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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)
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
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Verified questions
PRECALCULUS
Find the nth term of the arithmetic sequence with given first term a and common difference d. What is the 10th term? a = -5, d = 4
ALGEBRA
You are ordering a meal and have $15 to spend. The restaurant charges 6% sales tax. You plan to leave a 15% tip. The equation$ $c = x + 0.06 x + 0.15x$$ gives the total cost c of your meal, where x is the cost before tax and tip. What is the maximum amount you can spend before tax and tip?
ALGEBRA2
All 385 tickets for a high-school play sold in 10 days. The ticket receipts totaled $1960. If the cost of a child's ticket was$4 and the cost of an adult's ticket was $6, how many adult tickets were sold?
ALGEBRA2
The owners of a restaurant determine that the number of minutes that a customer waits to be served is normally distributed with a mean of 6 minutes and a standard deviation of 2 minutes. What is the probability that a randomly selected customer will be served in less than 4 minutes?