SAT Math Facts1
General Vocabulary
Integer = A number that is not a fraction or decimal. …-2, -1, 0, 1, 2…
Prime = A positive integer with no factors other than itself and 1.
1 is not prime. 2, 3, 5, 7, 11, 13…
Imaginary number = A multiple of i. = √−1.
Real number = A number without an imaginary component.
Ratio = fraction.
x is directly proportional to y: = for some constant k.
x is inversely proportional to y: = for some constant k.
General Facts
If + + = + + for all values of x, then a = d, b = e, and c = f.
If × = 0, then either a = 0 or b = 0.
− = ( + )( − ).
Exponential growth or decay: = (1 ± ) .
= 180°.
The angles of a triangle add up to 180°.
A straight line is 180°.
In a right triangle, + = .
Area
!"#!$% = #%!&'($% = )*
+
#"&'($% = ℎ
Volume
-#%!&'(.$&#/#"01 = )*ℎ
-!2$"'3%# = ℎ
5
-0/4%#% = 6 6
+
-!7'% = ℎ
6
+
-/2#&1"3 = )*ℎ
6
© 2016 Central Test Prep, LLC
1
This fact sheet is not intended to include all the information on which a student might be tested. It is intended to
highlight those areas that are typical test material and that students are particularly likely to have forgotten or not
have learned by the time they take the test. Do not rely on this fact sheet alone in preparing for your test.
1
SAT Math Facts1
Circles
( − ℎ) + ( − ) = = 8 = 2
Lines
Standard form: + = Slope-intercept form: = : + Point-slope form: − + = :( − + )
2 <2
Slope: : = ;<=
;
=
&
>
If line l is perpendicular to a line with slope >, then the slope of l is − &.
Parabolae
Quadratic formula: =
<>±√> ; <5&!
&
Standard form: = + + Intercept form: = ( − + )( − )
Vertex form: = ( − ℎ) + Found by factoring standard form.
Found by completing the square of standard
form.
Exponents
( 2 ) ? = 2?
+
<2 = A
+ = 2 × ? = 2@?
A
B
B
B = √ 2 = √
C = 1, if ≠ 0
2
Trigonometry
7//
E = 7//
&3H
E =
EF = 42/
GE = 42/
IF =
7//
&3H
0"'
42/
42/
&3H
&3H
GI = 7//
IF = !70
© 2016 Central Test Prep, LLC
1
This fact sheet is not intended to include all the information on which a student might be tested. It is intended to
highlight those areas that are typical test material and that students are particularly likely to have forgotten or not
have learned by the time they take the test. Do not rely on this fact sheet alone in preparing for your test.
2
SAT Math Facts1
Special triangles
3-4-5
30°-60°-90°
5-12-13
45°-45°-90°
Statistics
Average = The sum of the members of a set divided by the number of members of the set.
KL(M1, 7, 7, 9Q) =
+@R@R@S
5
=6
Mean = Average.
Median = Middle number of a set.
U(M8, 6, 7, 5, 3Q) = 6
U(M0, 9Q) = 4.5
Mode = The most common number in a set.
UG(M1, 7, 7, 9Q) = 7
Range = The difference between the largest number and the smallest number in a set.
YFL(M1, 7, 7, 9Q) = 8
Standard deviation = (Roughly speaking) a measure of how spread out a set of data are.
Z(M0,0,0,9,9,9Q) > Z(M1,2,3,6,7,8Q)
Useful Terms
Each:
Greater than:
Is/are:
Of:
Per:
Percent:
What:
×
+
=
×
÷
÷100
x
i.e. “What percent of 12 is 3 greater than 7?”
x
÷100 × 12 = 3
+
7
© 2016 Central Test Prep, LLC
1
This fact sheet is not intended to include all the information on which a student might be tested. It is intended to
highlight those areas that are typical test material and that students are particularly likely to have forgotten or not
have learned by the time they take the test. Do not rely on this fact sheet alone in preparing for your test.
3
SAT Math Facts1
Techniques
Cross multiplying
If two fractions are equal to each other, cross multiply.
&
>
=
!
3
= Dimensional analysis
Problems involving rates might ask you to find distance, given a walking speed, or water
used, given a rate of flow. Determine what units the answer should be in, and multiply
the given by the appropriate conversion factors to create a number in those units.
Kate runs 400 meters in 75 seconds. If she continues running at this rate, how many
miles will she run in 20 minutes?
400:
1:)
60E
480,000::)E:F
×
×
× 20:F =
= 4:)E
75E
1,600: 1:F
120,000E::F
Solving simultaneous equations
By substitution: Solve for one variable in terms of the other in one equation and
substitute the result into the other equation. Once you have solved for one variable, plug
that into either equation to solve for the remaining variable.
3 − 4 = 11
2 + 2 = 12
↓
+ =6
= 6−
3(6 − ) − 4 = 11
18 − 3 − 4 = 11
7 = 7
\=]
3 − 4 = 11
3 = 15
^=_
© 2016 Central Test Prep, LLC
1
This fact sheet is not intended to include all the information on which a student might be tested. It is intended to
highlight those areas that are typical test material and that students are particularly likely to have forgotten or not
have learned by the time they take the test. Do not rely on this fact sheet alone in preparing for your test.
4
SAT Math Facts1
By elimination: Alternatively, multiply one of the equations by a constant to get a
common term. Then add the two equations together or subtract one from the other to
eliminate that term. Once you have solved for one variable, plug that into either equation
to solve for the remaining variable.
3 − 4 = 11
2 + 2 = 12
↓
3 − 4 = 11
4 + 4 = 24
7 + 0 = 35
^=_
3 × 5 − 4 = 11
15 − 4 = 11
4 = 4
\=]
+
Eliminating complex denominators
Multiply both numerator and denominator by the complex conjugate of the denominator.
3 + 2
2 + 3
↓
3 + 2 2 − 3
×
2 + 3 2 − 3
6 − 9 + 4 − 6 4 − 6 + 6 − 9 6 − 5 + 6
4+9
12 − 5
13
© 2016 Central Test Prep, LLC
1
This fact sheet is not intended to include all the information on which a student might be tested. It is intended to
highlight those areas that are typical test material and that students are particularly likely to have forgotten or not
have learned by the time they take the test. Do not rely on this fact sheet alone in preparing for your test.
5
SAT Math Facts1
Long division of polynomials
You thought you were done with this technique, didn’t you? You can use this technique
to determine whether a binomial is a factor of a polynomial or manipulate rational
functions.
3 + 5
3 + 2 − 1
= − 1)3 + 2 − 1
−1
3 − 3
5 − 1
5 − 5
4
6 ; @<+
<+
= 3 + 5 +
5
<+
Factoring by grouping
Really, this is nearly the only reliable way to factor a polynomial with a cubic term.
Sometimes a cubic polynomial can be factored if instead of treating it as four separate
terms, you treat it as two binomials added together. Factor each one and notice that each
factored binomial turns out to have a new binomial as a common factor.
6 + 3 − 4 − 12 = 0
( 6 + 3 ) − (4 + 12) = 0
( + 3) − 4( + 3) = 0
( − 4)( + 3) = 0
( + 2)( − 2)( + 3) = 0
Completing the square
= − 6 + 10
− 10 = − 6
− 10 + 9 = − 6 + 9
− 1 = ( − 3)
= ( − 3) + 1
© 2016 Central Test Prep, LLC
1
This fact sheet is not intended to include all the information on which a student might be tested. It is intended to
highlight those areas that are typical test material and that students are particularly likely to have forgotten or not
have learned by the time they take the test. Do not rely on this fact sheet alone in preparing for your test.
6