Algebra II Mid Term Exam Study Guide
Determine the restricted values of x. Select all that apply.
-1 1 -3
solve the equation
12
Which values of x make the simplified form of the expression undefined? Select all that apply.
12 -8 6
solve the equation
5
Which of the following expressions are equivalent to
C. E.
Complete the inequalities that represent the solutions: Z < ? or ? < z < ?
Z < 1 or 3 < z < 9
solve for b
b = 7
Simplify:
b.
add
c.
Match a rational expression in column A with one shown in Column B:
A = 1 B = 3 C = 2
simplify
3.
Perform the necessary operation and simplify
a.
What is the simplified form of
a.
simplify
a.
Which of the following statements are true? Select all that apply.
a. b. e.
For all x > 3. Select all that apply.
a. b. e. f.
Select all that apply.
a. d. f.
Greg set the speed of his motor boat at a constant rate, r, and drove 12 miles up the river. He immediately turned around and drove back to where he started. Greg's total trip lasted exactly 1 hour. The speed of the current is 6 miles per hour downstream. For each quantity below, choose an expression to model that quantity in terms of r. Choices: The total time that Greg traveled, The amount of time Greg traveled downstream, or The amount of time Greg traveled upstream.
a. The amount of time Greg traveled downstream. b. The amount of time Greg traveled upstream c. The total time that Greg traveled.
Look for any restricted values of the domain and solve the equation for x.
b.
Reduce the given rational expression by using factoring techniques and properties of equality.
b.
Rewrite the rational expression as one rational term, reducing all common factors.
b.
evaluate
b.
simplify
b.
simplify:
b.
solve
b.
Which of the following expressions are equivalent to. Select all that apply.
b. d. h.
(image)
c.
Bob sells part of a 50-acre rectangular plot of land he owns so that he can still own a smaller rectangular plot within the original. After he makes the sale, Bob's remaining plot of land is half as long and half as wide as his original plot. What is the area of Bob's remaining plot of land?
c.
Factor the following completely:
c.
Which statements are true of the equation? Select all that apply.
d. e.
Pipe A can fill a tank 40 minutes, while Pipe B takes 60 minutes to fill the same tank. If both pipes are used at the same time, how long will it take to fill the tank?
d. 24 mintues
Solve for x in the rational equation
d. no solution
Identify the solution and extraneous solution, if it exists,
solution: -2 Extraneous solution: 4
Identify the solution and extraneous solution of the equation, if they exist. Solution: ? Extraneous solution: ?
solution: x = 6 extraneous solution: x = -2
Factor the following equation:
(6x + 5) (x - 3)
Shelly is (correct/incorrect) because you (can/cannot) cancel out the 4's before you add and then simplify the fraction.
Shelly is incorrect because you cannot cancel out the 4's before you add and then simplify the fraction.
Identify the quotient and remainder. Select both answers.
a. e.
multiply
b.
Which of the following statements are true about Hannah's claims? Select all that apply.
a. c.
Which of the following statements are true about Hannah's claims? Select all that apply.
a. d.
Rewrite and reduce the given rational expression, using factoring techniques. Then choose which options are equivalent expressions of the original rational expression
a. d. e.
Analyze each step of the expression. A mistake has been made affecting the rest of the work. Select the mistake made as well as the correct simplified form of the expression.
a. b.
Correctly solve the equation from the previous question, now that you have identified the student's mistake. Select all possible solutions of x.
a. b.
Simplify the expression. Select all that apply.
a. c.
Factor the following equation:
a. (x + 16) (x - 3)
What value(s) of x makes the rational expression undefined? Select all that apply. X ≠ ?
a. -3 e. 3
mutliply
b.
If Simone does all of the calculations correctly, what will be the numerator of the answer?
c.
Perform the necessary operation and simplify
c.
Sasha correctly subtracted the rational expressions. However, she did not write her answer in simplest form. What would her answer be simplest form?
c.
Solve for x in the rational equation
c.
How can you switch the terms in the denominator so that you will have factors that divide out? Simplify the below expression:
d.
Select the simplified form of the expression
d.
Select the simplified form of the expression:
d.
Solve for x:
d.
The amount of time Greg traveled downstream.
d.
What is the simplified form of the rational expression
d.
Which is the equivalent expression?
d.
evaluate
d.
multiply
d.
simplify
d.
Determine the solutions.
d. no solutions
Solve for m
m = 14
What should Jamal use as the common denominator?
b.
What value(s) of x makes the rational expression undefined? Select all that apply. X ≠ ?
5 -5 -3
Solve the equation. Remember to account for extraneous solutions.
6
Rewrite the rational expression as one rational term reducing all common factors.
D.
Determine the quotient of
a.
Divide:
a.
The amount of time Greg traveled upstream.
a.
The total time that Greg traveled.
a.
What rational expression describes the area of this rectangle?
a.
Solve/simplify the following:
c.
h(t) - k(t)
c.
multiply
c.
simplify
c.
solve
c.
Solve the following:
c. x = -4
Solve the following
c. x = 19
Determine the restricted values of x and the final solution values of the equation.
d.
A student has solve an equation incorrectly. Review the steps of the solution to determine the student's first mistake. Other mistakes may be due to this original mistake, so we only are concerned with identifying the first one on this practice problem.
e.
h(t) + k(t)
e.
