# Exam: 050293RR - RATIONAL EXPRESSIONS

Exam: 050293RR - RATIONAL EXPRESSIONS

1. Divide the following expression:

2. Your textbook says that the focal length f of a lens is given by the lensmaker's formula where r

3. Simplify the expression

4. Solve the following equation:

A. { }

B. t = 1

C. t = 2

D. t = –1

5. Which sum yields ?

6. 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?

7. Find the result of the polynomial division (3x

8. Simplify the following expression:

9. Perform the indicated operations and simplify the following expression:

10. 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?

11. Perform the indicated operations and simplify the following expression:

12. Solve the following equation:

A. z = 4

B. z = 6

C. z = –4

D. z = –6

13. The intensity I of light varies inversely with the square of the distance d from the source, expressed in the equation . If the intensity is of a candela 16 feet from the source, what is the constant of proportionality?

A. 2 candela-square-feet

B. 128 candela-square-feet

C. 32 candela-square-feet

D. 256 candela-square-feet

14. Solve this proportion for the variable:

A. y = –2

B. y = 2

C. y = 4

D. y = –4

15. Solve for k in .

A. k = 3

B. k = –1 and k = 3

C. k = –1 and k = 2

D. k = –1

16. Perform the indicated operations and simplify the following expression:

17. Divide the following expression:

18. Perform the indicated operations and simplify the following expression:

19. Divide the following expression:

20. Simplify the following expression:

Exam: 050294RR - RADICALS AND RATIONAL EXPONENTS

1. Simplify .

2. Simplify by rationalizing the denominator.

3. Which expression has the same value as 25½?

4. Which of these phrases best describes the standard deviation?

A. It is equal to the mean squared.

B. It is a radical expression using n variables.

C. It is a measure of variability.

D. It increases as more measurements are taken.

5. Which of these expressions is in simplified form?

6. Combine like radicals in .

7. Simplify .

8. Expand and simplify. Assume c = 0 and d = 0.

9. Solve for x.

A. –41

B. 50

C. 40

D. 4

10. Which of these points is 5 units away from the point (6, –1)?

11. Which of the following best describes imaginary numbers?

A. They are the values of expressions of the form for various real numbers a, as long as a ≠ 0.

B. They consist of two values, the principal imaginary number i and its negative –i.

C. They are the complex numbers.

D. They are not numbers, but are useful in solving equations.

12. Rationalize the denominator of assuming x = 0 and y = 0.

13. Simplify .

14. Simplify assuming the variables represent non-negative numbers.

15. Simplify i

16. Expand and simplify. Assume y = 0.

17. Compute the value of .

18. What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?

A. The mean is 4.86 and the standard deviation is 5.63.

B. The mean is and the standard deviation is approximately 5.6252.

C. The mean is and the standard deviation is approximately 5.6252.

D. The mean is and the standard deviation is 5.

19. Choose the best description of the radical expression .

A. It can be simplified, but the result is a complex number.

B. It can be simplified to –3.

C. It is in simplified form.

D. It can be simplified to , but no further.

20. Simplify .

21. Which of these expressions simplifies to ?

22. Solve for x.

23. To solve for x, begin with which of these steps?

A. Isolate one radical expression.

B. Square both sides of the equation.

C. Combine the two like radicals, then square both sides.

D. Eliminate the negative in the second radical expression.

24. Rationalize the denominator of .

25. What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?

A. None of the above.

B. It has area 22 square units.

C. It is isosceles.

D. It is a right triangle.

1. Divide the following expression:

2. Your textbook says that the focal length f of a lens is given by the lensmaker's formula where r

3. Simplify the expression

4. Solve the following equation:

A. { }

B. t = 1

C. t = 2

D. t = –1

5. Which sum yields ?

6. 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?

7. Find the result of the polynomial division (3x

8. Simplify the following expression:

9. Perform the indicated operations and simplify the following expression:

10. 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?

11. Perform the indicated operations and simplify the following expression:

12. Solve the following equation:

A. z = 4

B. z = 6

C. z = –4

D. z = –6

13. The intensity I of light varies inversely with the square of the distance d from the source, expressed in the equation . If the intensity is of a candela 16 feet from the source, what is the constant of proportionality?

A. 2 candela-square-feet

B. 128 candela-square-feet

C. 32 candela-square-feet

D. 256 candela-square-feet

14. Solve this proportion for the variable:

A. y = –2

B. y = 2

C. y = 4

D. y = –4

15. Solve for k in .

A. k = 3

B. k = –1 and k = 3

C. k = –1 and k = 2

D. k = –1

16. Perform the indicated operations and simplify the following expression:

17. Divide the following expression:

18. Perform the indicated operations and simplify the following expression:

19. Divide the following expression:

20. Simplify the following expression:

Exam: 050294RR - RADICALS AND RATIONAL EXPONENTS

1. Simplify .

2. Simplify by rationalizing the denominator.

3. Which expression has the same value as 25½?

4. Which of these phrases best describes the standard deviation?

A. It is equal to the mean squared.

B. It is a radical expression using n variables.

C. It is a measure of variability.

D. It increases as more measurements are taken.

5. Which of these expressions is in simplified form?

6. Combine like radicals in .

7. Simplify .

8. Expand and simplify. Assume c = 0 and d = 0.

9. Solve for x.

A. –41

B. 50

C. 40

D. 4

10. Which of these points is 5 units away from the point (6, –1)?

11. Which of the following best describes imaginary numbers?

A. They are the values of expressions of the form for various real numbers a, as long as a ≠ 0.

B. They consist of two values, the principal imaginary number i and its negative –i.

C. They are the complex numbers.

D. They are not numbers, but are useful in solving equations.

12. Rationalize the denominator of assuming x = 0 and y = 0.

13. Simplify .

14. Simplify assuming the variables represent non-negative numbers.

15. Simplify i

16. Expand and simplify. Assume y = 0.

17. Compute the value of .

18. What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?

A. The mean is 4.86 and the standard deviation is 5.63.

B. The mean is and the standard deviation is approximately 5.6252.

C. The mean is and the standard deviation is approximately 5.6252.

D. The mean is and the standard deviation is 5.

19. Choose the best description of the radical expression .

A. It can be simplified, but the result is a complex number.

B. It can be simplified to –3.

C. It is in simplified form.

D. It can be simplified to , but no further.

20. Simplify .

21. Which of these expressions simplifies to ?

22. Solve for x.

23. To solve for x, begin with which of these steps?

A. Isolate one radical expression.

B. Square both sides of the equation.

C. Combine the two like radicals, then square both sides.

D. Eliminate the negative in the second radical expression.

24. Rationalize the denominator of .

25. What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?

A. None of the above.

B. It has area 22 square units.

C. It is isosceles.

D. It is a right triangle.

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