Absolute values
• Suppose a > 0, then
|x| = a if and only if x = ±a,
|x| < a if and only if −a < x < a,
|x| > a if and only if x > a or x < −a.
Laws of exponents
Natural logarithm
• ln(x) = y if and only if ey = x,
• ln(xy) = ln(x) + ln(y),
• ln(x/y) = ln(x) + ln(y),
• ln(x2) = a ln(x)
Trigonometry
Equations of lines
• The slope of a nonvertical line that passes through the points (x1, y1) and
(x2, y2)
is
.
The slope of a vertical is not defined.
• Point- slope form of the equation of a line : An equation of the line passing
through the point (x1, y1) and having slope m is
y − y1 = m(x − x1).
• Slope - intercept form of the equation of a line: An equation of the line with
slope m and y - intercept b is
y = mx + b.
