Formula Chart for Algebra on the SBAC Test
Have you ever painted by number? It’s probably the easiest way to paint, and you usually get great results from it. Solving Algebra problems on the SBAC Test is similar. If you are careful and follow the rules, you’ll achieve your goal! Now, what rules are we talking about?
The rules for Algebra are expressed in the form of equations, and the most important ones are shown in the following formula chart. Even though you won’t be able to use the chart during the actual test, getting to know the rules will prepare you, and we suggest you use them to solve our FREE practice problems at Union Test Prep.
Also check out our formula charts for the other four areas of math on the SBAC test:
Algebra Formulas for the SBAC
Category  Formula  Symbols  Comment 

General 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 

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

General Algebra 
\(\frac{x^a}{x^b} = x^{ab}\)  a, b, x = any real number  
General Algebra 
\((x^a)^b=x^{a \cdot b}\)  a, b, x = any real number  
General Algebra 
\((x \cdot y)^a=x^a \cdot y^a\)  a, x, y = any real number  
General Algebra 
\(x^1 = x\)  x = any real number  
General Algebra 
\(x^0 = 1\)  x = any real number  
General Algebra 
\(x^{a} = \dfrac {1}{x^a}\)  a, x = any real number  
General Algebra 
\(x^{\frac {a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a\)  a, b, x = any real number  
General Algebra 
\(\frac{x}{\sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}} = \frac{x \sqrt{y}}{y}\)  x, y = any real number 

Series  \(a_n = a \cdot r^{n1}\)  \(a_n\) = \(n^{th}\) term of a geometric series \(a\) = first term of the geometric series \(r\) = common ratio 
For a geometric series \(\displaystyle\sum<br>_{i=1}^{n} a_1 r^{i1}\) 
Series  \(S_n = \frac{a \cdot (r^n 1)}{r1}\)  \(S_n\) = sum of \(n\) terms \(a\) = first term of a geometric series \(r\) = common ratio 
For a geometric series \(\displaystyle\sum<br>_{i=1}^{n} a_1 r^{i1}\) 
Computing Interest 
\(SI = P \cdot IR \cdot t\)  SI = simple interest P = Principal (amount borrowed) IR = Interest Rate t = time (same units as IR) 

Computing Interest 
\(A_{SI} = P + SI = P \cdot (1 + IR \cdot t)\)  \(A_{SI}\) = Future value to be paid (for SI) P = Principal (amount borrowed) SI = simple interest IR = Interest Rate t = time (same units as IR) 

Computing Interest 
\(A_{CI} = P \cdot (1 + \frac{IR}{n})^{n \cdot t}\)  \(A_{CI}\) = Future value to be paid (for CI) P = Principal (amount borrowed) IR = Interest Rate n = number of times interest is compounded per unit t t = time (same units as IR) 

Linear Equations 
\(A \cdot x + B \cdot y = C\)  A, B, C = any real number y = dependent variable x = independent variable 
Standard form 
Linear Equations 
\(y = m \cdot x + b\)  y = dependent variable m = slope x independent variable b = yaxis intercept 
SlopeIntercept form Try to convert any given linear equation to this form. 
Linear Equations 
\(m = \frac{(y_2y_1)}{(x_2x_1)}\)  m = slope \(y_n\) = dependent variable (at point n) \(x_n\) = independent variable (at point n) 
This is a rearranged version of the pointslope form. 
Linear Equations 
\(yy_1 = m(xx_1)\)  \((x_1, y_1)\) = point on the line y = dependent variable x = independent variable m = slope 
Pointslope form 
Quadratic Equations 
\(x = \dfrac{b \pm \sqrt{b^24ac}}{2a}\)  a, b, c = constants c = yaxis intercept x = xaxis intercept 
Quadratic Formula for an equation in the form \(ax^2+bx+c=0\) 
Quadratic Equations 
\((a \pm b)^2 =a^2 \pm 2 \cdot a \cdot b + b^2\)  a, b = constants or variables  Square of sum or difference 
Quadratic Equations 
\(a^2  b^2 = (a+b)(ab)\)  a, b = constants or variables  Difference of squares 
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