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.


  • Math 2

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