ACT Math Formulas

Quadratic Formula

-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)

ac+ad+bc+bd

a(b+c)

ab+ac

sine ratio

opposite ÷ hypotenuse

cosine ratio

adjacent ÷ hypotenuse

tangent ratio

opposite ÷ adjacent

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).

Radius (Radii)

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