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
a>1 and decay if 0>a>1
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]
(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
a>1 and decay if 0>a>1
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]
