SAT MATH CHECKLIST: Facts and Formulas - Ivy Global
SAT MATH CHECKLIST: Facts and Formulas
Numbers and Arithmetic
Sum of consecutive integers
Sum of the consecutive integers from 1 to an integer n
+ + 1 + + 2 ... (n + 1) ? 2
Adding or multiplying even or odd integers
even + even = even odd + odd = even odd + even = odd
even even = even odd odd = odd odd even = even
Cross-multiplication
If = , then = .
Percent increase or percent decrease
? 100%
Exponent rules Absolute value
1 =
0 = 1
-
=
1
= +
=
-
( ) =
= ()
=
()
=
If = 4, then = 4 = -4 If < 4, then - 4 < < 4
If > 4, then < -4 > 4
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Algebra and Functions
Difference of squares
2 - 2 = ( + )( - )
Properties of inequalities
The inequality is reversed by taking the negative of both sides taking the reciprocal of both sides multiplying or dividing both sides by a negative number
Rates
= ?
Domain of a function
The set of all the "input" numbers for which the function still works
Range of a function Formula for slope
Facts about slope
Linear functions Quadratic functions Translation of = (), a units vertically and b units horizontally
The set of all the "output" numbers
=
rise run
=
2 2
- -
1 1
Horizontal lines have slopes of zero. Vertical lines have undefined slopes. Non-vertical parallel lines have equal slopes. Non-vertical perpendicular lines have slopes
whose product is -1.
= +
= 2 + +
- = ( - )
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Geometry
Angle sums
Sum of the interior angles of a polygon with n sides
The sum of any number of angles that form a straight line is 180?.
The sum of any number of angles around a point is 360?.
Two angles that add to 90? are called complementary angles.
Two angles that add to 180? are called supplementary angles.
180?( - 2)
Vertical angles
= and =
Transversals Exterior angle of a triangle
= = = = = = + = 180? and + = 180?
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= +
Classification of triangles
Pythagorean Theorem
2 + 2 = 2
Special right triangles
Triangle inequality Area of a triangle
The sum of the lengths of two sides of a triangle is always greater than the length of the third side
1 = 2
Area of a parallelogram or rectangle
=
Area of a trapezoid Area and circumference of a circle
1 = 2 ( + )
= 2 = = 2
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Arc length (L) and area (A)
? 2 = 360? ? 2 = 360?
Volume and surface area of a rectangular solid
= = 2 + 2 + 2
Diagonal of a rectangular solid
2 = 2 + 2 + 2
Volume and surface area of a right cylinder
= 2 = 22 + 2
Distance formula Midpoint formula
= (2 - 1)2 + (2 - 1)2
(
1
+ 2
2
,
1
+ 2
2
)
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