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:
But, for the Passport to Advanced Math questions, here are the necessary formulas:
Category  Formula  Symbols  Comment 

Passport to Advanced Math 
\(x+a=b \Rightarrow x=ba\) \(xa=b \Rightarrow x=b+a\) \(x \cdot a=b \Rightarrow x=b \div a\) \(x \div a=b \Rightarrow x=b \cdot a\) \(x^a=b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}= b \Rightarrow x= b^a\) \(a^x=b \Rightarrow x=\frac{log\ b}{log\ a}\) 
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 
\(\dfrac{x^a}{x^b}=x^{ab}\)  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 
\(a^2  b^2 = (a+b)(ab)\)  a, b = constants or variables  Difference of squares 
Passport to Advanced Math 
\(a^3b^3 = (ab)(a^2 + ab + b^2)\)  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 
\(x = \dfrac{b \pm \sqrt{b^24ac}}{2a}\)  a, b, c = constants c = yaxis intercept x = xaxis intercept 
Quadratic formula 
Passport to Advanced Math 
\(x = \dfrac{b}{2a}\)  a, b = constants x = axis of symmetry 
Axis of symmetry 
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