Algebra Review
| Linear
Equations Standard Form of an Equation -- Ax + By = C Slope-Intercept Form of an Equation -- y = mx + b Calculating Slope -- m = y - y1 / x2 - x1 Point Slope Formula -- y - y1 = m (x -x1) Distance Formula -- D = ¯(x2 - x1)2 + (y2 - y1)2 Midpoint Formula -- ( x1 + x2 /2, y1 + y2 /2 ) |
Factoring Difference of Two Squares a2 - b2 = (a + b)( a - b) Perfect- Square Trinomials a2 + 2ab + b2 = (a + b)2 a2 - 2ab + b2 = (a - b)2 Sum of Two Cubes a3 + b3 = (a + b)(a2 - ab + b2) Difference of Two Cubes a3 - b3 = (a - b)(a2 + ab + b2) |
||||||||
| Powers Multiplication ---(xa)(xb) = xa+b Division ---xa ÷ xb = xa-b Zero and Negative ---x0 = 1 ---x-a = 1/ xa Others ---(xa)b = xab ---(xy)a = xa ya ---(x/y)a = xa / ya Fractions ---x1/a = a¯ x |
Conic Sections Circles ---Standard Form (x - h)2 + (y - k)2 = r2 (h,k) is the center ---General Form x2 + y2 + Dx + Ey + F = 0 D = -2h E = -2k F = h2 + k2 - r2 Parabolas Standard Form x2 = 4py focus (0, p) and directrix y = -p or y2 = 4px focus (p,0) and directrix x = -p Ellipses Standard Form x2 / a2 + y2 / b2 = 1 foci (-c,0) and (c,0) with a2 = b2 + c2 Hyperbola Standard Form x2 / a2 - y2 / b2 = 1 foci (-c,0) and (c,0) with c2 = a2 + b2 |
||||||||
|
Logarithms |
Quadratic Formula x = -b ± ¯b2 - 4ac 2a |
||||||||