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:

Functions

Geometry

Number and Operations

Statistics and Probability

Algebra Formulas for the SBAC

Category	Formula	Symbols	Comment
General Algebra	\(x+a=b \Rightarrow x=b-a\) \(x-a=b \Rightarrow x=b+a\) \(x \cdot a=b \Rightarrow x=b \div a\) \(x \div a=b \Rightarrow x=b \cdot a\) \(x^a=b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}= b \Rightarrow x= b^a\) \(a^x=b \Rightarrow x=\frac{log\ b}{log\ a}\)	a, b = constants x = variable
General Algebra	\(x^a \cdot x^b = x^{a+b}\)	a, b, x = any real number
General Algebra	\(\frac{x^a}{x^b} = x^{a-b}\)	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	\(a_n = a \cdot r^{n-1}\)	\(a_n\) = \(n^{th}\) term of a geometric series \(a\) = first term of the geometric series \(r\) = common ratio	For a geometric series \(\displaystyle\sum<br>_{i=1}^{n} a_1 r^{i-1}\)
Series	\(S_n = \frac{a \cdot (r^n -1)}{r-1}\)	\(S_n\) = sum of \(n\) terms \(a\) = first term of a geometric series \(r\) = common ratio	For a geometric series \(\displaystyle\sum<br>_{i=1}^{n} a_1 r^{i-1}\)
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 = y-axis intercept	Slope-Intercept form Try to convert any given linear equation to this form.
Linear Equations	\(m = \frac{(y_2-y_1)}{(x_2-x_1)}\)	m = slope \(y_n\) = dependent variable (at point n) \(x_n\) = independent variable (at point n)	This is a rearranged version of the point-slope form.
Linear Equations	\(y-y_1 = m(x-x_1)\)	\((x_1, y_1)\) = point on the line y = dependent variable x = independent variable m = slope	Point-slope form
Quadratic Equations	\(x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)	a, b, c = constants c = y-axis intercept x = x-axis 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	\(a^2 - b^2 = (a+b)(a-b)\)	a, b = constants or variables	Difference of squares