,Test Bank For Precalculus: Mathematics for Calculus
Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A
1. List the elements from the given set that are rational numbers.
1 1 3
0, − 2, 50, , 0.521, 2 2, 1.23, − 6 , 4, 4
2. State the property of real numbers being used.
(2x + 3y ) + 4z = 2x + (3y + 4z )
3. Perform the indicated operations.
1
12
1 1
−
8 12
4. Evaluate each expression.
7 0 3−3 1 −2
(a) 2−1 (b) (c)
3 40 5
5. Evaluate the expression.
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.
8. Simplify the expression.
6
a2b
a1/ 3b
1
,Test Bank For Precalculus: Mathematics for Calculus
Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A
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.
( ) (
x2 x 2 −1 − 25 x 2 −1)
11. Perform the indicated operation and simplify.
2 3
+ +
x x −1 ( x − 1)2
2
, Test Bank For Precalculus: Mathematics for Calculus
Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A
12. Rationalize the denominator.
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.
8x + 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 + y2 + 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.
3
Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A
1. List the elements from the given set that are rational numbers.
1 1 3
0, − 2, 50, , 0.521, 2 2, 1.23, − 6 , 4, 4
2. State the property of real numbers being used.
(2x + 3y ) + 4z = 2x + (3y + 4z )
3. Perform the indicated operations.
1
12
1 1
−
8 12
4. Evaluate each expression.
7 0 3−3 1 −2
(a) 2−1 (b) (c)
3 40 5
5. Evaluate the expression.
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.
8. Simplify the expression.
6
a2b
a1/ 3b
1
,Test Bank For Precalculus: Mathematics for Calculus
Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A
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.
( ) (
x2 x 2 −1 − 25 x 2 −1)
11. Perform the indicated operation and simplify.
2 3
+ +
x x −1 ( x − 1)2
2
, Test Bank For Precalculus: Mathematics for Calculus
Stewart/Redlin/Watson - Precalculus 7e Chapter 1 Form A
12. Rationalize the denominator.
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.
8x + 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 + y2 + 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.
3
