# 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
Equations
$$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$$ a, b, c = constants
c = y-axis intercept
x = x-axis intercept
$$ax^2+bx+c=0$$
$$(a \pm b)^2 =a^2 \pm 2 \cdot a \cdot b + b^2$$ a, b = constants or variables Square of sum or difference
$$a^2 - b^2 = (a+b)(a-b)$$ a, b = constants or variables Difference of