Mathematics III - Chapter 6 Test Review
Short Answer
Pre-Test
1. Determine the inverse of the function
. State whether the inverse is also
a function. Explain.
2. Simplify each expression using the definition of
rational exponents.
a.
b.
8. Rationalize the denominator of the expression
using rational exponents.
a.
9. Calculate the product
properties of exponents.
b.
3. Rationalize the denominator of the expression
using rational exponents.
4. Calculate the product
properties of exponents.
using the
5. The continuous compound interest formula is
where
is the original principal, P is
the balance after t years, and r is the annual interest
rate written as a decimal. Samantha deposited $1450
in a bank CD earning 4.2% interest compounded
continuously.
a. Write an equation to model the balance in
Samantha’s account at the end of t years.
b. What will be the balance in Samantha’s CD after
3.5 years?
Post-Test
6. Determine the inverse of the function
. State whether the inverse is also
a function. Explain.
7. Simplify each expression using the definition of
rational exponents.
using the
10. The continuous compound interest formula is
, where
is the original principal, P is
the balance after t years, and r is the annual interest
rate written as a decimal. Kevin deposited $950 in a
bank CD earning 3.9% interest compounded
continuously.
a. Write an equation to model the balance in Kevin’s
account at the end of t years.
b. What will be the balance in Kevin’s CD after 2.5
years?
Mid-Chapter Test
11. The formula for the surface area of a sphere is
, where r is the radius of the sphere.
a. Write the surface area formula as a function, f, of
the radius. What is the domain of this function?
b. What is the domain of the surface area function in
terms of the problem situation?
c. Which portion of the graph models surface area?
Explain.
d. Graph the surface area function and the line
in the first quadrant. Then sketch the
inverse of the surface area function.
a.
b.
16. Simplify each radical.
a.
b.
e. Determine the inverse of the surface area
algebraically. Is the inverse a function? Is the
inverse in terms of the problem situation a
function? Explain.
12. Determine the inverse of each function. State
whether the inverse is also a function. Explain.
a.
17. Perform each multiplication or division by
converting to rational exponents.
a.
b.
b.
13. Simplify each expression using the definition of
rational exponents.
18. Rationalize each denominator using rational
exponents.
a.
a.
b.
b.
c.
14. Write each expression in radical form.
19. Calculate each product and quotient using the
properties of exponents.
a.
a.
b.
b.
End of Chapter Test
15. Write each expression in exponential form and
simplify if possible.
20. Consider the cubic function
.
a. Determine the inverse of
b. Is the inverse of
algebraically.
also a function? Explain.
21. Simplify each expression using the definition of
rational exponents.
25. The continuous compound interest formula is
, where
is the original principal, P is
the balance after t years, and r is the annual interest
rate written as a decimal. Nicole deposited $1200 in
a bank CD earning 3.6% interest compounded
continuously.
a. Write an equation to model the balance in
Nicole’s account at the end of t years.
a.
b. What will be the value of Nicole’s CD after 4.5
years?
b.
22. Simplify each radical.
a.
c. If Nicole’s money stays deposited at the same
interest rate with no additional deposits and no
withdrawal, to the nearest tenth of a year, how
long will it take for the value of the account to
double? Explain your work.
b.
23. Perform each multiplication or division by
converting to rational exponents.
26. The formula for radioactive decay is
,
where N is the amount of radioactive material after
time t,
is the original amount, and
is the
half-life. Barium-140 has a half-life of 12.74 days.
a.
a. Write an equation for the decay of 200 grams of
Barium-140.
b.
24. The formula to determine the balance of a
compound-interest bank account after t years is
, where P is the current balance,
is the original principal, r is the annual interest
rate written as a decimal, and n is the number of
times per year that the interest is compounded. Zach
deposited $800 in a bank CD earning 4.0% interest
compounded quarterly (four times a year).
a. Write an equation to model the balance in Zach’s
account at the end of t years.
b. What will be the value of Zach’s CD after 18
months?
c. How long will it take for the value of the account
to reach $1000 to the nearest tenth of a year?
Explain your work.
b. How much radioactive material will be left after
20 days to the nearest tenth of a kilogram?
c. When will there be 10 kilograms of the
radioactive material left to the nearest day?
Explain your work.
Mathematics III - Chapter 6 Test Review
Answer Section
SHORT ANSWER
1. ANS:
The inverse is not a function because the original quadratic function is not one-to-one.
PTS: 1
2. ANS:
REF: Ch6.L1
STA: MM2A5
TOP: Pre Test
PTS: 1
TOP: Pre Test
3. ANS:
REF: Ch6.L2
STA: MM3A2a | MM3A2b
PTS: 1
TOP: Pre Test
4. ANS:
REF: Ch6.L3
STA: MM3A2a | MM3A2b
PTS: 1
TOP: Pre Test
5. ANS:
a.
REF: Ch6.L3
STA: MM3A2a | MM3A2b
a.
b.
b.
The balance in Samantha’s account after 3.5 years will be $1679.61.
PTS: 1
6. ANS:
REF: Ch6.L6
STA: MM3A2g
TOP: Pre Test
The inverse is not a function because the original quadratic function is not one-to-one.
PTS: 1
7. ANS:
REF: Ch6.L1
STA: MM2A5
TOP: Post Test
PTS: 1
TOP: Post Test
8. ANS:
REF: Ch6.L2
STA: MM3A2a | MM3A2b
PTS: 1
TOP: Post Test
9. ANS:
REF: Ch6.L3
STA: MM3A2a | MM3A2b
PTS: 1
TOP: Post Test
10. ANS:
a.
REF: Ch6.L3
STA: MM3A2a | MM3A2b
a.
b.
b.
The balance in Kevin’s account after 2.5 years will be $1047.29.
PTS: 1
REF: Ch6.L6
STA: MM3A2g
11. ANS:
a.
The domain of the function is all real numbers.
TOP: Post Test
b. The domain in terms of the problem situation is all real numbers greater than or equal to zero.
c. Only the first quadrant models surface area because surface area cannot be negative.
d.
e.
The equation of the inverse relation for the original function is
. This relation is not a function because
the original quadratic function is not one-to-one. The function in terms of the problem situation is one-to-one. So,
the inverse in terms of the problem situation is a function and is represented by
PTS: 1
12. ANS:
REF: Ch6.L1
STA: MM2A5
TOP: Mid Ch Test
.
a.
The inverse is a function because all linear functions are one-to-one.
b.
The inverse is not a function because the original quadratic function is not one-to-one.
PTS: 1
13. ANS:
REF: Ch6.L1
STA: MM2A5
TOP: Mid Ch Test
a.
b.
c.
PTS: 1
REF: Ch6.L2
TOP: Mid Ch Test
14. ANS:
STA: MM3A2a | MM3A2b
a.
b.
PTS: 1
REF: Ch6.L2
STA: MM3A2a | MM3A2b
TOP: Mid Ch Test
15. ANS:
a.
b.
PTS: 1
REF: Ch6.L2
TOP: Mid Ch Test
16. ANS:
STA: MM3A2a | MM3A2b
a.
b.
PTS: 1
REF: Ch6.L3
TOP: Mid Ch Test
17. ANS:
STA: MM3A2a | MM3A2b
a.
b.
PTS: 1
REF: Ch6.L3
TOP: Mid Ch Test
18. ANS:
STA: MM3A2a | MM3A2b
a.
b.
PTS: 1
REF: Ch6.L3
TOP: Mid Ch Test
19. ANS:
STA: MM3A2a | MM3A2b
a.
b.
PTS: 1
REF: Ch6.L3
TOP: Mid Ch Test
20. ANS:
a.
STA: MM3A2a | MM3A2b
b. The inverse is a function because the original cubic function is one-to-one.
PTS: 1
21. ANS:
a.
b.
REF: Ch6.L1
STA: MM2A5
TOP: End Ch Test
PTS: 1
TOP: End Ch Test
22. ANS:
REF: Ch6.L2
STA: MM3A2a | MM3A2b
REF: Ch6.L3
STA: MM3A2a | MM3A2b
REF: Ch6.L3
STA: MM3A2a | MM3A2b
a.
b.
PTS: 1
TOP: End Ch Test
23. ANS:
a.
b.
PTS: 1
TOP: End Ch Test
24. ANS:
a.
b.
The value of Zach’s account after 18 months will be $849.22.
c. I would graph the exponential function
and the linear function
on the same screen in
my graphing calculator. I would use my calculator to determine where the two graphs intersect. The point of
intersection is approximately (5.606, 1000). So, to the nearest tenth of a year, it would take about 5.6 years for the
value of the account to reach $1000.
PTS: 1
25. ANS:
a.
REF: Ch6.L6
STA: MM3A2g
TOP: End Ch Test
b.
The value of Nicole’s account after 4.5 years will be $1411.03.
c. I would graph the exponential function
and the linear function
on the same screen in
my graphing calculator. I would use my calculator to determine where the two graphs intersect. The point of
intersection is approximately (19.254, 2400). So, it would take about 19.3 years for the value of the account to
double.
PTS: 1
26. ANS:
REF: Ch6.L6
STA: MM3A2g
TOP: End Ch Test
a.
b.
There will be approximately 67.4 kg of Barium-140 left after 20 days.
c. I would graph the exponential function
and the linear function
on the same screen in
my graphing calculator. I would use my calculator to determine where the two graphs intersect. The point of
intersection is approximately (55.06, 10). So, there will be 10 kg of Barium-140 left after 55 days.
PTS: 1
REF: Ch6.L6
STA: MM3A2g
TOP: End Ch Test