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SAT Math basic concepts Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Basic concept

Basic concepts
algebra numbers
power /sqrt
different format of same expression
MADSPM­:mu­lti­pli­cat­ion­/di­vis­ion­/power multiply
minus power: recipr­ocal, 3-1=1/3; 3-2=1/sqrt(3)
square root:x1/2
Solve the equeation
move variables to onside; do same op on both side
Solve the inequa­lit­ies­:same as equation, negative change direction
Solving ration equati­on:­common denomi­nator; zero denomi­nut­or(no solution); infinite solution
Absolute number
Solution is negative?
simult­aneous equation
multip­le/­add­/su­btract together; solve the equation to get the solution
Word =>e­quation
is, are, were, did, does, costs =; what (or any unknown value) any variable (x, y, k, b) ; more, sum + ; less, difference − of, times, product × (multiply) ratio, quotient, out of, per ÷ (divide)


coordinate plane
slope-­int­ercept form
parallel lines: no solution
perpen­dicular lines: negative reciprocal slope)
distance formula
Pythag­orean triplets 3-4-5,­5-12-13
sqrt((­x1-x2)2 + (y1-y2)2)
midpoint formula
point of inters­ection
solve x: formula 1=formula 2
solve y: plug back in x
Other: PITA(a­rit­hme­tic), graph (no linear)

Charts and graphs

Line Graph
Bar Graph (or Histogram)
Two-Way Table
Figure Facts
variable, unit, relati­on,­legend ruler
# of outcomes you want/ #of possible outcome


Review basic defini­tions again before the test to make sure you don’t get stuck on the “little words.”
When you have to manipulate exponents, remember your MADSPM rules
To solve equations for a variable, isolate the variable. Make sure you perform the same operations on both sides of the equation
Inequa­lities can be worked just like equations, until you have to multiply or divide by a negative number. Then you need to flip the inequality sign.
When solving radical and rational equations, be on the lookout for extraneous solutions. They are answers you get that don’t work when plugged back into the original equation.
The absolute value of a number is the positive distance from zero, or practi­cally, making the thing inside the | | sign positive. Everything inside the | | is equal to the positive and the negative value of the expression to which it is equal. Also remember that | | work like ( ); you need to complete all the operations inside the | | before you can make the value positive.
To solve simult­aneous equations, simply add or subtract the equations. If you don’t have the answer, look for multiples of your solutions. When the simult­aneous equation question asks for a single variable and addition and subtra­ction don’t work, try to make something disappear. Multiply the equations by a constant to make the coeffi­cie­nt(s) of the variab­le(s) you want go to zero when the equations are added or subtra­cted.
When writing a system of equations, start with the most straig­htf­orward piece of inform­ation.
You can also use the equations in the answer choices to help you narrow down the possib­ilities for your equations. Eliminate any answers in which an equation doesn’t match your equation.
Parallel lines have the same slope and no solutions. If two lines have the same slope and infinitely many solutions, they are actually the same line. Perpen­dicular lines have slopes that are negative recipr­ocals of one another.
Rather than worrying about the distance formula, connect the two points and make the resulting line the hypotenuse of a right triangle. Then you can use the Pythag­orean Theorem to find the distance.
The coordi­nates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) will be .
When you encounter charts, carefully check the chart for inform­ation you should note, and remember that you can use your answer sheet as a ruler to help you locate inform­ation or to draw a line of best fit.
Probab­ility is a fractional value between 0 and 1 (inclu­sive), and it is equal to the number of outcomes the question is asking for divided by the total number of possible outcomes. It can also be expressed as a percent.
When doing Grid-In questions, be sure to keep to the left, and don’t bother reducing fractions if they fit in the allotted spaces.