CLEP College Algebra

(a+bi)(a-bi) - i^2 =1 a+bi/ci - multiply by i/i and simplify additive inverse to a - -a arithmetic sequence - an= a1 + (n-1)d combination of n choose r - nCr= n!/r!(n-r)! determinant of 2x2 matrix - a b c d = ad-bc determine whether a function is a growth or decay - when the equation is in the form of y=a^x the graph is growth if a1 and decay if 0a1 determine whether a graph is odd, even, or neither - even- if the graph is symmetrical with respect to y-axis odd- if the graph is symmetrical with respect to the origin (I and III and II and IV are mirror images) determine whether a graph matches that of an algebraic function - plug x-values into the function to find the value of y, and determine if those points are on the graph determine whether a sequence is arithmetic, geometric, or neither - if there is a common difference, it is arithmetic. if there is a common ratio, it is geometric discriminant used to determine the number of real solutions - b^2-4ac = 0 is 2 real solutions =0 is 1 real solution 0 is 0 real or 2 imaginary solutions diving expressions with powers - x^m/ x^n = x^m-n equation of line slope-intercept form (given m and y-intercept) - y=mx+b m is slope and b is y intercept factorial - n! = n(n-1)(n-2)... 3(2)(1) factoring diff. of two squares - x^2-y^2 = (x-y)(x+y) factoring perfect squares - x^2+2xy+y^2=(x+y)^2 x^2-2xy+y^2=(x-y)^2 factoring: sum and difference of 2 cubes - x^3+y^3=(x+y)(x^2-xy+y^2) x^3-y^3=(x-y)(x^2+xy+y^2) find ln=y - y =e^x, most answers are left in terms of e find the additive inverse of (expression) - solve the equation for y: y + (expression) = 0 it is the negative of the expression find the inverse f^-1 of y = f(x) - interchange x and y and solve for y find the sum of an infinite geometric series - if |r|1, Sn =a1/1-r otherwise the sum is infinite find the sum of the first n terms of a geometric series - Sn=[a1(1-r^n)]/1-r find the sum of the first n terms of an arithmetic series - Sn= n/2 [2a1+(n-1)d]