Tan.ApplCalcBrf9-ch01sec01
Student: ___________________________________________________________________________
1.  
True    False
 
2. Suppose  and  are real numbers other than zero and that . State whether the inequality is true or false.

True    False
 
3. Determine whether the statement below is true for all real numbers b.

|b + 8| = |b| + 8 
True    False
 
4. If a > b, then a - c  <  b - c. 
True    False
 
5. A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression

where x (in thousands) is the number of units produced.

What production range will enable the manufacturer to realize a profit of at least $18,000 on the commodity?
 
A. Between 4,000 and 9,000 units.
B. Between 4,000 and 6,000 units.
C. Between 1,000 and 6,000 units.
D. Between 1,000 and 8,000 units.
E. Between 1,000 and 9,000 units.
 
6. Rationalize the numerator of the expression.

 
A. 
B. 
C. 
D. 
E. 
 
7. Rationalize the denominator of the expression.

 
A. 
B. 
C. 
D. 
E.       
 
8. Use the fact that  to evaluate the expression without using a calculator.

 
A. 3.162
B. 31.62
C. 3,162
D. 31,620
E. 316,200
 
9. Use the fact that  to evaluate the expression without using a calculator.

 
A. 
B. 
C. 
D. 
E. 
 
10. Simplify the expression. (Assume that r, s, and t are positive.)

 
A. 
B. 
C. 
D. 
E. 
 
11. Evaluate the expression.

 
A. 4,096
B. –1,024
C. –6,561
D. 6,561
E. –4,096
 
12. Determine whether the statement is true or false.

 
A. False
B. True
 
13. Determine whether the statement is true or false.

 
A. True
B. False
 
14. Show the interval [6, 8) on a number line.
 
A. 
B. 
C. 
D. 
E. 
 
15. Evaluate the expression.

 
A. 
B. 
C. 
D. 
E. 
 
16. Evaluate the expression.

 
A. 
B. 
C. 
D. 
E. 
 
17. Suppose  and  are real numbers other than zero and that . State whether the inequality is true or false.

 
A. False
B. True
 
18. Evaluate the expression.

 
A. 
B. 1
C. 3
D. 9
E. 
 
19. Rewrite the expression using positive exponents only.

 
A. 
B. 
C. 
D. 
E. 
 
20. Simplify the expression. (Assume x and y are positive.)

 
A. 
B. 
C. 
D. 
E. 
 
21. Determine whether the statement below is true for positive real numbers a.

|a + 8| = |a| + 8
 
A. True
B. False
 
22. Rationalize the denominator of the expression.

 
A. 
B. 
C. 
D. 
E. 
 
23. Rationalize the numerator of the expression.

 
A. 
B. 
C. 
D. 
E. 
 
24. Find the maximum profit P (in dollars) given that

.
 
A. $ 15,650
B. $ 7,600
C. $ 15,200
D. $ 16,100
E. $ 22,800
 
25. Find the minimum profit P (in dollars) given that

.
 
A. $ 
B. $ 
C. $ 
D. $ 
E. $ 
 
26. A salesman's monthly commission is 15% on all sales over $11,000. If his goal is to make a commission of at least $2,400/month, what minimum monthly sales figures must he attain?
 
A. $ 13,400
B. $ 12,200
C. $ 15,800
D. $ 24,600
E. $ 27,000
 
27. Simplify the expression.

 
A. 
B. 
C. 
D. 
E. 
 
28. The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality

What is the smallest diameter a ball bearing in the batch can have?
 
A. 0.4 inches
B. 0.46 inches
C. 0.47 inches
D. 0.43 inches
E. 0.45 inches
 
29. Evaluate the expression.

 
A. 1
B. 9
C. 6
D. 8
E. 4
 
30. Determine whether the statement is true or false.

If a < b,  then  a - c  >  b - c.
 
A. True
B. False
 
31. Find the values of x that satisfy the inequalities.

 and 
 
A. 
B. 
C. 
D. 
E. 
 
32. Find the values of x that satisfy the inequalities.

 and 
 
A. 
B. 
C. 
D. 
E. 
 
33. Evaluate the expression.

 
A. 
B. 
C. 
D. 
E. 
 
34. Simplify the expression.

 
A. 
B. 
C. 
D. 
E. 
 
35. Use the fact that the  to evaluate the expression without using a calculator.

Round the answer to the nearest thousandth. 
 
A. 15.588
B. 43.075
C. 5.196
D. 46.765
E. 24.994
 
36. Evaluate the expression.

________________________________________
 
37. Use the fact that  to evaluate the expression without using a calculator.

________________________________________
 
38. Evaluate the expression.

________________________________________
 
39. Evaluate the expression.

________________________________________
 
40. Find the maximum profit P (in dollars) given that

.

$ __________ 
________________________________________
 
41. A salesman's monthly commission is 15% on all sales over $15,000. If his goal is to make a commission of at least $3,300/month, what minimum monthly sales figures must he attain?

$ __________ 
________________________________________
 
42. The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality

What is the largest diameter a ball bearing in the batch can have? Give your answer to two decimal places, if necessary.

__________ inches 
________________________________________
 
43. Evaluate the expression.

________________________________________
 
44. Use the fact that the  to evaluate the expression without using a calculator.

Round the answer to the nearest thousandth, if necessary. 
________________________________________
 
45. Match each interval with the corresponding number line.

Choose the correct letter for each question.
 
1.  	     (-6, ) 	  ____ 	
2.  	      	  ____ 	
3.  	     (-, 6] 	  ____ 	
4.  	      	  ____ 	
 
46. Match each pair of inequalities with the corresponding values of x.

Choose the correct letter for each question.
 
1.  	      and  	  ____ 	
2.  	      and  	  ____ 	
3.  	      and  	  ____ 	
4.  	      and 
 	  ____ 	
 
47. Simplify the expression. (Assume that r, s, and t are positive.)

 

 

 
48. Rationalize the numerator of the expression.

 

 

 
49. Rewrite the expression using positive exponents only.

 

 

 
50. Simplify the expression. (Assume x and y are positive.)

 

 

 
51. Rationalize the denominator of the expression.

 

 

 
52. Rationalize the numerator of the expression.

 

 

 
53. Simplify the expression.

 

 

 
54. Evaluate the expression.

 

 

 
55. Simplify the expression.

 

 

 
56. A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression

where x (in thousands) is the number of units produced.

What production range will enable the manufacturer to realize a profit of at least $14,000 on the commodity?

 

 

 
57. Determine whether the statement is true or false.

 

 

 

Tan.ApplCalcBrf9-ch01sec01 Key
 
1.  
FALSE
 
2. Suppose  and  are real numbers other than zero and that . State whether the inequality is true or false.

FALSE
 
3. Determine whether the statement below is true for all real numbers b.

|b + 8| = |b| + 8 
FALSE
 
4. If a > b, then a - c  <  b - c. 
FALSE
 
5. A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression

where x (in thousands) is the number of units produced.

What production range will enable the manufacturer to realize a profit of at least $18,000 on the commodity?
 
A. Between 4,000 and 9,000 units.
B. Between 4,000 and 6,000 units.
C. Between 1,000 and 6,000 units.
D. Between 1,000 and 8,000 units.
E. Between 1,000 and 9,000 units.
 
6. Rationalize the numerator of the expression.

 
A. 
B. 
C. 
D. 
E. 
 
7. Rationalize the denominator of the expression.

 
A. 
B. 
C. 
D. 
E.       
 
8. Use the fact that  to evaluate the expression without using a calculator.

 
A. 3.162
B. 31.62
C. 3,162
D. 31,620
E. 316,200
 
9. Use the fact that  to evaluate the expression without using a calculator.

 
A. 
B. 
C. 
D. 
E. 
 
10. Simplify the expression. (Assume that r, s, and t are positive.)

 
A. 
B. 
C. 
D. 
E. 
 
11. Evaluate the expression.

 
A. 4,096
B. –1,024
C. –6,561
D. 6,561
E. –4,096
 
12. Determine whether the statement is true or false.

 
A. False
B. True
 
13. Determine whether the statement is true or false.

 
A. True
B. False
 
14. Show the interval [6, 8) on a number line.
 
A. 
B. 
C. 
D. 
E. 
 
15. Evaluate the expression.

 
A. 
B. 
C. 
D. 
E. 
 
16. Evaluate the expression.

 
A. 
B. 
C. 
D. 
E. 
 
17. Suppose  and  are real numbers other than zero and that . State whether the inequality is true or false.

 
A. False
B. True
 
18. Evaluate the expression.

 
A. 
B. 1
C. 3
D. 9
E. 
 
19. Rewrite the expression using positive exponents only.

 
A. 
B. 
C. 
D. 
E. 
 
20. Simplify the expression. (Assume x and y are positive.)

 
A. 
B. 
C. 
D. 
E. 
 
21. Determine whether the statement below is true for positive real numbers a.

|a + 8| = |a| + 8
 
A. True
B. False
 
22. Rationalize the denominator of the expression.

 
A. 
B. 
C. 
D. 
E. 
 
23. Rationalize the numerator of the expression.

 
A. 
B. 
C. 
D. 
E. 
 
24. Find the maximum profit P (in dollars) given that

.
 
A. $ 15,650
B. $ 7,600
C. $ 15,200
D. $ 16,100
E. $ 22,800
 
25. Find the minimum profit P (in dollars) given that

.
 
A. $ 
B. $ 
C. $ 
D. $ 
E. $ 
 
26. A salesman's monthly commission is 15% on all sales over $11,000. If his goal is to make a commission of at least $2,400/month, what minimum monthly sales figures must he attain?
 
A. $ 13,400
B. $ 12,200
C. $ 15,800
D. $ 24,600
E. $ 27,000
 
27. Simplify the expression.

 
A. 
B. 
C. 
D. 
E. 
 
28. The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality

What is the smallest diameter a ball bearing in the batch can have?
 
A. 0.4 inches
B. 0.46 inches
C. 0.47 inches
D. 0.43 inches
E. 0.45 inches
 
29. Evaluate the expression.

 
A. 1
B. 9
C. 6
D. 8
E. 4
 
30. Determine whether the statement is true or false.

If a < b,  then  a - c  >  b - c.
 
A. True
B. False
 
31. Find the values of x that satisfy the inequalities.

 and 
 
A. 
B. 
C. 
D. 
E. 
 
32. Find the values of x that satisfy the inequalities.

 and 
 
A. 
B. 
C. 
D. 
E. 
 
33. Evaluate the expression.

 
A. 
B. 
C. 
D. 
E. 
 
34. Simplify the expression.

 
A. 
B. 
C. 
D. 
E. 
 
35. Use the fact that the  to evaluate the expression without using a calculator.

Round the answer to the nearest thousandth. 
 
A. 15.588
B. 43.075
C. 5.196
D. 46.765
E. 24.994
 
36. Evaluate the expression.

64
 
37. Use the fact that  to evaluate the expression without using a calculator.

3,162
 
38. Evaluate the expression.

6
 
39. Evaluate the expression.

1
 
40. Find the maximum profit P (in dollars) given that

.

$ __________ 
24,550
 
41. A salesman's monthly commission is 15% on all sales over $15,000. If his goal is to make a commission of at least $3,300/month, what minimum monthly sales figures must he attain?

$ __________ 
37,000
 
42. The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality

What is the largest diameter a ball bearing in the batch can have? Give your answer to two decimal places, if necessary.

__________ inches 
0.14
 
43. Evaluate the expression.

1
 
44. Use the fact that the  to evaluate the expression without using a calculator.

Round the answer to the nearest thousandth, if necessary. 
11.312
 
45. Match each interval with the corresponding number line.

Choose the correct letter for each question.
 
1.  	     (-6, ) 	  3 	
2.  	      	  4 	
3.  	     (-, 6] 	  1 	
4.  	      	  2 	
 
46. Match each pair of inequalities with the corresponding values of x.

Choose the correct letter for each question.
 
1.  	      and  	  2 	
2.  	      and  	  3 	
3.  	      and  	  4 	
4.  	      and 
 	  1 	
 
47. Simplify the expression. (Assume that r, s, and t are positive.)

 
48. Rationalize the numerator of the expression.

 
49. Rewrite the expression using positive exponents only.

 
50. Simplify the expression. (Assume x and y are positive.)

 
51. Rationalize the denominator of the expression.

 
52. Rationalize the numerator of the expression.

 
53. Simplify the expression.

 
54. Evaluate the expression.

 
55. Simplify the expression.

 
56. A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression

where x (in thousands) is the number of units produced.

What production range will enable the manufacturer to realize a profit of at least $14,000 on the commodity?

 
57. Determine whether the statement is true or false.