CLEP COLLEGE COMPOSITION 2026
STUDY GUIDE PRACTICE
QUESTIONS DETAILED SOLUTIONS
◉ multiplicative inverse to a (when a does not =0). Answer: 1/a
◉ raising expression to a negative exponent. Answer: 1/b^n
◉ multiplying expressions with powers. Answer: x^n + x^m = X^m+n
◉ raising expressions to powers. Answer: (x^m)^n = x^mn
◉ diving expressions with powers. Answer: x^m/ x^n = x^m-n
◉ fractional exponents. Answer: x^1/2 = sq rt. X
x^m/n = n rt. of x^m
◉ multiplying radicals. Answer: (sq a)(sq b) = sq ab
◉ factoring diff. of two squares. Answer: x^2-y^2 = (x-y)(x+y)
◉ factoring perfect squares. Answer: x^2+2xy+y^2=(x+y)^2
, x^2-2xy+y^2=(x-y)^2
◉ factoring: sum and difference of 2 cubes. Answer:
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). Answer: m = rise over run y2-y1/x2-
x1
◉ equation of line slope-intercept form (given m and y-intercept).
Answer: y=mx+b m is slope and b is y intercept
◉ point slope form (given two points). Answer: (y-y1)=m(x-x1)
◉ intercept form (given x and y intercept). Answer: x/a + y/b =1
◉ slope of perpendicular lines. Answer: inverses on each other ex. m=b
inverse slope is 1/2
◉ discriminant used to determine the number of real solutions. Answer:
b^2-4ac = > 0 is 2 real solutions
=0 is 1 real solution
< 0 is 0 real or 2 imaginary solutions
STUDY GUIDE PRACTICE
QUESTIONS DETAILED SOLUTIONS
◉ multiplicative inverse to a (when a does not =0). Answer: 1/a
◉ raising expression to a negative exponent. Answer: 1/b^n
◉ multiplying expressions with powers. Answer: x^n + x^m = X^m+n
◉ raising expressions to powers. Answer: (x^m)^n = x^mn
◉ diving expressions with powers. Answer: x^m/ x^n = x^m-n
◉ fractional exponents. Answer: x^1/2 = sq rt. X
x^m/n = n rt. of x^m
◉ multiplying radicals. Answer: (sq a)(sq b) = sq ab
◉ factoring diff. of two squares. Answer: x^2-y^2 = (x-y)(x+y)
◉ factoring perfect squares. Answer: x^2+2xy+y^2=(x+y)^2
, x^2-2xy+y^2=(x-y)^2
◉ factoring: sum and difference of 2 cubes. Answer:
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). Answer: m = rise over run y2-y1/x2-
x1
◉ equation of line slope-intercept form (given m and y-intercept).
Answer: y=mx+b m is slope and b is y intercept
◉ point slope form (given two points). Answer: (y-y1)=m(x-x1)
◉ intercept form (given x and y intercept). Answer: x/a + y/b =1
◉ slope of perpendicular lines. Answer: inverses on each other ex. m=b
inverse slope is 1/2
◉ discriminant used to determine the number of real solutions. Answer:
b^2-4ac = > 0 is 2 real solutions
=0 is 1 real solution
< 0 is 0 real or 2 imaginary solutions
