Exam: 050293RR - Rational Expressions
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Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. Simplify the following expression:
A.
B.
C.
D.
2. Your textbook says that the focal length f of a lens is given by the lensmaker's formula
where r1 and r2 are the radii of the two circular surfaces. If those radii are 4 and 6 respectively, find f.
A. 4
B.
C.
D. 16.67
3. Perform the indicated operations and simplify the following expression:
A.
B.
C.
Exam: 050293RR - Rational Expressions
D.
4. After t hours of work, Group A completes of a job and Group B completes of the same job.
What expression represents the amount the two teams would complete after t seconds, working together?
A.
B.
C.
D.
5. Perform the indicated operations and simplify the following expression:
A.
B.
C.
D.
6. Express this sentence as a formula: z varies directly with the square of s.
A.
B.
C.
D.
7. Solve for k in .
A. k = –1 and k = 3
B. k = 3
C. k = –1 and k = 2
D. k = –1
8. Divide the following expression:
(x2 + 10x + 21) ÷ (x + 7) A. x + 5
B. x − 2
C. x2 + 3
D. x + 3
9. It costs $500 to have a booth at the fair for one day and $2.75 for Aunt Ida to produce one of her famous shepherd's pies. What is the function that gives the average cost in dollars per pie for one of Aunt Ida's days at the fair?
A.
B.
C.
D.
10. Divide the following expression:
A. 5z2 + 7z
B. 3z2 + 7z + 3 and a remainder of –9
C. 3z + 7
D. 3z2 + 16z + 3 and a remainder of 6
11. Simplify .
A. –a8b–7
B. –a4b–7
C. –a4b3
D. –a8b3
12. Factor and simplify .
A.
B. It is already fully simplified.
C.
D.
13. Simplify the expression
A.
B.
C.
D.
14. Perform the indicated operations and simplify the following expression:
A.
B.
C.
D.
15. The total resistance R of two resistors in parallel is given by where R1 is the resistance of the
first and R2 the resistance of the second. Solve that equation for R1 and simplify.
A.
B.
C.
D.
16. Simplify the expression
A.
B.
C.
D.
17. Perform the indicated operations and simplify the following expression:
A.
B.
C.
D.
18. Which sum yields ?
A.
B.
C.
D.
19. Solve this proportion for the variable:
A. y = 4
B. y = –2
C. y = 2
D. y = –4
20. Solve the following equation:
A. z = 6
B. z = –4
C. z = 4
D. z = –6
