Math Things to Know for the SAT

x¹

x

x⁰

1

x^m * xⁿ

x^m+n This law states that when multiplying two exponential expressions with the same base, you can add the exponents.

x^m / xⁿ

x^m-n This law states that when dividing two exponential expressions with the same base, you can subtract the exponents.

(x^m)ⁿ

x^mn This law states that when raising an exponential expression to another exponent, you can multiply the exponents.

(xy)^m

x^my^m This law states that when raising a product of two bases to an exponent, you can distribute the exponent to both bases.

(x / y)^m

(x^m / y^m) This law states that when raising a fraction to an exponent, each part of the fraction is raised to that exponent.

x^-m

1 / m^x This law states that a negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent.

dividing fractions

keep change flip

2r

Diameter of a Circle. r is the radius

(Theta / 360) x 2(3.14)( r )

Formula for the arc length of a circle, where ( \theta ) is the angle in degrees and ( r ) is the radius.

(Theta / 360) x 3.14(r²)

Area of a sector of a circle, where ( \theta ) is the angle in degrees and ( r ) is the radius.

30-60-90 Triangle

Shorter leg is ½ the length of the hypotenuse. Longer leg is 3^1/2 (sqrt3) times longer than the shorter leg. 1:2:3^1/2. Angle opposite to 3^1/2 is 60 degrees.

(x - h)² + (y - k)² = r²

Equation of a circle in standard form, where (h, k) is the center and r is the radius.

x² + ax + b →(x + a/2)² + b - (a/2)²

Formula for Completing the Square.

pi radians

180 degrees

ax² + bx + c

Standard form of a quadratic function

y = a(x - p)(x - q)

Intercept form of a quadratic function where p and q are the x-coordinates of the roots.

-(b/a) and c/a

Sum of the roots and product of the roots. Based on the Standard form of quadratic functions.

y = a(x - h)² + k

Vertex Form of a quadratic function. (h,k) is the vertex.

b² - 4ac

Discriminant. Part of the quadratic formula.

b² - 4ac > 0. Discriminant is positive.

Two real solutions. 2 x-intercepts

b² - 4ac = 0

One real solution. One x-intercept.

b² - 4ac < 0. Discriminant is negative.

No real solution. No x-intercept.

y = (1 + a)x and y = (1 - a)x

Percent Increase where x is what you’re increasing or decreasing and a is the percentage you are increasing or decreasing it by in decimals or fractions.

((new value - original value)/ original value) x 100

Percent Change

Compound Interest

A = final amount

P = Initial Principal Balance

r = Interest Rate

n = Number of times interest is applied per time period

t = Number of time periods

y = ab^t/k

Exponential Growth and Decay

y = value after t units of time.

a = Initial Value aka coefficient.

b = growth factor greater than 1 for growth and less than 1 for decay. Aka base

k = Time required for y to change by a factor of b. Must be in the same unit of t.