College Algebra Midterm Exam
questions with solved answers
distance formula - answersd=√(x₂-x₁)² + (y₂-y₁)²
midpoint formula - answersm= (x₁+x₂)/2 , (y₁+y₂)/2
what is the first step when simplifying rational expressions/polynomials? -
answersFACTOR FIRST
once you simplify a rational expression, what is the last step before finishing? -
answersmake sure your answer is completely factored out
5 questions to ask when factoring - answers1. search and rescue (look for GCF, then
factor out)
2. difference of squares? x²-a²= (x+a)(x-a)
3. difference of cubes? x³-a³= (x-a)(x²+ax+a²)
4. sum of cubes? x³+a³= (x+a)(x²-ax+a²)
5. double bubble: factor by grouping ( )( )
√x²= ? - answers|x|
3 steps of completing the square - answers1. factor out the coefficient of the quadratic
term
2. multiply the coefficient of the linear term by ½
3. square the result to form the constant
standard form equation of a circle (center at h,k) - answers(x-h)² + (y-k)²= r²
standard form equation of a circle (center at 0,0) - answersx²+y²= r²
general form of a circle - answersx²+y²+ax+by+c= 0
how to graph a circle using the general equation - answers1. use completing the square
method to determine the center and radius
2. find two of each x-int and y-int by replacing each variable with 0
3. leave each coordinate for x and y intercepts in radical form
4. graph
slope formula - answersm= (y₂-y₁)/ (x₂-x₁)
point-slope form - answersy-y₁= m(x-x₁)
questions with solved answers
distance formula - answersd=√(x₂-x₁)² + (y₂-y₁)²
midpoint formula - answersm= (x₁+x₂)/2 , (y₁+y₂)/2
what is the first step when simplifying rational expressions/polynomials? -
answersFACTOR FIRST
once you simplify a rational expression, what is the last step before finishing? -
answersmake sure your answer is completely factored out
5 questions to ask when factoring - answers1. search and rescue (look for GCF, then
factor out)
2. difference of squares? x²-a²= (x+a)(x-a)
3. difference of cubes? x³-a³= (x-a)(x²+ax+a²)
4. sum of cubes? x³+a³= (x+a)(x²-ax+a²)
5. double bubble: factor by grouping ( )( )
√x²= ? - answers|x|
3 steps of completing the square - answers1. factor out the coefficient of the quadratic
term
2. multiply the coefficient of the linear term by ½
3. square the result to form the constant
standard form equation of a circle (center at h,k) - answers(x-h)² + (y-k)²= r²
standard form equation of a circle (center at 0,0) - answersx²+y²= r²
general form of a circle - answersx²+y²+ax+by+c= 0
how to graph a circle using the general equation - answers1. use completing the square
method to determine the center and radius
2. find two of each x-int and y-int by replacing each variable with 0
3. leave each coordinate for x and y intercepts in radical form
4. graph
slope formula - answersm= (y₂-y₁)/ (x₂-x₁)
point-slope form - answersy-y₁= m(x-x₁)
