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CLEP College Algebra study guide exam
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CLEP College Algebra study guide exam
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CLEP College Algebra study guide examadditive inverse to a - ANS -a
multiplicative inverse to a (when a does not =0) - ANS 1/a
raising expression to a negative exponent - ANS 1/b^n
multiplying expressions with powers - ANS x^n + x^m = X^m+n
raising expressions to powers - ANS (x^m)^n = x^mn
diving expressions with powers - ANS x^m/ x^n = x^m-n
fractional exponents - ANS x^1/2 = sq rt. X
x^m/n = n rt. of x^m
multiplying radicals - ANS (sq a)(sq b) = sq ab
factoring diff. of two squares - ANS x^2-y^2 = (x-y)(x+y)
factoring perfect squares - ANS x^2+2xy+y^2=(x+y)^2
x^2-2xy+y^2=(x-y)^2
factoring: sum and difference of 2 cubes - ANS x^3+y^3=(x+y)(x^2-xy+y^2)
x^3-y^3=(x-y)(x^2+xy+y^2)
slope of line (given two points) - ANS m = rise over run y2-y1/x2-x1
equation of line slope-intercept form (given m and y-intercept) - ANS y=mx+b m is slope
and b is y intercept
point slope form (given two points) - ANS (y-y1)=m(x-x1)
intercept form (given x and y intercept) - ANS x/a + y/b =1
slope of perpendicular lines - ANS inverses on each other ex. m=b inverse slope is 1/2
discriminant used to determine the number of real solutions - ANS b^2-4ac = > 0 is 2 real
solutions
=0 is 1 real solution
< 0 is 0 real or 2 imaginary solutions
, logarithm addition - ANS log a + log b = log ab
logarithm subtraction - ANS log a - log b = log a/b
logarithm power rule - ANS log a^b = b log a
arithmetic sequence - ANS an= a1 + (n-1)d
sum of arithmetic sequences - ANS Sn= n/2[2a1+(n-1)d] or
Sn= n/2 (a1+a2)
geometric sequence - ANS an=a1r^n-1 where a1 is the first term, r is the common ratio and
n is number of terms
sum of geometric sequences - ANS Sn= [a1(1-r^n)]/ 1-r
sum of infinite geometric sequences - ANS Sn= a1/1-r
a1 is the first term, r is the common ratio, and n is the number of terms
factorial - ANS n! = n(n-1)(n-2)... 3(2)(1)
combination of n choose r - ANS nCr= n!/r!(n-r)!
determinant of 2x2 matrix - ANS a b
c d = ad-bc
find the additive inverse of (expression) - ANS solve the equation for y: y + (expression) = 0
it is the negative of the expression
raise expression to a negative number - ANS 1/ (expression)^n
raise to a fractional power - ANS expression^1/n = n rt (expression)
to determine whether a graph is a function - ANS vertical line test
determine whether a graph matches that of an algebraic function - ANS plug x-values into
the function to find the value of y, and determine if those points are on the graph
given y=f(x) find the domain - ANS domain will be infinity, infinity with 3 exceptions
1. any value of x that makes the denominator 0
2. any value of x that makes an even root of a negative number
3. any value of x that makes a term into the log of zero or the log of a negative number
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