Exam: 050294RR Radicals and Rational Exponents
1. Solve for x.
A. x = 2
B. The two solutions for are complex numbers.
C. x = 4 or x = –4
D. x = 2 or x = 8
2. Simplify assuming the variables represent non-negative numbers.
A.
B.
C.
D.
3. Rationalize the denominator of .
A.
B.
C.
D.
4. Simplify .
A.
B.
C.
D.
5. Which of these phrases best describes the standard deviation?
A. It increases as more measurements are taken.
B. It is a radical expression using n variables.
C. It is equal to the mean squared.
D. It is a measure of variability.
6. Which expression has the same value as 25
A.
B.
C.
D.
½
?
7. What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?
A. It is a right triangle.
B. It has area 22 square units.
C. None of the above.
D. It is isosceles.
8. Choose the best description of the radical expression .
A. It can be simplified to –3.
B. It can be simplified, but the result is a complex number.
C. It can be simplified to , but no further.
D. It is in simplified form.
9. Simplify by rationalizing the denominator.
A.
B.
C.
D.
10. Two children in nearby houses attempt to use walkie-talkies to communicate. The walkie-talkies reach
one quarter of a mile (1320 feet). From one child's house to the other, the walk along the city sidewalks is
as follows: Proceed 450 feet from the first house to the nearest corner, turn right 90° and proceed another
1050 feet. Are the children's houses within the 1320-foot range of one another? Choose the best answer.
A. No, because the distance is greater than 1320 feet.
B. Yes, as the distance formula indicates.
C. Yes, because city blocks are much smaller than one quarter of a mile.
D. No, but if the turn were to the left instead, they would be within range.
11. Compute the value of .
A.
B.
C.
D.
12. To solve for x, begin with which of these steps?
A. Square both sides of the equation.
B. Combine the two like radicals, then square both sides.
C. Isolate one radical expression.
D. Eliminate the negative in the second radical expression.
13. Simplify .
A.
B.
C.
D.
14. Which of these expressions is in simplified form?
A.
B.
C.
D.
15. If the hypotenuse of a right triangle is 6m and one side is 4m, what is the length of the other side?
A.
B.
C.
D.
16. Simplify .
A.
B.
C.
D.
17. 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 not numbers, but are useful in solving equations.
D. They are the complex numbers.
18. What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?
A. The mean is and the standard deviation is 5.
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 4.86 and the standard deviation is 5.63.
19. Solve for x.
A. 40
B. 4
C. –41
D. 50
20. Which of these points is 5 units away from the point (6, –1)?
A.
B.
C.
D.
21. Simplify .
A.
B.
C.
D.
22. Which of these radical expressions simplifies to x?
A.
B.
C.
D.
23. Solve for x.
A.
B.
C.
D.
24. Rationalize the denominator of assuming x = 0 and y = 0.
A.
B.
C.
D.
25. Expand and simplify. Assume c = 0 and d = 0.
A.
B.
C
