Math 113 Final Exam Review
(2025/2026) questions n answers
When simplifying radical operation expressions with different radicands, once you simplify the
expression what do you do with the left over coefficient? - correct answer ✔✔Multiply the
original coefficient with the new term that is outside the radical.
Anything to the zero power equals? - correct answer ✔✔1 (you don't need to include 1 back
into the equation when simplifying)
The opposite of multiplication is? - correct answer ✔✔Addition
The opposite of division is? - correct answer ✔✔Subtracting
A negative sign outside of the radical means the answer will be? - correct answer ✔✔Negative
A negative under a radical sign means the answer will be? - correct answer ✔✔Impossible
How to solve radical equations? - correct answer ✔✔1. Isolate the radical
2. Square both sides of the equation
3. Solve the resulting equation
(steps may lead to extraneous solutions, so always check your answers!)
How to solve rational equations? - correct answer ✔✔1. Factor the denominators
2. Identify the restrictions
3. Multiply both sides of the equations by the LCD
,4. Solve as usual
5. Check answers against the set of restrictions
When determining the LCD of rational equations what should you do? - correct answer ✔✔Use
one of the factors found in all the denominators
What are the three methods to solve quadratic equations? - correct answer ✔✔1. Factoring
2. Using the quadratic equation
3. Completing the square
What is the quadratic equation form? - correct answer ✔✔Ax^2 + Bx + C = 0
How to factor? - correct answer ✔✔1. Put all terms on one side of the equal sign, leaving zero
on the other side
2. Factor
3. Set each factor equal to zero
4. Solve each of these equations
What is the quadratic formula? - correct answer ✔✔x = -b ± √( b^2 - 4ac ) / ( 2a )
How to complete the square? - correct answer ✔✔1. Put the equation into Ax^2 + Bx + C = 0
form
2. Make sure that A=1, if not multiply thru the equation by 1/a
3. using the values of b from the new equation, add (b/2)^2 to both sides of equation to form
perfect square on left side of the equation
4. Find the square root of both sides of equation
5. Solve the resulting equation
, > - correct answer ✔✔Greater than
< - correct answer ✔✔Less than
≥ - correct answer ✔✔Greater than or equal to
≤ - correct answer ✔✔Less than or equal to
The use of brackets in inequalities mean? - correct answer ✔✔The endpoint
The use of parentheses in inequalities means? - correct answer ✔✔Excluded
What are compound inequalities? - correct answer ✔✔Inequalities that are separated with
AND/OR
"AND"/"OR" in equalities ALWAYS ONLY use? - correct answer ✔✔Parentheses
"AND" inequalities are? - correct answer ✔✔The intersection of both inequalities
"OR" inequalities? - correct answer ✔✔Can satisfy one or both inequalities
The notation f(x)? - correct answer ✔✔Defines a function named f. This reads as "y is a function
of x".
Parentheses in function notation mean? - correct answer ✔✔The endpoint is NOT included
(2025/2026) questions n answers
When simplifying radical operation expressions with different radicands, once you simplify the
expression what do you do with the left over coefficient? - correct answer ✔✔Multiply the
original coefficient with the new term that is outside the radical.
Anything to the zero power equals? - correct answer ✔✔1 (you don't need to include 1 back
into the equation when simplifying)
The opposite of multiplication is? - correct answer ✔✔Addition
The opposite of division is? - correct answer ✔✔Subtracting
A negative sign outside of the radical means the answer will be? - correct answer ✔✔Negative
A negative under a radical sign means the answer will be? - correct answer ✔✔Impossible
How to solve radical equations? - correct answer ✔✔1. Isolate the radical
2. Square both sides of the equation
3. Solve the resulting equation
(steps may lead to extraneous solutions, so always check your answers!)
How to solve rational equations? - correct answer ✔✔1. Factor the denominators
2. Identify the restrictions
3. Multiply both sides of the equations by the LCD
,4. Solve as usual
5. Check answers against the set of restrictions
When determining the LCD of rational equations what should you do? - correct answer ✔✔Use
one of the factors found in all the denominators
What are the three methods to solve quadratic equations? - correct answer ✔✔1. Factoring
2. Using the quadratic equation
3. Completing the square
What is the quadratic equation form? - correct answer ✔✔Ax^2 + Bx + C = 0
How to factor? - correct answer ✔✔1. Put all terms on one side of the equal sign, leaving zero
on the other side
2. Factor
3. Set each factor equal to zero
4. Solve each of these equations
What is the quadratic formula? - correct answer ✔✔x = -b ± √( b^2 - 4ac ) / ( 2a )
How to complete the square? - correct answer ✔✔1. Put the equation into Ax^2 + Bx + C = 0
form
2. Make sure that A=1, if not multiply thru the equation by 1/a
3. using the values of b from the new equation, add (b/2)^2 to both sides of equation to form
perfect square on left side of the equation
4. Find the square root of both sides of equation
5. Solve the resulting equation
, > - correct answer ✔✔Greater than
< - correct answer ✔✔Less than
≥ - correct answer ✔✔Greater than or equal to
≤ - correct answer ✔✔Less than or equal to
The use of brackets in inequalities mean? - correct answer ✔✔The endpoint
The use of parentheses in inequalities means? - correct answer ✔✔Excluded
What are compound inequalities? - correct answer ✔✔Inequalities that are separated with
AND/OR
"AND"/"OR" in equalities ALWAYS ONLY use? - correct answer ✔✔Parentheses
"AND" inequalities are? - correct answer ✔✔The intersection of both inequalities
"OR" inequalities? - correct answer ✔✔Can satisfy one or both inequalities
The notation f(x)? - correct answer ✔✔Defines a function named f. This reads as "y is a function
of x".
Parentheses in function notation mean? - correct answer ✔✔The endpoint is NOT included
