Formula Chart for the Passport to Advanced Math Questions on the SAT® Test

Just as there are requirements to get a passport to travel, you’ll need to fulfill a series of requirements if you want to ace the 16 Passport to Advanced Math Questions on the SAT® Test. The most important requirement is the ability to analyze, rewrite, and manipulate mathematical expressions, but that requires practice.

That’s why we have the tools you need at Union Test Prep! You can check our study guides and try your hand at our Passport to Advanced Math practice test. And you can check the following chart, which has the essential formulas you’ll need to manipulate and analyze and get your passport!

We also have formula charts for the other three areas of math covered on the SAT® Math Test:

1. Heart of Algebra

2. Problem-Solving and Data Analysis

3. Additional Topics

But, for the Passport to Advanced Math questions, here are the necessary formulas:

Category	Formula	Symbols	Comment
Passport to Advanced Math	\(x+a=b \Rightarrow x=b-a\) \(x-a=b \Rightarrow x=b+a\) \(x \cdot a=b \Rightarrow x=b \div a\) \(x \div a=b \Rightarrow x=b \cdot a\) \(x^a=b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}= b \Rightarrow x= b^a\) \(a^x=b \Rightarrow x=\frac{log\ b}{log\ a}\)	a, b = constants x = variable
Passport to Advanced Math	\(\dfrac{a}{b} + \dfrac{c}{d}= \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Passport to Advanced Math	\(\dfrac{a}{b} \cdot \dfrac{c}{d}= \dfrac{(a \cdot c)}{(b \cdot d)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Passport to Advanced Math	\(\dfrac{a}{b} \div \dfrac{c}{d}= \dfrac{(a \cdot d)}{(b \cdot c)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Passport to Advanced Math	\(a\dfrac{b}{c} = \dfrac{(a \cdot c)+b}{c}\)	a, b, c = any real number	Remember to simplify the fraction if possible.
Passport to Advanced Math	\(x^a \cdot x^b = x^{a+b}\)	a, b, x = any real number
Passport to Advanced Math	\(\dfrac{x^a}{x^b}=x^{a-b}\)	a, b, x = any real number
Passport to Advanced Math	\((x^a)^b=x^{a \cdot b}\)	a, x = any real number
Passport to Advanced Math	\((x \cdot y)^a=x^a \cdot y^a\)	a, b, x, y = any real number
Passport to Advanced Math	\(x^1 = x\)	x = any real number
Passport to Advanced Math	\(x^0 = 1\)	x = any real number
Passport to Advanced Math	\(x^{-a} = \dfrac {1}{x^a}\)	a, x = any real number
Passport to Advanced Math	\(x^{\frac {a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a\)	a, b, x = any real number
Passport to Advanced Math	\(a^x =b \Rightarrow log_ab = x\)	a, b, x = any real number
Passport to Advanced Math	\(ln(x) = log_ex\)	x = any real number e = euler’s number
Passport to Advanced Math	\(a^{log_ax} = x\)	a, x = any real number
Passport to Advanced Math	\(log(a \cdot b) = log(a) + log(b)\)	a, b, = any real number
Passport to Advanced Math	\(log(a \div b) = log(a) - log(b)\)	a, b, = any real number
Passport to Advanced Math	\(log(a)^b = b \cdot log(a)\)	a, b, = any real number
Passport to Advanced Math	\(log_ax= log_bx \cdot log_ab\)	a, b, x = any real number
Passport to Advanced Math	\(log_ab = \dfrac{log_xb}{log_xa}\)	a, b, x = any real number
Passport to Advanced Math	\(log_aa=1\)	a = any real number
Passport to Advanced Math	\(log(1) = 0\)
Passport to Advanced Math	\((a \pm b)^2 =a^2 \pm 2 \cdot a \cdot b + b^2\)	a, b = constants or variables	Square of sum or difference
Passport to Advanced Math	\(a^2 - b^2 = (a+b)(a-b)\)	a, b = constants or variables	Difference of squares
Passport to Advanced Math	\(a^3-b^3 = (a-b)(a^2 + ab + b^2)\)	a, b = constants or variables	Difference of cubes
Passport to Advanced Math	\(a^3+b^3 = (a+b)(a^2 - ab + b^2)\)	a, b = constants or variables	Sum of cubes
Passport to Advanced Math	\(x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)	a, b, c = constants c = y-axis intercept x = x-axis intercept	Quadratic formula
Passport to Advanced Math	\(x = \dfrac{-b}{2a}\)	a, b = constants x = axis of symmetry	Axis of symmetry