Formulas for Math on the CSET®: Number Sense, Algebra, and Statistics
The time has come. You have to take the CSET® Test, but you don’t remember a lot of math, or maybe you want to have a sense of what lies ahead. There are certain areas we sometimes overlook or forget about from past education. For the CSET® Test, it’s very important to have a broad and complete understanding of the different concepts in math. That’s why we’ve prepared the following chart with the essential formulas for Math on the CSET®. Stop wondering if you remember every concept, instead, print this chart and start solving the problems we have for you at Union Test Prep:
Free Math Practice for the CSET® Multiple Subjects Test
You’ll also want access to our other formula chart for the CSET® Multiple Subjects Test math section:
Formula Chart for Geometry and Measurement Problems
Formulas for Number Sense, Algebra, and Statistics
Category  Formula  Symbols  Comment 

Number Sense 
\(a+b=b+a\) \(a \cdot b = b \cdot a\) 
a, b = any constant or variable  Commutative Property 
Number Sense 
\(a+(b+c)=(a+b)+c\) \(a \cdot (b \cdot c)=(a \cdot b) \cdot c\) 
a, b, c = any constant or variable  Associative Property 
Number Sense 
\(a \cdot (b+c)=a \cdot b + a \cdot c\)  a, b, c = any constant or variable  Distributive Property 
Number Sense 
\(a+0=a\)  a = any constant or variable  Identity Property of Addition 
Number Sense 
\(a \cdot 1 = a\)  a = any constant or variable  Identity Property of Multiplication 
Number Sense 
\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}\)  a, b, c, d = any real number  Remember to simplify the fraction if possible. 
Number Sense 
\(\dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{(a \cdot c)}{(b \cdot d)}\)  a, b, c, d = any real number  Remember to simplify the fraction if possible. 
Number Sense 
\(\dfrac{a}{b} \div \dfrac{c}{d}=\dfrac{(a \cdot d)}{(b \cdot c)}\)  a, b, c, d = any real number  Remember to simplify the fraction if possible. 
Number Sense 
\(a\dfrac{b}{c}=\dfrac{(a \cdot c)+b}{c}\)  a, b, c = any real number  Remember to simplify the fraction if possible. 
Algebra  \(x+a=b \Rightarrow x=ba\) \(xa=b \Rightarrow x=b+a\) \(x \cdot a=b \Rightarrow x=b \div a\) \(x \div a=b \Rightarrow x=b \cdot a\) \(x^a=b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}= b \Rightarrow x= b^a\) \(a^x=b \Rightarrow x=\frac{log\ b}{log\ a}\) 
a, b = constants x = variable 

Algebra  \(x^a \cdot x^b=x^{a+b}\)  a, b, x = any real number 

Algebra  \(\dfrac{x^a}{x^b}=x^{ab}\)  a, b, x = any real number  
Algebra  \((x^a)^b = x^{a \cdot b}\)  a, b, x = any real number  
Algebra  \((x \cdot y)^a = x^a \cdot y^a\)  a, x, y = any real number  
Algebra  \(x^1=x\)  x = any real number  
Algebra  \(x^0=1\)  x = any real number  
Algebra  \(x^{a}= \dfrac{1}{x^a}\)  a, x = any real number  
Algebra  \(x^{\frac {a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a\)  a, b, x = any real number  
Algebra  \(\dfrac{x}{\sqrt{y}} \cdot \dfrac {\sqrt{y}}{\sqrt{y}} = \dfrac{x \sqrt{y}}{y}\)  x, y = any real number  
Algebra  \(y=m \cdot x + b\)  y = dependent variable m = slope x = independent variable b = y axis intercept 
SlopeIntercept Form. Try to convert any given linear equation to this form. 
Quadratic Equations 
\(x= \dfrac{b \pm \sqrt{b^24 \cdot a \cdot c}}{2 \cdot a}\)  a, b, c = constants c = y axis intercept x = variable 
Quadratic Formula for equation in form \(ax^2 + bx + c = 0\) 
Statistics  \(Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF\)  Du = Desired Unit Su = Starting Unit CF = Conversion Factor 
Multiple steps may be needed. 
Statistics  \(a \cdot b\% =a \cdot \dfrac{b}{100}\)  a = any real number b% = any percent 
Remember to simplify if possible 
Statistics  \(\% = \dfrac{\vert ba \vert }{b} \cdot 100= \dfrac{c}{b} \cdot 100\)  % = % increase or decrease a = new value b = original value c = amount of change 

Statistics  \(\overline{x}= \dfrac{\Sigma x_i}{n}\)  \(\overline{x}\) = mean \(x_i\) = value of each measurement n = number of measurements 

Statistics  \(Md=(\dfrac{n+1}{2})^{th} term\)  Md = median n = number of measurements (odd) 

Statistics  \(Md=\dfrac{(\frac{n}{2})^{th} term + (\frac{n+1}{2})^{th} term }{2}\)  Md = median n = number of measurements (even) 

Statistics  \(s=\sqrt{\Sigma(x_i\overline{x})^2/(n1)}\)  s = standard deviation \(\overline{x}\) = mean \(x_i\) = value of each measurement n = number of measurements 

Statistics  \(V = s^2\)  v = Variance s = standard deviation 

Statistics  \(CV=RSD=100 \cdot \dfrac{s}{\overline{x}}\)  CV = Coefficient of variation RSD = Relative standard deviation s = standard deviation 

Statistics  \(p= \dfrac{d}{t}\)  p = probability of an event d = number of ways the desired event can occur t = total number of events 
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