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Chapter 7 Test Review (Pre-AP)
Pre-AP Algebra II – Chapter 7 Test Review
Standards/Goals:
 A.CED.2.: I can create exponential equations with two variables.
 G.2.a./F.IF.7.e.: I can graph exponential functions showing both their intercepts and end behavior,
while considering both the domain and range of the relation/function.
 G.2.a./F.BF.4.a: I can write equations and expressions using logarithms.
 G.2.a./F.LE.4.: I can solve an exponential and logarithmic equations.
 G.2.a./F.IF.8.:
o I can write an exponential function utilizing transformations that will affect its graph.
o I can solve real-life problems using exponential equations.
 G.2.a./G.2.b./F.LE.4.:
o I can solve an equation with a natural logarithm.
o I can simplify an expression with a natural logarithm.
 G.2.b./F.IF.7.e.: I can graph logarithmic functions.
 G.2.b./F.BF.4.a:
o I can write equations and expressions using logarithms.
o I can convert exponential equations to logarithmic form and logarithmic equations back into
exponential form.
 (Pre-Calculus Standard: F.2.b.)/ F.LE.4:
o I can expand and condense logarithms using the product, quotient, and power properties.
o I can evaluate logarithms using the change of base formula.
Recognizing exponential growth vs. exponential decay.
 Be able to identify what an exponential growth equation/function looks like
 Be able to identify the y-intercept in an exponential equation.
#1. Write the standard form here and be able to identify its parts and how its graph will look:
#2. Be able to identify what an exponential decay equation/function looks like.
#3. Be able to distinguish what the graph of growth vs. decay functions look like.
o What type of function is shown: f(x) = 5 ?
o Which of the following is an exponential growth function?
#1. M(t) = - 9.0
OR
#2. M(t) = 9.0
Use the properties of logarithms to condense the following expression as much as possible, writing the
answer as a single term with a coefficient of 1. All exponents should be positive.
#4.
#5.
#6. 4 ln 7 – ln 9
#7. 2 log 7 + 3 log 3
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Chapter 7 Test Review (Pre-AP)
Use the change of base formula and your calculator to evaluate the following logarithmic expressions:
Round your answer to TWO decimal places.
#8.
#9.
#10.
⁄
#11. Write the exponential equation
in its logarithmic form.
#12. What property is being illustrated below:
Compare each function as a transformation of its parent function. (Identify its
transformations.) State the y-intercept of each.
#13. y = -5·(7)x – 2+18
#14. y = − (9) x + 1 + 18
#15. y = -2 e x -5 – 1
Compare each function as a transformation of its parent function. (Identify its
transformations.) Additionally, state the domain and range of each.
#16. y = - 7 ln (x – 7)
#17. y = - ¾ log2 x + 14
#18. y = 0.75 log4 (x +1) – 6
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Chapter 7 Test Review (Pre-AP)
#19. Consider the following: f(x) =
a. Name the domain and range of the function:
b. Find a formula for the inverse
, if possible.
c. Name the domain and range for the inverse
.
#20. Consider the following: f(x) =
a. Name the domain and range of the function:
b. Find a formula for the inverse
, if possible.
c. Name the domain and range for the inverse
.
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Chapter 7 Test Review (Pre-AP)
STEM PROBLEMS:
#21. Consider the following situation:
A certain species of deer is to be introduced into a forest, and wildlife experts estimate the
( ⁄ )
population will grow according to P(t) =
where ‘t’ represents the
number of years from the time of introduction.
a. What is the TRIPLING TIME for this population of deer?
b. How long will it take for the population to reach 6822 deer, according to this model?
#22. Mr. Andersen put $1000 into an account that earns 4.5% annual interest. The interest is
compounded annually and there are no withdrawals. How much money will be in the account
at the end of 30 years?
#23. A manufacturer bought a new rolling press for $48,000. It has depreciated in value at an
annual rate of 15%. What is its value 5 years after purchase? Round to the nearest hundred
dollars.
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Chapter 7 Test Review (Pre-AP)
#24. In June, a rural South American town was hit by an earthquake with a magnitude of 7.9 on
the Richter scale. The same town was hit by another earthquake with a magnitude of 6.1 in
August. How many times more intense was the earthquake in June? Use the formula:
to solve the problem.
#25. Given the following problem.
The concentration
of a certain drug in the bloodstream after minutes is given by the
formula
What is the concentration after 20 minutes? Round to 3
decimal places.
#26. Given the following problem.
Dolores invests $7100 in a new savings account which earns 5.3% annual interest, compounded
continuously. What will be the value of her investment after 3 years? Round to the nearest
cent.
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Chapter 7 Test Review (Pre-AP)
#27. Consider the following:
a. What is the vertex of this quadratic?
b. What is the axis of symmetry?
c. What is the minimum or maximum value?
d. What is the domain and range of this function? Write answers in interval form and set
form, as well.
e. What is the y-intercept? Write answer in coordinate form.
f. What is the discriminant value and how many real and how many imaginary solutions
will it have?
g. What are the solutions/x-intercepts to the equation?
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Chapter 7 Test Review (Pre-AP)
#28. Consider the functions:
√
h(x) = √
g(x) =
√
m(x) = √
a. What is the exact value of f(-10)? Simplify your answer completely.
b. What is the domain of f(x)?
c. Find the domain of m(h(x)).
d. What is the domain of g(x)?
e. Find h(g(20)).
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Chapter 7 Test Review (Pre-AP)
#29. Solve the following minimization/maximization problem. Reduce all fractions to the
lowest terms.
A rancher has 600 feet of fencing to put around a rectangular field and then
subdivide the field into 2 identical smaller rectangular plots by placing a fence
parallel to one of the field's shorter sides.
Step 1: Find the dimensions that maximize the enclosed area.
Step 2: Find the maximum area of the rectangle in Step 1
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Chapter 7 Test Review (Pre-AP)
#30. Solve the equation and write answer as a simplified logarithm.
#31. Solve the equation and write answer as a simplified logarithm.
#32. Write an equivalent form of: 7 ln w – 5 ln y + 8 ln z.
#33. If
and
√
well as the domain of g( f(x) )?
√
#34. Write the following in logarithmic form:
, then what is the domain of each function, as
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Chapter 7 Test Review (Pre-AP)
Solve each equation:
#35.
#36.
#37.
#38.
Expand the following logarithms.
#39. log
#41. log
#40. log
√
#42. Log √