Maths (Radicals and rational exponent) 050294RR

Student ID: 70694744

Exam: 050294RR - Radicals and Rational Exponents

When you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until you hit Submit Exam. If you need to exit before completing the exam, click Cancel Exam.

Questions 1 to 25: 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. 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 is a right triangle.

C. It has area 22 square units.

D. It is isosceles.

2. Simplify (6 − i)(2 + i). A. 11 + 8i

B. 13 + 4i

C. 13 − 8i D. 11 + 4i

3. 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 approximately 5.6252.

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

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

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

4. Which expression has the same value as 25½?

A.

B.

C.

D.

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

A.

B.

C.

D.

6. Simplify .

A.

B.

C.

D.

7. Simplify by rationalizing the denominator.

A.

B.

C.

D.

8. Simplify i23. A. 1

B. –i

C. i

D. –1

9. Choose the best description of the radical expression .

A. It is in simplified form.

B. It can be simplified to –3.

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

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

10. Which of these expressions is in simplified form?

A.

B.

C.

D.

11. Expand and simplify. Assume y ≥ 0.

A.

B.

C.

D.

12. Combine like radicals in .

A.

B.

C.

D.

13. 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, but if the turn were to the left instead, they would be within range.

B. Yes, as the distance formula indicates.

C. Yes, because city blocks are much smaller than one quarter of a mile.

D. No, because the distance is greater than 1320 feet.

14. Which of these phrases best describes the standard deviation? A. It increases as more measurements are taken.

B. It is equal to the mean squared.

C. It is a radical expression using n variables.

D. It is a measure of variability.

15. Solve for x.

A.

B.

C.

D.

16. Rationalize the denominator of assuming x ≥ 0 and y ≥ 0.

A.

B.

C.

D.

17. 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.

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

A. Eliminate the negative in the second radical expression.

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

C. Square both sides of the equation.

D. Isolate one radical expression.

19. 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.

20. Simplify .

A.

B.

C.

D.

21. Which of these expressions simplifies to ?

A.

B.

C.

End of exam

D.

22. Solve for x.

A. 4

B. 40

C. 50

D. –41

23. Rationalize the denominator of .

A.

B.

C.

D.

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

A.

B.

C.

D.

25. Simplify .

A.

B.

C.

D.