
(sub 2) (sub 2)
m= slope
b= y-intercept (the y-coordinate of the point where the line croses the y-axis)
Quadratic Function Facts:
They have graphs that are?
The equation is? If a is pos?neg?
If you look where the graph crosses the x-axis?
ax^2 +bx+c If a is pos the parabola opens up and if a is negative the parabola opens down
If you look at where the graph crosses the x-axis, you can find that roots (or solutions) to the quadratic function that defines the graph
If the equation looks like y= b- x^2 ?
Then the parabola opens down and b is the maximum value
Transforming Graphs
If the number is outside of the ()S of the original function?
If the number is inside?
Outside of ()s- graph moves up or down
Inside of ()s - graph moves left or right
If a geometric shape and a graph intersect, follow these steps: (2)
1. Use the information given about the shape to find a point on the graph
2. Use taht point to find the value of the constant in the equation of the graph
Not 1,2,3 .. 1000, just counting...
Carol has to choose the option for her new car. She can order one or more of the following: power windows, a sunroof, a leather interior. If she can order one or more of the options, how many ways can she combine
x x
x x
x x
x x x
A square anda circle have equal areas. What ist he ratio of the side of the square to the radius of the circle?
s^2 = pi r^2
say the side is 2 and so the are is 4
4= pi r^2
divide by pi
take the square root
answer: sq root of pi : 1
If you square a positive fraction less than 1, what happens?
it gets smaller
Third Side Rule
The length of the third side of ANY triangle MUSt always be?
less than the sum of the lengths of the other two sides
Greater than their difference
Distance Formula?
sq root of (x - xsub2) + (y-ysub2)
Midpoint Formula?
Just average the coordinates of the endpoints
(x+xsub2/2 , y+ysub2/2)
Geometric Sequence Formula
Finding the nth term in a sequence
nth term =?
nth term = (first term) * (mulipliers)^n-1
Exponential Growth
If ETS asks you to find a final amount..Final amount=?
Final amount= (Original amount) * (Growth Multiplie) ^number of changes
Distance (or work) =

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