# SAT and ACT Math formulas

Math formulas for problems found on the SAT and ACT. While the SAT lists many of the formulas at the beginning of each math test, the ACT does not. And, you will save time if you memorize these.

#### Terms in this set (59)

-b±[√b²-4ac]/2a
• Slope
(y₂-y₁)/(x₂-x₁)
• Slope-Intercept
y=mx+b
• a³-b³
(a-b)(a²+ab+b²)
• a³+b³
(a+b)(a²-ab+b²)
• a²-b²
(a-b)(a+b)
• a²-2ab+b²
(a-b)²
• a²+2ab+b²
(a+b)²
• (a+b)(c+d)
• a(b+c)
ab+ac
• sine ratio
opposite ÷ hypotenuse
• cosine ratio
• tangent ratio
• A function is ___________ a relation
always
• Direct Variation
y=kx
• Inverse Variation
y=k/x
• Slope intercept form
y=mx+b
• Point-Slope form
y-y₁=m(x-x₁)
• Standard form
Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
• Undefined
When there is a vertical line that has different y points, but the same x point
• Zero
When there is a horizontal line that has different x points, but the same y point
• Dividing by a negative number in an inequality
You must flip the sign
• Graphing < or > on a coordinate plane
dotted line
• Graphing ≥ or ≤ on a coordinate plane
solid line
• Graphing ≥ or > on a coordinate plane
shade upwards or to the right
• Graphing ≤ or < on a coordinate plane
shade downwards or to the left
• Infinitely many solutions
when the system of equations have the same slope and y-intercept
• One solution
when the system of equations have different slopes
• No solution
when the system of equations have the same slope but different y-intercepts
• All direct variations are ____________________
linear functions
• A linear function is a function that _____________ a line
graphs
• A parent function is the simplest ____________ of a function
equation
• Linear parent function
y=x or f(x)=x
• Elimination method
solving systems by adding or subtracting equations to eliminate a variable
• Solution of the system of linear equations
Any ordered pair in a system that makes all the equations true
• Graphing method
Graphing the system of equations and finding the point at which they intersect
• Substitution method
Replacing one variable with an equivalent expression containing the other variable
• Absolute value equation
A V-shaped graph that points upward of downward
• Translation
A shift of a graph horizontally, vertically, or both, which results in a graph of the same shape and size, but in a different position.
• Area of a circle
Πr²
• Area of a square
s², where s = length of a side
• Area of a triangle
½(base x height) [or (base x height)÷2]
• Area of a trapezoid
½(b₁ +b₂) x h [or (b₁ +b₂) x h÷2]
• Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
• Perimeter of a square
4s (where s = length of a side)
• Perimeter (circumference) of a circle
2 pi r
• Area of rectangle, square, parallelogram
A=bh
• Circumference of a circle
∏d OR 2∏r
• Area of a sector
x°/360 times (∏r²), where x is the degrees in the angle
• length of a sector
x°/360 times (2 pi r), where x is the degrees in the angle
• Circle
Is the set of points which are all the same distance (its radius) from a certian point( the center).
A segment connecting the center of a circle to any point on the circle
• Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
• Chord
The distance from one point on the circle to another point on the circle.
• Sector
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
• Arc
Part of a circle connecting two points on the circle.
• Central Angle
An ange whose vertex is the center of the circle
• Circumference Formula
C =∏d
• Area of Circles
A=∏r2