3rd Quarter Test P.I. Review Homework
A2. Evaluate numerical
Evaluate each of the following. Show your work!
2
N.1 expressions with negative

 8 3
and/or fractional
exponents, without the aid
of a calculator (when the
3
answers are rational
 1 4
 
numbers)

 81 
1)
A2. Solve an application which
A.6 results in an exponential
function
Marisa invests $300 at a bank that offers 5% compounded continuously
according to the formula V  Pe
rt
where V is the value of the account in t years,
P is the principal initially invested, and r is the rate of interest. How long will it
take the investment to double? Round to the nearest year. (Solve
algebraically.)
2)
A2. Apply the rules of
A.8 exponents to simplify
Simplify the following expression:
expressions involving
negative and/or fractional
exponents

4x 4 y 8

1
2
x 10 y 4
3)
A2. Rewrite algebraic
A.9 expressions that contain
negative exponents using
only positive exponents
Simplify the following expression using only positive exponents:
x 3 y 2
x 4 y
4)
A2. Rewrite algebraic
Rewrite the following as a radical expression:
1
A.10 expressions with fractional
3
5
xy
exponents as radical
expressions
 
5)
A2. Rewrite algebraic
Rewrite the following using exponents instead of radicals:
A.11 expressions in radical form
16x 4 y 3
as expressions with
fractional exponents
6)
1
A2. Evaluate exponential
A.12 expressions, including
those with base e
Using your calculator, evaluate the following expression to the nearest
hundredth:
A2. Evaluate logarithmic
A.18 expressions in any base
Evaluate the following expression. Show your work.

7e  11
2
3
4
7)
log 2 8  4 log 3
1
9
8)
A2. Apply the properties of
A.19 logarithms to rewrite
logarithmic expressions in
equivalent forms
Expand the following logarithm:

 Solve for x:
3log5 2  log5 7  log5 x
9)
A2. Solve exponential equations Solve for x: 9 2 x  27 x 2
A.27 with and without common
bases
Solve for x to the nearest hundredth:
2100  5(2) x  400
10)
2
 xy 
log  3 
 z 


A2. Solve a logarithmic
Solve the following equation:
A.28 equation by rewriting as an
exponential equation
4log3 (2 x  7)  8
Solve the following equation to the nearest tenth: ln  4 x   ln 8  2
11)
x
A2. Graph logarithmic
Graph y  2 and its inverse. Find the equation of
A.54 functions, using the inverse the inverse. Be sure to solve for y.
of the related exponential
function
12)
A2. Solve trigonometric
A.68 equations for all values of
the variable from 0° to
360°
Solve the following equation where 0°<x<360°. Round to the nearest degree.
5cos x  8  7
13)
Assuming x is an acute angle, find the measure of x to the nearest minute.
A2. Use inverse functions to
A.64 find the measure of an
 Sin(x)=.6870
angle, given its sine, cosine,
or tangent

Tan(x)=4.7
14)
3
Round each of the following values to the nearest ten thousandth.
A2. Determine the
A.66 trigonometric functions of
any angle, using technology  Sin(63°20’)=
15)
A2. Restrict the domain of the Why is it necessary to restrict the domain of sine, cosine, and tangent to
A.63 sine, cosine, and tangent
ensure the existence of their inverse functions? What are the restricted
functions to ensure the
domains for each of the three functions?
existence of an inverse
function
16)
A2. Sketch the graph of the
A.65 inverses of the sine, cosine,
and tangent functions
Identify each of the three graphs.
17)
A2. Solve for an unknown side In
A.73 or angle, using the Law of
Sines or the Law of Cosines
,
,
, and
. Find AC to the nearest tenth.
Note: This PI includes any
type of word problem we
learned that involves using
the trig. laws.
In
degree.
,
,
, and
18)
4
. Find
to the nearest tenth of a
A2. Determine the area of a

A.74 triangle or a parallelogram,
given the measure of two
sides and the included
angle
Find the area of a triangle to the nearest square meter if two sides are 7m
and 9m and the included angle is 56°20’. Round to the nearest tenth.
 Find the area of the
parallelogram.
19)
A2. Determine the solution(s)
A.75 from the SSA situation
(ambiguous case)
If
,
, and
constructed?
, how many distinct triangles that may be
20)
A2. Differentiate between
S.9 situations requiring
permutations and those
requiring combinations
Decide if a permutation or combination is better for each situation.
 Picking a team captain, pitcher, and shortstop from a group.

Picking three team members from a group.

Picking two colors from a color brochure.

Picking first, second and third place winners.

Picking three winners.
21)
A2. Calculate the number of
How many different ways can you arrange the letters in the word, Applebees?
S.10 possible permutations (nPr)
of n items taken r at a time
22)
5
A2. Calculate the number of

S.11 possible combinations (nCr)
of n items taken r at a time
I own 16 different shirts and 8 pairs of pants. How many different sets of
clothes consisting of 5 shirts and 3 pairs of pants could I bring on vacation?
 15 
 
10
 Calculate:  
23)
A2. Use permutations,

S.12 combinations, and the
Fundamental Principle of
Counting to determine the
number of elements in a
sample space and a specific
subset (event)
Jacob’s five favorite candies are Milky Way, Three Musketeers, Skittles,
Star Burst, and Reeces Pieces. If he has one of each, in how many
different orders can he eat the candy?

In how many different orders can he eat the candy if he wants to eat the
Skittles first and either the Star Burst or Three Musketeers second?

Find the probability that a dart hits in the circular target given that it hits
somewhere on the square board. The radius of the circle is 5 cm and the
length of a side of the board is 30 cm. Round to the nearest percent.

If the probability that a person wins their first race is
24)
A2. Calculate theoretical
S.13 probabilities, including
geometric applications
probability they win their second race is
1
, what is the probability they
4
lose the first race and win the second race?
25)
6
2
and the
5
A2. Calculate empirical
S.14 probabilities
Jane gets 13 heads on 20 coin flips. What is Jane’s empirical probability that
of getting heads based on those trials. Compare this to the theoretical
probability of getting heads on a coin toss. Do you think the difference could
happen by chance?
26)
A2. Know and apply the binomial The probability of rain on any day in April is 45%.
 What is the probability that it rains exactly three days this week?
S.15 probability formula to
events involving the terms
exactly, at least, and at
most
Round to the nearest
percent.
 What is the probability it rains at most three days this week?

What is the probability it rains at least three days this week?
27)
A2. Know and apply sigma
N.10 notation
Find the value of: 2
3
3
n
( n  1)
n 1
28)
3
A2. Apply the binomial theorem
Expand using the binomial theorem:  3 x  5 
A.36 to expand a binomial and

determine a specific term
of a binomial expansion
Work for 2nd problem:
 What is the middle term in the expansion of
29)
a)
b)
7
c)
?
d)
A2. Determine amplitude,
A69 period, frequency, and
 
 
 ?
2 
 

d)
right
2
 What is the phase shift in the equation y  100 cos  3  x 
phase shift, given the
a) 100 left
graph or equation of a
b) 100 right
periodic function
c)

left
2
30)
 Which of the following graphs represents sec(x)? Identify the other three graphs.
A2. Sketch and recognize the
A.71 graphs of the functions
y=sec x, y = csc x, y = tan x,
y = cot x
31)
A2. Write the trigonometric
A72 function that is
represented by a given
Write the equation of the following 2 trigonometric functions.

periodic graph

32)
8
A2. Sketch and recognize one
A70 cycle of a function of the

Sketch one period of the graph y = -3cos(2x)
form y =A sinBx or
y=AcosBx
Find the following values for y = -3cos(2x):
amplitude:
period:
frequency:
domain:
range:
33)
9
(Don’t forget your tables!!!)