Question Bank in line with Precalculus Mathematics for Calculus,Stewart,7e

Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A


1. List the elements from the given set that are rational numbers.

 1 1 
0,  2, 50, , 0.521, 2 2, 1.23,  , 3
4, 4
 2 6 

2. State the property of real numbers being used.

 2x  3 y   4z  2x  3 y  4z 
3. Perform the indicated operations.

1
12
1 1

8 12

4. Evaluate each expression.

2
3 3
0
7 1
(a)   21 (b) (c)  
3 40 5

5. Evaluate the expression.

3 48

6. Find the set A  C if A   x | x  4  and C   x | 2  x  6  .



7. Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote
positive numbers.

3 3
r 2 s 64r 4 s 2

8. Simplify the expression.

6
 a 2b5/ 3 
 1/ 3 
a b 

9. A hummingbird’s heart can beat 1260 times per minute. Estimate the number of times its heart will
beat in 2 years. State your answer in scientific notation.

10. Factor the expression completely.

 
x 2 x 2  1  25 x 2  1  
11. Perform the indicated operation and simplify.

 2 3
 
x x  1  x  12

,Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A


12. Rationalize the denominator.

2
6 2

13. Find all real solutions of the quadratic equation.

8 16
z2  z  0
5 25

14. Caitlin drove from Greensville to Bluesburg at a speed of 50 mi/h. On the way back, she drove at 75
1
mi/h. The total trip took 7 h of driving time. Find the distance between these two cities.
2

15. Solve the absolute value inequality. Express the answer using interval notation.

8 x  5  15

16. Two points P and Q are given.

P  0, 8  , Q  11, 8

(a) Find the distance from P to Q.
(b) Find the midpoint of the line segment PQ.

17. Find the equation of the circle with center  1, 7  and radius 2 .

18. Determine whether the equation represents a circle, a point, or has no graph. If the equation is that of a
circle, find its center and radius.

5
x2  y 2  x  2 y  3
4

19. Test the equation for symmetry and sketch its graph.

y  x2  16

20. Find an equation for the line that passes through the point  5,1 and is perpendicular to the line
x  3 y  16  0 .

21. Find the equation of a line that passes through the point  7,  and the midpoint of  2, 4  and  3, 4  .

22. Hooke’s Law states that if a weight w is attached to a hanging spring, then the stretched length s of the
spring is linearly related to w. For a particular spring we have the equation s  0.4w  3.5 , where s is
measured in inches and w in pounds. How long is the spring when a 5-lb weight is attached?

23. Determine the values of the variable for which the expression is defined as a real number.

1/2
 1 
 2 
 x  2 x  15 

,Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A


24. In a certain city, the property tax collected for a home varies directly to the valuation of the property.
The tax collected on a $105, 000 home is $2,846 per year. What is the value of a home if the tax
collected is $1, 735 ?

25. The resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire
50 m long and 0.01 m in diameter has a resistance of 25 ohms . Find the resistance of a wire made of
the same material that is 20 m long and has diameter 0.02 m.

, ANSWER KEY

Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A


1
1. 0,  2, 50, 0.521, 1.23,  , 4
6

2. Associative Property for addition

3. 2

2
33
0
7 1 1 1
4. (a)   21  (b)  (c)    25
3 2 40 27 5

5. 3 48  12


6.  x | 2  x  4 

7. 4r 2 s

8. a10b6

9. 1.32  109


   
10. x 2 x 2  1  25 x 2  1   x  1 x  1 x  5  x  5 


3x 2  x  1
11.
x  x  1
2




12. 3 1
2

13. z 

14. 225 mi

15. (, )  (, )

16. (a) 11
 11 
(b)  , 8 
 2 

17. x  2 x  y  14 y  48  0
2 2



 1 
18. center   , 1 , radius 3
 2 