# Math 2 example statements

If you’re at a Math 2 level, you’ll prob­a­bly be fa­mil­iar with most or all of these sen­tences and for­mu­las, or you would be able to un­der­stand what they meant on a sur­face level if you were to look them up.

The quadratic for­mula states that the roots of ev­ery quadratic ex­pres­sion $$ax^2 + bx + c$$ are equal to $$\displaystyle \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. The ex­pres­sion un­der the square root, $$b^2 - 4ac$$, is called the dis­crim­i­nant, and de­ter­mines how many roots there are in the equa­tion.

The imag­i­nary num­ber $$i$$ is defined as the pri­mary root of the quadratic equa­tion $$x^2 + 1 = 0$$.

To solve the sys­tem of lin­ear equa­tions $$\begin{matrix}ax + by = c \\ dx + ey = f\end{matrix}$$ for $$x$$ and $$y$$, the value of $$x$$ can be com­puted as $$\displaystyle \frac{bf - ce}{bd - ae}$$.

The power rule in calcu­lus states that $$\frac{d}{dx} x^n = nx^{n-1}$$.

All the solu­tions to the equa­tion $$m^n = n^m$$ where $$m < n$$ are of the form $$m = (1 + \frac 1x)^x$$ and $$n = (1 + \frac 1x)^{x+1}$$, where $$x$$ is any pos­i­tive real num­ber.

Parents:

• Math 2

Do you work with math on a fairly rou­tine ba­sis? Do you have lit­tle trou­ble grasp­ing ab­stract struc­tures and ideas?

• Mathematics

Math­e­mat­ics is the study of num­bers and other ideal ob­jects that can be de­scribed by ax­ioms.