# Important Algebra Formulas to Know for the ISEE Math Tests

Is it easy to remember everything you’ve learned in school? Of course not! The two math tests on the ISEE Quantitative Reasoning and Mathematics Achievement will put your math knowledge to the test. Don’t worry if you don’t recall everything. Union Test Prep has you covered. We have formula charts for all four math areas assessed by the ISEE Math tests.

The Algebra chart is below and you can find the others at these links:

For more information, feel free to check out our FREE study guides, practice questions, and flashcards.

## Algebra Formulas for the ISEE Math Tests

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, b, x = any real number
General
Algebra
$$x^1 = x$$ x = any real number
General
Algebra
$$x^0 = 1$$ x = any real number
General
Algebra
$$x^{-a} = \frac {1}{x^a}$$ 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
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 linear
equation to this form.
Linear
Equations
$$m = \frac{(y_2 - y_1)}{(x_2 - x_1)}$$ m = slope
$$y_n$$ = independent variable (point n)
$$x_n$$ = dependent variable (point n)
This is a rearrangement of the
point-slope form.
Linear
Equations
$$y-y_1 = m(x-x_1)$$ $$(x_1,y_1)$$ = point on the line
m = slope
y = independent variable
x = dependent variable
Point-slope form
Equations
$$f(x) = ax^2 + bx + c$$ a, b, c = constants
c = y axis intercept
x = variable
Standard form
Equations
$$f(x) = a(x-h)^2 + k$$ a = constant
h = constant (horizontal shift)
k = constant (vertical shift)
x = variable
Vertex form
Equations
$$x= \frac{-b \pm \sqrt{b^2-4 \cdot a \cdot c}}{2 \cdot a}$$ a, b, c = constants
c = y axis intercept
x = variable (x intercept)
Equations
$$x= \frac{-b}{2a}$$ a, b = constants
x = axis of symmetry
Axis of symmetry
$$(a \pm b)^2 = a^2 \pm 2 \cdot a \cdot b + b^2$$ a, b = constants or variables Square of a sum or difference
$$a^2 - b^2 = (a-b) \cdot (a+b)$$ a, b = constants or variables Difference of two squares
$$a^3 - b^3 = (a-b) \cdot (a^2+ab+b^2)$$ a, b = constants or variables Difference of two cubes
$$a^3 + b^3 = (a+b) \cdot (a^2-ab+b^2)$$ a, b = constants or variables Sum of two cubes