PRE-CALCULUS
Second Semester Review Problems
Lesson 6.1.1 Solving Trig Equations
1.
Solve the given equation on the domain [0, 2 ] .
a.
2.
2 cos x  3  0
b.
2 sin x  2  0
c.
3 tan x  3
4 cos x  1  1
c.
3 tan x   3
c.
cos   0
Solve the given equation for all values of x.
a.
2 sin x  2  3
b.
Lesson 6.1.2 Inverse Sine and Cosine
  if it is defined.
1.
Find the exact value of cos1 12
2.
Find the exact value of sin1  12 if it is defined.
3.
Evaluate the given equation for  in radians. Give exact answers.
 
a.
cos   1
b.
sin  
1
2
4.
Solve the given equation for 0  x  2 . Round answers to three decimal places.
a.
5.
sin x  0.7
b.
cos x  0.2
c.
sin x  0.4
Solve the given equation for   x   . Round answer to three decimal places.
a.
cos x  0.9
b.
sin x  0.6
c.
cos x  0.3
Lesson 6.1.3 The Ambiguous Case of the Law of Sines
1.
In ABC , A  22º , a  6, and b  12 . There are two possibilities for the remaining
measurements of the triangle. Calculate the measurements of each possible triangle.
2.
In ABC , A  35º , a  9, and b  10 . There are two possibilities for the remaining
measurements of the triangle. Calculate the measurements of each possible triangle.
3.
In ABC , B  33º , a  15, and b  10 . Determine the missing measurements of all possible
triangles.
4.
In ABC , B  24º , b  20, and c  35 . Determine the missing measurements of all possible
triangles.
Lesson 6.1.4 Graphs of Tangent and Inverse Tangent
1.
Find the angle of inclination that the given line makes with the x-axis.
a.
y
2
3
x4
b.
y  2  53 (x  4)
c.
2x  7y  5




2.
Use what you know about the graph of f (x)  tan x to graph f (x)  tan x  4  1 .
3.
Use what you know about the graph of f (x)  tan x to graph f (x)  tan x  3  2 .
4.
Use what you know about the graph of f (x)  tan1 x to graph f (x)  tan1 (x  2)  1 . What
are the domain and range?
5.
Use what you know about the graph of f (x)  tan1 x to graph f (x)  tan 1 (x  3)  2 . What
are the domain and range?
Lesson 6.2.1 Graphing y  a sin b(x  h)  k
1.
Graph the given equation.
a.
y  2 cos 2(x   )   1
b.
y  2 sin
c.
y  3 cos 2 (x  1)   2
d.
y  2 sin
2 (x  2) 1
 x    1
1
2
3
Lesson 6.2.2 Angle Sum and Difference Formulas
1.
Use the angle sum or difference formula to find the exact value of the given expression.
a.
2.
cos 105º
b.
c.
sin 165º
tan(15º )
Use the angle sum or difference formula to simplify the given expression and find its exact value.
a.
sin 74º cos 14º  cos 74º sin 14º
b.
cos 12º cos 18º  sin 12º sin 18º
3.
Find the exact value of sin(x  y) if sin x  45 in Quadrant II and tan y  12
in Quadrant III.
5
4.
5
Find the exact value of cos(x  y) if cos x  53 in Quadrant I and sin y   13
in Quadrant III.
5.
Prove that sin(  x)  cos(  x)  sin x  cos x .
Lesson 6.2.3 Modeling With Periodic Functions
1.
Write the equation of a sinusoidal function that rises from a minimum point at (4, 6) to a
maximum point at (7, 11).
2.
Write the equation of a sinusoidal function that rises from a minimum point at (–2, –1) to a
maximum point at (3, 9).
3.
The center of a Ferris wheel is 40 feet off of the ground and the wheel has a radius of 30 feet. If it
takes 7 minutes to make one complete revolution, write a sinusoidal equation to model the height of
a rider above the ground, assuming they get on at the bottom.
4.
The amount of daylight each day in Fairbanks, Alaska can be modeled sinusoidally. The maximum
amount of daylight is 21.8 hours and occurs on June 21st(t = 172). The minimum amount of
daylight is 3.7 hours and occurs on December 21st (t = 355). Write an equation to model the
situation using time in days and t = 1 as January 1st.
Lesson 6.3.1 Double- and Half-Angle Formulas
1.
Find the exact value of the given trig expression.
a.

sin 13
12
b.
cos 58
2.
Find sin 2b if tan b   43 and cos b  0 .
3.
Find tan 2x if cot x  2 and   x  32 .
4.
Find cos 2x if tan x   43 and 2  x   .
5.
Use a double-angle or half-angle formula to simplify the given expression.
a.
1cos 6x
2
b.
cos2 8x  sin2 8x
c.

tan 11
12
c.
2 sin 4x cos 4x
Lesson 6.3.2 Solving More Complex Trig Equations
1.
Find the solutions to the given trig equation for 0  x  2 .
a.
sin2 x  sin x  cos2 x
b.
tan x cos x  cos x
c.
sin2 x  cos x  1  0
d.
2 sin x cos x   sin x
2.
Use the trig formulas you have learned to simplify or expand the given trig equation and then solve
for all values of x.
a.
cos 4x cos x  sin 4x sin x 
c.
cos 2x  3 sin x  2
1
2
b.
sin 2x  sin x  0
d.
sin 5x cos 3x  cos 5x sin 3x  1
Lesson 6.1.1 Answers
1.
a.
x
5
6
2.
a.
x

6
, 76
 2 n,
5
6
 2 n
b.
x

b.
x

2.
 6
4
3
, 34
 2 n,
5
3
 2 n
c.
x

c.
x
5
6
c.

2
Lesson 6.1.2 Answers
1.

3
3.
a.

b.

6
4.
a.
x = 0.775, 2.366
b.
x = 1.369, 4.914
c.
x = –0.412 = 5.872, 3.553
a.
x  2.69  2 n, 3.593  2 n
b.
x  0.644  2 n, 2.498  2 n
c.
x  1.266  2 n, 5.017  2 n
5.
3
, 43
 n
Lesson 6.1.3 Answers
1.
B  48.5º , C  109.5º , c  15.1 or B  131.5º , C  26.5º , c  7.15
2.
B  39.6º , C  105.4º , c  15.13 or B  140.4º , C  4.6º , c  1.26
3.
A  54.8º , C  92.2º , c  18.3 or A  125.2º , C  21.8º , c  6.8
4.
A  110.6º , C  45.4º , a  46 or A  21.4º , C  86.6º , a  17.94
Lesson 6.1.4 Answers
1.
a.
33.7º
b.
59.04º
y
2.
4
2
x
–2
–4
c.
–15.95º
3.
y
4
2
x
–2
–4
4.
y
x
5.
y
x
Lesson 6.2.1 Answers
1.
a.
b.
y
y
4
4
2
2
x
x
2
–2
–2
–4
–4
4
y
c.
d.
2
y
4
1
x
1
2
x
2
–1
–2
–2
–4
Lesson 6.2.2 Answers
2 6
4
6 2
4
1.
a.
b.
2.
a.
3.
4
15
4.
 14
15
5.
sin(  x)  cos(  x) 
(sin  cos x  cos  sin x)  (cos  cos x  sin  sin x) 
(sin x)  ( cos x) 
sin x  cos x
3
2
c.
2  3
3
2
b.
* sin   0, cos   1
Lesson 6.2.3 Answers
3 (x  4) 8.5
y  2.5 sin 3 (x  5.5)  8.5
1.
y  2.5 cos
2.
y  5 cos
3.
h(t)  30 cos
5 (x  2) 4
h(t)  30 sin
4.
27 t  40





or y  5 cos 5 (x  3)  4 or y  5 sin 5 (x  0.5)  4


or h(t)  30 cos 27 (t  3.5)  40 or
27 (t  1.75) 40
2
(t  10)  16.45
365
2
y  12.75 sin 365
(t  91)  16.45
y  12.75 cos

or y  2.5 cos 3 (x  7)  8.5 or


2
or y  12.75 cos 365
(t  172)  16.45 or
Lesson 6.3.1 Answers

2 3
2
1.
a.
2.
 24
25
3.
 94 5
4.
5.
2 2
2
b.

b.
cos16x
b.
x
2.
 74 3
c.
sin 8x
5
5
a.
sin 3x
Lesson 6.3.2 Answers
1.
c.
, 32 , 4 , 54
x

c.
x
3
2
d.
x  0,  , 23 , 43
a.
x

b.
x  0,  , 3 , 53
c.
x
7
6
d.
x
6
9
, 56 , 2

a.
, 59
, 116 , 32
2

4
Lesson 7.1.1 Describing Functions: Increasing, Decreasing, Concavity
1.
State the intervals on which the given function is increasing, decreasing, concave up, and concave
down.
a.
b.
y
y
f(x)
f(x)
x
x
2.
Sketch the graph of a function that contains the points (–3, 1), (1, –2), and (5, 3), is only increasing
on (–1, 3), and only concave up on (, 2) .
3.
Sketch the graph of a function that contains the points (–3, 5), (0, –4), and (4, 6), is decreasing on
(, 0) and (5, ) , and is concave up on (, 3) .
4.
Sketch the graph of a function that has a vertical asymptote at x  3 , a horizontal asymptote at
y  2 , contains the points (1, 1) and (4, –3), and is concave down only on
(3, ) .
5.
Sketch each function and determine the intervals on which it is increasing, decreasing, concave up,
and concave down.
a.
2

 (x  3)  2   x  1
f (x)  
 (x  1)2  6 1  x  

b.
 (x  4)2  4   x  2
f (x)  
2
2  x  
 x  4
c.
 x  3  2   x  1
f (x)  
1 x  
 (x  3)  6
Lesson 7.1.2 Describing Functions: Even and Odd
1.
Determine if the given function is odd, even, or neither.
a.
f (x)   x 2  2
b.
x 5 (x  1)
c.
3x 3  1x
2.
Is the graph of the function shown below even, odd, or neither?
y
a.
b.
y
x
x
y
y
c.
d.
x
3.
x
Part of the graph of f (x) is shown. Complete the graph on the interval 10  x  10 so that it
has the specified features. There are many possible correct graphs. Be creative!
a. period = 11, odd for 4  x  4
b. period = 12, even for 4  x  4
y
y
x
c. period = 10, odd for 4  x  4
x
d. period = 10, even for 4  x  4
y
y
x
x
Lesson 7.2.1 Setting up Word Problems
1.
A rectangle is inscribed in a circle with a radius of 10 m. The area of the rectangle is 160 m2.
What is the perimeter of the rectangle?
2.
A sheet of metal is twice as long as it is wide. 1.5 inch squares are cut out of each corner so that it
can be formed into an open-topped box. If the area of the original piece of sheet metal is 98 cm2,
what will the volume of the box be?
3.
A 26-foot ladder is 14 feet further up a wall than its foot is away from the base of the wall. How
high up the wall is the ladder?
4.
Find a function which models the surface area S of a cube in terms of its volume V.
5.
A farmer has 600 meters of fencing and wants to make two side-byside rectangular enclosures as shown in the diagram. What is the
maximum area that he can enclose?
Lesson 7.2.2 Using “u” Substitution
1.
Solve.
a.
(n2  1)2  15(n2  1)  50  0
b.
(m2  2)  2(m2  2)  63  0
c.
4(x  5)  3 x  5  1
d.
2(x  3)4  7(x  3)2  30
2.
Solve the system.
a.
 5 x  5 y  10
 x
 25  25 y  75
b.
 2 x  2 y  12
 x
 4  4 y  48
c.
 log 3 A  log 5 B  3

 log 3 A  log 5 B  1
d.
 2 log 2 M  log 3 N  0

 5 log 2 M  3 log 3 N  2
Lesson 7.2.3 Polynomial Division
1.
5 4
3
2
Find the quotient and remainder of 5x  x 6xx16x 2x6 .
2.
3
2 2x17
Find the quotient and remainder of x 6xx5
.
3.
3 x 2  x6
Find the quotient and remainder of x 4x2
.
4.
5  x 4 5
Find the quotient and remainder of 6x x1
.
5.
Find the quotient and remainder when P(x)  x 4  x 2  5x  1 is divided by x  1 .
Lesson 7.2.4 The Binomial Formula and Pascal’s Triangle
 .
5
1.
Use Pascal’s triangle to expand 1y  y
2.
4
Use Pascal’s triangle to expand 3  x3 .
3.
 3 y4 
Use the Binomial theorem to expand and simplify the first 4 terms of  x2  6 
y
x 
4.
Find the term containing x 8 in the expansion of (y  2x)14 .
5.
4
Find the coefficient of the term containing x 5 in the expansion of x25  53
x




18
12
.
.
Lesson 7.1.1 Answers
1.
a.
Inc. (3, ) , Dec. (, 3)
b.
Inc. (, 1)  (2, ) , Dec. (1, 2)
Con. up (, 1)  (2, )
Con. up (0.5, )
Con. down (1, 2)
Con. down (, 0.5)
2.
Possible sketch:
3.
Possible sketch:
4.
y
y
y
x
x
5.
a.
Possible sketch:
y
b.
f(x)
y
x
c.
f(x)
f(x)
y
x
x
x
Inc. (, 3)  (1, )
Inc. (4, 0)
Inc. (3, 3)
Dec. (3,1)
Dec. (, 4)  (0, )
Dec. (, 3)  (3)
Con. up (1, )
Con. up (, 2)
Con. up (,1)
Con. down (, 1)
Con. down (2, )
Con. down (1, )
Lesson 7.1.2 Answers
1.
a.
even
b.
neither
2.
a.
odd
b.
neither
c.
even
d.
neither
c.
odd
3.
a.
Sample answer:
b.
Sample answer:
y
y
x
3.
c.
x
Sample answer:
b.
Sample answer:
y
y
x
x
Lesson 7.2.1 Answers
1.
53.6 meters
2.
66 cm3
3.
24 feet
4.
S6
5.
15,000 m2
3 V 
2
Lesson 7.2.2 Answers
1.
2.
a.
n  2, 3
b.
m   11
c.
79
x   16
d.
x  9, 
a.
(1.332, 0.237), (0.237, 1.332)
b.
(3, 2)
c.
(9, 5)
d.
14 , 81
2.
x3  x  3 
4.
6x 4  5x 3  5x 2  5x  5
2.
81  36x  6x 2 
4.
768768y6 x 8
1
2
Lesson 7.2.3 Answers
1.
5x 4  4x 3  10x 2  4x  6 
3.
x 2  2x  3
5.
x 3  x 2  2x  3 
12
x1
2
x5
2
x1
Lesson 7.2.4 Answers

1.
1
y5
3.
x 36
y24
5.
31824
125x 5
5
y3
 10y  10y  5y 3  y5
 12
x 27
y18
 66
x18
y12
 220
x9
y6
4
9
1 x4
x 3  81
Lesson 8.1.1 Limits at Infinity
1.
2.
Identify the dominant term in each of the following expressions.
a.
5x 3  4x 6  2x 2  1
b.
45x 3  27x 5  2x 8
c.
x 6  5x 2
d.
12x  4x 2  x 5  3
e.
53  3x 7  4x 2  5x
f.
17x  3 x 3
lim 3500(4 x )  5 x
c.
Evaluate the following limits.
a.
lim 12x 3  1.2 x
b.
x
d.
lim  3x 2  42 log x
x
e.
lim 15 x  x
x
x
lim 5  4x  x 2
lim x  4 x 5
f.
x
x
Lesson 8.1.2 Limits of Rational Functions (at infinity)
1.
Evaluate the given limits.
a.
lim
(x 2 1)(x 2 1)
x (2 x 2  3)(2 x 2 5)
b.
3x 2  x2
x 5 x 2  4 x1
c.
lim
3x 3 x 2
x (x1)3
d.
7x 3  x
x (2x1)(3x 2 1)
e.
x2  4
x
x 3  x1
f.
4 x 2  3x1
x 2 3x 2
lim
lim
lim
lim
2.
3.
Find the first five terms of the recursively-defined sequence.
a.
1 ; a 0
an1  1a
1
b.
mn1  3(mn  2); m1  1
c.
pn1  5   pn  ; p1  1
d.
kn1  (2kn )(1  kn1 ); k1  1, k2  3
n
2
Find the first five terms of the recursively-defined sequence. Then write a formula for the sequence
that is not recursive.
a.
bn1  bn  5, b1  3
b.
bn1  bn  12 , b1  8
Lesson 8.1.3 Limits of Rational Functions (at a point)
1.
Evaluate the given limits.
a.
lim
x 2 25
x5 x5
b.
x 2 9
x3 1  1
3 x
c.
lim
x1
x1 x 2 1
d.
x 2 9
2
x3 2 x  7 x 3
e.
11
4 x
x4 x 4
f.
x 3 8
x2 x 2  4
lim
lim
lim
lim
Lesson 8.2.1 The Number e
1.
Evaluate each expression without using a calculator.
a.
ln e4
ln 1
e
b.
eln
c.
ln 5 x  ln 5 x1
d.
2 ln er
eln 1/ 

7
Lesson 8.2.2 Applications of e
1.
Suppose $500,000 was invested with a 4% interest rate for a period of 20 years. What difference
would there be in the final value of the investment if the interest was invested continuously instead
of monthly?
2.
$3,000 was invested for 8 years with the interest compounded continuously. If the investment is
worth $7,700 at the end of 8 years, what was the interest rate?
3.
How long will it take any investment to quadruple if it earns 5.6% interest, compounded
continuously?
4.
A 32 gram sample of radioactive iodine decays in such a way that the mass m (grams) remaining
after t days is given by:
m(t)  32e0.089t
a.
After how many days are there only 14 grams remaining?
b.
What is the half-life of the iodine?
Lesson 8.1.1 Answers
1.
2.
a.
4x 6
b.
2x 8
c.
x6
d.
x5
e.
3x 7
f.
3 x3
a.

b.

c.

d.

e.

f.

Lesson 8.1.2 Answers
1.
2.
3.
a.
1
4
b.
3
5
c.
3
d.
7
6
e.
0
f.
4
3
a.
2, –1, 12 , 2, –1
b.
–1, –9, –33, –105, –321
c.
2, 1, 4, –9, –116
d.
1, 3, 12, 96, 2496
b.
8, 4, 2, 1, 12
3, –2, –7, –12, –17
bn  5n  8
bn  8
12 
n1
Lesson 8.1.3 Answers
1.
a.
10
b.
54
c.
1
2
d.
6
5
e.
1
 16
f.
3
Lesson 8.2.1 Answers
1.
a.
–4
b.
7
c.
ln 5
d.
2 r
Lesson 8.2.2 Answers
1.
$1480.42
2.
11.78%
3.
24.76 years
4.
a.
9.3 days
b.
7.79 days
Lessons 9.1.3 and 9.1.4 Slope, Average Velocity, and Rates of Change
1.
2.
3.
A car travels such that its distance from home is d(t)  3t 2  2 miles for t  1 to t  7 hours of
travel.
a.
Calculate the average rate of change for each 1-hour interval.
b.
Use the information from part (a) to find a formula for the velocity of car at any time t.
A ball is thrown off the top of a building and lands on the ground below. The function
h(t)  16t 2  64t  48 gives the ball’s height in feet with respect to time in seconds.
a.
When will the ball hit the ground?
b.
Make a table of time versus height. Use 1-second increments. Use the table to sketch a
graph of the function over the interval that fits this situation.
c.
Find the average velocity for each 1-second time interval that the ball is in the air.
d.
What is happening to the average velocity of the ball with respect to the time?
e.
What does the average velocity tell you about the change in position of the ball?
A rocket is launched off of a platform such that its height is determined by the function
h(t)  16t 2  128t  4 , where time is in seconds.
a.
When will the rocket hit the ground?
b.
Make a table of time versus height. Use 1-second increments. Use the table to sketch a
graph of the function over the interval that fits this situation.
c.
Find the average velocity for each 1-second time interval that the ball is in the air.
d.
What is happening to the average velocity of the ball with respect to the time?
e.
What does the average velocity tell you about the change in position of the ball?
4.
Determine the average rate of change for the function 2x 2  x between x  3 and x  3  h .
Simplify your answer completely.
5.
Determine the average rate of change for the function f (x)  x 2  6x between x  2 and
x  2  h . Simplify your answer completely.
6.
Determine the average rate of change for the function f (x)  1x  2x between x  5 and
x  5  h . Simplify your answer completely.
7.
A man standing on a bridge drops a coin into a water fountain from a height of 105 ft. The height
of the coin with respect to time is given by the function h(t)  105  16t 2 , where t is in seconds
and t  0 . Find the average speed of the coin for the first 2 seconds after it is dropped. What is
the average speed of the coin between 2 seconds and the time it takes to hit the water?
Lessons 9.2.1 and 9.2.2 Finding Slope at a Point and Slopes of Tangent and
Secant Lines
1.
2.
3.
Let f (x)  5x  3x  1 .
a.
Calculate the average rate of change of f (x) from x  3 to x  4 .
b.
Find the average rate of change of f (x) from x  5 to x  5  h .
c.
Evaluate the expression in part (b) as h  0 . What does this tell you about the function at
x  5?
Let f (x)  2 x  x .
a.
Calculate the average rate of change of f (x) from x  3 to x  4 .
b.
Find the average rate of change of f (x) from x  9 to x  9  h .
c.
Evaluate the expression in part (b) as h  0 . What does this tell you about the function at
x  9?
Let f (x)  3x 2  4 .
a.
Calculate the average rate of change of f (x) from x  10 to x  12 .
b.
Find the average rate of change of f (x) from x  11 to x  11  h .
c.
Evaluate the expression in part (b) as h  0 . What does this tell you about the function at
x  11 ?
4.
Find the slope of the line tangent to the graph of y  x 2  3x  1 at the point (4, 29).
5.
Find the slope of the line tangent to the graph of y  x  3x 2 at the point (–1, –4).
6.
Find the slope of the line tangent to the graph of y  2x  3x at x  1 .
7.
Find a formula for the slope of a secant line for any interval from x  a to x  b for the function
f (x)  x 2 .
Lessons 9.3.2 and 9.3.3 Finding Instantaneous Velocity and Slope Functions
1.
Let f (x)  x  x . Calculate the average rate of change on the interval [x, x  h] . Then find the
instantaneous rate of change by taking the limit as h  0 .
2.
Let f (x)  2x  2x 2 . Calculate the average rate of change on the interval [x, x  h] . Then find
the instantaneous rate of change by taking the limit as h  0 .
3.
Let f (x)  12 x  x 2 . Calculate the average rate of change on the interval [x, x  h] . Then find
the instantaneous rate of change by taking the limit as h  0 .
4.
A particle moves in a straight line with its position give by the equation s(t)  t 2  3t  5 , where
s is measured in feet and t is measured in seconds. Find the velocity at any time t = a by using
the formula:
s(ah)s(a)
h
h0
lim
5.
A stone is dropped into a pond causing a ripple in the water. Find the rate of change of the area A
of the circle with respect to the radius when r  3.5 ft.
Lesson 9.3.4 The Definition of a Derivative
1.
2.
3.
Find the derivative of the given function.
a.
f (x) 
c.
e.
x1
x
b.
2
x
f (x)  3x 2  2x  1
d.
f (x)  (x  1)(x  2)
f (x)  5x
f.
f (x)   5x
Let f (x)  5x 2 .
a.
Compute f (3) .
c.
How and why are your answers to parts (a) and (b) related?
Let f (x)   4x .
b.
Compute f (3) .
4.
5.
a.
Compute f (3) .
c.
How and why are your answers to parts (a) and (b) related?
b.
Compute f (3) .
A small car travels according to a distance function d(t)  3t 2  7t  5 for 0  t  10 .
a.
Find a function to model the velocity at any time t.
b.
Find the velocity of the car at t  5 seconds.
A small car travels according to a distance function d(t)  2t 2  5t  4 for 0  t  10 .
a.
Find a function to model the velocity at any time t.
b.
Find the velocity of the car at t  5 seconds.
Lessons 9.1.3 and 9.1.4 Answers
t interval
d(t) change
1.
2.
1-2
9
a.
b.
v(t)  6t
a.
At t  4.65 seconds.
2-3
15
3-4
21
4-5
27
5-6
33
6-7
39
b.
3.
See graph at right.
t
h(t)
0
48
1
96
2
112
3
96
4
48
t
 h(t)
0-1
48
1-2
16
2-3
–16
3-4
–48
4-5
–80
5
–32
c.
d.
It is decreasing by 32 over each interval. It changed from
positive to negative after 2 seconds.
e.
Positive velocity indicates that the ball is rising for 2 seconds. The velocity then changes to a
negative value indicating that the ball is falling.
a.
At t  8.03 seconds.
b.
See graph at right below.
t
h(t)
c.
0
4
t
 h(t)
1
116
0-1
112
2
196
1-2
80
3
244
2-3
48
4
260
3-4
16
5
244
4-5
–16
d.
It is decreasing by 32 over each interval. It changed
from positive to negative after 4 seconds.
e.
Positive velocity indicates that the ball is rising for 4
seconds. The velocity then changes to a negative
value indicating that the ball is falling.
6
196
5-6
–48
7
116
6-7
–80
8
4
7-8
–112
9
–140
8-9
–144
4.
AROC = 11 + 2h
5.
AROC = 10 + h
6.
1
AROC = 2  5(5h)
7.
0 - 2 seconds: AROC = 32 ft/sec
2 - 2.56 seconds: AROC = 73 ft/sec
Lessons 9.3.2 and 9.3.3 Answers
1.
2.
AROC = 1 
lim AROC  1 
1
x  xh
h0
AROC = 2  4 x  2h
1
2 x
lim AROC  2  4x
h0
3.
AROC = 12  2x  h
4.
2a  3
5.
7
lim AROC 
h0
1
2
 2x
Lesson 9.3.4 Answers
1.
a.
f (x)  
c.
f (x)  6x  2
e.
f (x) 
1
x2
5
5x

5x
x
b.
f (x)  
d.
f (x)  2x  1
f.
f (x) 
5
x2
1
x x
2.
3.
a.
–30
c.
The graph is a parabola that is symmetric across the y-axis. Therefore the slopes at the
corresponding points x and –x will also be opposite.
a.
4
9
b.
b.
30
4
9
c.
The graph is symmetric about the origin, therefore the slopes of the corresponding points x
and –x will be the same. Or, if you rotate the tangent line 180º, it will still have the same
slop.
4.
a.
v(t)  6t  7
b.
23
5.
a.
v(t)  4t  5
b.
15
Lesson 10.1.1 Introduction to Vectors
1.
Use the diagram at right to answer the questions below.
q
2.
a.
Find the component form of each vector.
b.
Draw q + s and state the component form of the resultant vector.
s
Use the diagram at right to answer the questions below.
a
a.
Find the component form of each vector.
b.
Draw a + b and state the component form of the resultant vector.
b
g
h
3.
Use the diagram at right to answer the questions below.
a.
Find the component form of each vector.
b.
Draw g + h and state the component form of the resultant vector.
Lesson 10.1.2 Working With Vectors
1.
2.
3.
Draw the vector c = 2i – 3j.
a.
Find the magnitude and direction of c.
b.
Find a unit vector with the same direction as c.
c.
Add 12 c and –2c to your drawing.
Draw the vector d = –i + 2j.
a.
Find the magnitude and direction of d.
b.
Find a unit vector with the same direction as d.
c.
Add 3d and –2d to your drawing.
Use the diagram at right to answer the questions below.
k
m
l
a.
4.
Find the component form of each vector below.
i.
k – 2l
ii.
3m + 4k
iii.
1
l
3
b.
Find a vector with the same magnitude as k but a different direction.
c.
Find a vector with the same direction as m, but a different magnitude.
Use the diagram at right to answer the questions below.
a.
n
Find the component form of each vector below.
p
r
5.
i.
n – 2p
ii.
3r + 4n
iii.
1
p
3
b.
Find a vector with the same magnitude as r but a different direction.
c.
Find a vector with the same direction as n, but a different magnitude.
Find the component form of the given vector.
a.
magnitude = 5, direction = 135º
b.
magnitude = 7, direction = 240º
Lesson 10.1.3 Applications of Vectors
1.
A jet is flying at 400 mph on a course with a bearing of 30º. If the jet experiences a crosswind
blowing due south at 20 mph, find the resultant speed and direction of the jet.
2.
A plane is flying at 530 mph on a course with a bearing of 55º. If the wind is blowing at 40 mph
with a bearing of 125º, find the resultant speed and direction of the plane.
3.
A boat is trying to cross a straight river that is 2 miles wide. The speed of the boat is 25 mph, but
the current is pushing the boat downstream at 17 mph. How long will it take the boat to cross the
river and how far downstream from the original starting point will the boat end up?
4.
A plane flies 620 miles from Q to W with a bearing of 320º. It then flies 580 miles from W to R
with a bearing of 200º. How far will the plane need to fly to return to Q and with what bearing?
5.
Given the forces F1  10, 3 , F2  4,1 , and F3  5, 8 acting on point P, find the
resultant force, its magnitude, and direction.
Lesson 10.1.1 Answers
q+s
q
1.
2.
a.
q = 2, 3 , s = 4, 1
b.
See diagram at right.
a.
a = 3, 2 , b = 2, 3
s
q + s = 2, 2
b
a+b
a
3.
a + b = 1, 5
b.
See diagram at right.
a.
g = 1, 5 , h = 1, 5
b.
See diagram at right.
g
g + h = 2, 0
h
g+h
c
c
Lesson 10.1.2 Answers
–2c
1.
See diagram at right.
a.
c.
b.
13
2 13
13
i
3 13
13
j
See diagram at right.
d
3d
2.
See diagram at right.
a.
3.
4.
–2d
b.
5
c.
See diagram at right.
a.
i.
4, 4
ii.
48, 9
iii.
5 ,0
3
b.
Answers vary.
a.
i.
9, 11
ii.
21, 4
6, 4

5
5
i  2 55 j
c.
Answers vary.
2, 8
0, 2
iii.
b.
5.
a.
Answers vary.

5 2
2
4, 5
c.
, 5 22
b.
Lesson 10.1.3 Answers
1.
382.2 mph with a bearing of 31.5º
2.
545 mph with a bearing of 59º
3.
0.08 hours = 4.8 minutes, 1.36 miles downstream
4.
601 miles with a bearing of 83.3º
97  9.85 with a bearing of 246º
5.
Lesson 11.1.1 Plotting Polar Coordinates by Hand
1.
Using a polar grid, plot the given points.
a.
A  2, 23


b.
B  1, 6

c.
C  4, 53


d.
D  3, 74



Answers vary. 18, 2
 27 , 
7 3
2
e.
2.

E  5,  4

f.

F  2,  56

Identify each of the polar coordinates on the given polar graph.
a.
b.
A
A
B
B
D
3.
4.
C
D
C
Find two other ways to write the given (polar) point in polar coordinates.


a.
A  6, 34
c.
C  2, 54




b.
B  3,  6
d.
D  3,  23


Transform each of the given rectangular coordinates to polar coordinates.
a.
A  (3, 3)
c.
C  5 3, 5




b.
B  2, 2 3
d.
D  4, 4 3


5.
Simplify.
a.
 25
b.
c.
7  27
d.
9
4
8 36
2
Lesson 11.1.2 Graphs of Polar Equations (Calculator)
1.
2.
Sketch the curve for the given polar equation using your graphing calculator.
a.
r  2  4 cos 
b.
r  3  5 sin 
c.
r
d.
r  134sin 
6
32 cos 
Simplify.
12  i 
a.
(2  5i)  (4  3i)
b.
2i
c.
(6  3i)2
d.
(2  5i)(4  3i)
Lesson 11.1.3 Rotating Polar Graphs and Transforming Equations
1.
Transform the given equation from rectangular form to polar form.
a.
y  2x 2  5x
b.
y  2x  1
c.
2.
4.
x  3y2  2y
4x  y  5
d.
Transform the given equation from polar form to rectangular form.
a.
r  2 sin 
b.
r  4 cos   0
c.
r
d.
r tan   3r 2 cos 
b.
2 4
2 4
d.
35i
15i
7
3 sin  2 cos 
Simplify.
a.
c.
8 64
32
5
43i
Lesson 11.2.1 Graphing Complex Numbers
1.
2.
Plot the given complex number and state the absolute value of the number.
a.
5  4i
b.
3  7i
c.
9i
d.
1 8i
Find the polar form of the given complex number.
3.
a.
z  1 i
b.
z  1  ( 3)i
c.
z  3  (3 3)i
d.
z  i(1  ( 3)i)
Find the rectangular form of the given complex number. Use exact values.
    i sin   
b.
z  2 cos
    i sin   
d.
z  4 cos
a.
z  8 cos
c.
z  7 cos
3
4
3
4
2
3
2
3
    i sin   
7
6
7
6
    i sin   
11
6
11
6
Lesson 11.2.2 Powers and Roots of Complex Numbers
1.
2.
z
Given z1 and z2 , find z1z2 and z1 . Express your answer in both trigonometric and a  bi form.
2
   i sin  , z  4 cos    i sin  
 3 cos   i sin  , z  9 cos    i sin   
 25 cos    i sin   , z  5 cos   i sin  
a.
z1  12 cos
b.
z1
c.
z1
3
2
5
6
4
3
3
4
2
2
5
6
4
3
2
3
2
3
4
3
3
Use DeMoivre’s Theorem to find the given complex number.
a.
( 3  i)4
b.
(2  2i)16
c.
(3  3 3i)7
Lesson 11.1.1 Answers
D
1.
A
See diagram at right.
F
B
C
E
2.
3.
a.
 
A  2, 3
B  4,  
 
D  2,  6 
C  3, 54
d.
a.
A  3 2, 34
c.
C  10,  6
a.
c.
c.
5.
b.
  

B  3, 116 , 3, 56 , 3,  76 
C  2, 4 , 2,  74 , 2,  34 
D  3, 3 , 3,  53 , 3, 43 
a.
b.
4.
 
B  2, 56 
C  4, 43 
D  3,  3 
A  5, 6
A  6,  54 , 6, 74 , 6,  4




 
b.
B  4, 3
d.
D  8, 43
5i
b.
3
2
7  3i 3
d.
4  3i

i

Lesson 11.1.2 Answers
1.
a.
b.
c.
d.
y
x
2.
a.
2  8i
b.
2i
c.
27  36i
d.
23  20i
Lesson 11.1.3 Answers
1.
2.
a.
r
3 sin 
cos2 
b.
r
1
2 cos  sin 
c.
r
2 cot 
3
d.
r
5
4 cos  sin 
a.
x 2  (y  1)2  1
b.
(x  2)2  y2  4
3.
4.
c.
2x  3y  7
a.
d.
y  3x 2
3r  2 tan   6  1
b.
3sin   43  4r cos   43  5
c.
r
d.
8 cos   34  1  tan   34
e.
tan   23  5
f.
r
a.
–4
b.
–i
c.


3
   
2 sin   5 cos   5
6
6


2015i
7
d.








10
3

4 cos  
7 sin   3
5
5
53i
15
   
 13  15 i
Lesson 11.2.1 Answers
1.
y
(b)
(c)
2
See graph at right.
(a)
2.
3.
(d)
a.
41
b.
58
c.
82
d.
65
    i sin   
    i sin   
a.
z  2 cos
c.
z  6 cos
a.
z  4 2  (4 2 )i
b.
z   3i
c.
z   27 
d.
z  2 3  2i
7
4
7
4
    i sin    d.
4
3
7 3
2
4
3
i
b.
z  2 cos
2
3
2
3
   i sin  
z  2 cos
3
3
x
Lesson 11.2.2 Answers
1.
2.
a.
z1z2  48cis
53  24  (24
b.
z1z2  27cis
54   272 2  272 2 i,
z1
z2

c.
z1z2  125cis
76   1252 3  1252 i,
z1
z2
 5cis
a.
16cis
b.
224 cis(12 )  224 cis(0)  224
c.
6 7 cis
3)i,
223  16cis 43  8  (8
z1
z2
 3cis( )  3
1
3
 
cis  4 
2
6

2
6
i
2  5i
3)i
3  627  672 3 i
Lesson 12.1.1 Basic Matrix Operations
1.
4
 1 3 1 
 6  , C   7 9  , and D   4
B

If A  
,

 3 8 
 7
 
 2 0 5 



 3 
0
, find each of the
5 3 
2
following matrices or write “impossible.”
a.
A B
b.
3C
c.
CD
d.
DA
e.
BD
f.
AB
2.
9 3 
 3 1 
 1 1 


If A  
 , B   0 2  , C  5 1 2 , and D   2 8  , find each of the
8
4




 1 4 
following matrices or write “impossible.”
3.
4.
a.
A B
b.
3C
c.
CD
d.
DA
e.
BD
f.
AB
3 2
a b 
and G  

.
4
c d 
Let F  
5
a.
Find FG .
b.
Find values for a, b, c, and d such that FG  I .
 2 1 
a b 
and G  

.
3 
c d 
Let F  
5
a.
Find FG .
b.
Find values for a, b, c, and d such that FG  I .
Lesson 12.1.2 Solving Systems Using Matrices
1.
Write the given system as a matrix equation and then solve it using an inverse matrix.
a.
 4 x  7y  6

 3x  5y  5
c.
 x  2y  z  2

 2x  3y  5z  4
 4x  8y  3z  13

b.
 5x  2y  27

 2x  5y  6
d.
 3x  y  5z  14

 2z  4
 x
 7x  2y  15z  26

Lesson 12.1.3 Applications of Matrices
1.
Tickets to a school play cost different amounts for students, adults, and senior citizens. At Friday’s
performance there were 121 students, 184 adults, and 32 senior citizens with ticket sales of $1779.
At Saturday’s performance there were 183 students, 160 adults, and 25 senior citizens with tickets
sales of $1769. At Sunday’s performance there were 127 students, 189 adults, and 54 senior
citizens with ticket sales of $1920. What was the price of each type of ticket?
2.
A toy company knows from past sales that during the month of October they will sell
approximately 152 of Toy A, 200 of Toy B, and 327 of Toy C. During November they will sell
approximately 137 of Toy A, 234 of Toy B, and 126 of Toy C. During December they will sell
approximately 125 of Toy A, 257 of Toy B, and 91 of Toy C. If they would like their sales to total
approximately $17,000 each month, how much should they sell each type of toy for?
3.
Wayne has $1, $5, and $10 bills in his wallet worth $137. There are as many $10 bills as $1 and $5
bills combined and he has 22 bills in all. How many of each denomination of bill does Wayne have
in his wallet?
4.
Erin is getting ready for a triathlon. During three different days of training she recorded the
following data: Swimming for half an hour, cycling for 1 hour, and running for 45 minutes covered
a total distance of 21.2 miles. Swimming for 40 minutes, cycling for 75 minutes, and running for 1
hour covered a total distance of 27 miles. Swimming for 45 minutes, cycling for 65 minutes, and
running for 50 minutes covered a total distance of 23.4 miles. What is Erin’s average speed for
each event?
5.
An investor has decided to invest his $1,000,000 in three different types of bonds. The municipal
bonds pay 4.7% annual interest, the corporate bonds pay 6% annual interest, and the short-term
bonds pay 4.2% annual interest. After 1 year the bonds have accumulated a total of $458,750 in
interest. If the investor placed twice as much in municipal bonds as in corporate bonds, how much
did she invest in each type of bond?
Lesson 12.2.1 Using Matrices to Complete Linear Transformations
1.
Find the image of each of the following points after transformation by the given matrix.
Points: (3, –5), (–8, 5), and (–4, –7)
a.
2.
3.
 4
 –2

9
4 
b.
 0 9
 –3 5 


c.
 4 –2 
 –1 7 


Find the transformation matrix that takes:
a.
(–6, –7) to (14, –10) and (–2, 3) to (–6, 2).
b.
(–5, 5) to (–5, –25) and (1, –8) to (–6, 54).
c.
(–2, –5) to (–37, 35) and (–8, 1) to (–1, 35).
Find the matrix associated with rotating counterclockwise through the given angle.
a.
60º
b.
135º
c.
270º
Lesson 12.2.2 Composition of Transformations
1.
2.
a.
Find the matrix that would double the distance a point is from the origin.
b.
Find the matrix that would rotate a point 45º counterclockwise.
c.
Find the matrix that would rotate a point 45º counterclockwise and double its distance from
the origin.
a.
Find the matrix that would rotate a point 120º counterclockwise.
b.
Find the matrix that would triple the distance a point is from the origin.
c.
Find the matrix that would rotate a point 120º counterclockwise and triple its distance from
the origin.
3.
Find a matrix that will reflect a point across the y-axis and double its distance from the origin.
4.
Find a matrix that will triple the distance a point is from the origin and reflect it across the x-axis.
Lesson 12.2.3 Properties of Transformations
1.
2
The linear transformation M is described by 
0
0
.
2
1
a.
Describe the effect of M on any point p  (x, y) .
b.
Geometrically describe the linear transformation M.
c.
Find M 1 .
2.
3.
4.
5.
 1 0 
.
2 
The linear transformation M is described by 
0
a.
Describe the effect of M on any point p  (x, y) .
b.
Geometrically describe the linear transformation M.
c.
Find M 1 .
 1 3
.
1 
Find the image of the four points (2, 0), (–3, 0), (2, 4), and (–3, 4) by the matrix M  
0
a.
Graph the original points.
b.
Graph the image.
c.
Geometrically describe the linear transformation M.
1
Find the image of the four points (–1, 3), (–3, 0), (1, 0), and (3, 3) by the matrix M   1

a.
Graph the original points.
b.
Graph the image.
c.
Geometrically describe the linear transformation M.
2
0
.
1 
 3 1 
x
and let a and b be of the form   .

2
y
Let M  
 4
a.
Find a vector a such that Ma  a .
b.
Find a vector b such that Mb  2b .
6.
3
Let M  
 1
a.
1 
and let a and b be of the form
3 
Find a vector a such that Ma  2a .
x
y .
 
b.
Find a vector b such that Mb  4b .
Lesson 12.1.1 Answers
a.
impossible
b.
 21 27 
 9 24 


c.
26
 81
 68 34

d.
 5 6 1 
 9 5 8 


e.
impossible
f.
 25 
7
 
a.
 2 0 
 8 2 


b.
15
c.
45
d.
impossible
e.
impossible
f.
 3 5 
 8 16 


3.
a.
 3a  2c 3b  2d 
 5a  4c 5b  4d 


b.
a  2, b  1, c   52 , d 
4.
a.
 2a  1c 2b  1d 
 5a  3c 5b  3d 


b.
a  3, b  1, c  5, d  2
1.
2.
3 6 
3
2
1
27 
24 
Lesson 12.1.2 Answers
1.
a.
c.
4 7 x  6 
 3 5   y    5 

   
x  65, y  38
 1 2 1   x   2 
 2 3 5   y    4 

   
 4 8 3   z   13 
x  5, y  3, z  3
b.
d.
 5 2   x   27 
 2 5   y    6 

   
x  7, y  4
 3 1 5   x   14 
 1 0 2   y    4 

  

 7 2 15   z   26 
x  8, y  0, z  2
Lesson 12.1.3 Answers
1.
student = $3, adult = $7, senior citizen = $4
2.
Toy A  $63.45 , Toy B  $34.88 , Toy C  $1.16
3.
$1 bills = 7, $5 bills = 4, $10 bills = 11
4.
swim = 1.37 mph, bike = 15.2 mph, run = 7.09 mph
5.
municipal = $482,142, corporate = $241, 071, short-term = $276,785
Lesson 12.2.1 Answers
1.
a.
(–2, 7), (22, –52), (30, –64)
c.
(17, –18), (–37, 51), (–9, –41)
b.
(15, 2), (–15, –47), (21, –71)
2.
a.
0

 2
3.
a.
 12

  3 2
1
2

1
3
1
2
2



b.
 2 2 
 1 7 


b.


 
2
2
2
2
c.
 1 5 
 7 5 




 2 2 
c.
 0 1 
1 0 




2 
2
c.
 2

  2
2

2 
3 3
c.
  32

  3 3 2
2
2
Lesson 12.2.2 Answers
1.
a.
2 0 
0 2 


  12

  3 2
2.
a.
3.
 2 0 
 0 2


4.
3 0 
 0 3 


b.


 1 2 
3
2
b.


 
2
2
2
2
2
3 0
0 3


2


 3 2 
Lesson 12.2.3 Answers
1.
a.
(x, y)  (2x, 1 2 y)
b.
It is a horizontal stretch by a factor of 2 and a vertical compression by a factor of 2 (or a
vertical stretch by a factor of ½).
2
2.
3.
c.
 1 0
M 1   2

 0 2
a.
(x, y)  (x, 2y)
b.
It is a reflection across the y-axis and a vertical stretch by a factor of 2.
c.
 1
M 1  
0
0
1 
2
original
y
(2, 6), (3, 9), (2, 10), (3, 5)
image
x
a, b. See graph at right. It is scaled by 2’s.
c.
4.
It is a vertical shearing. Students may say that it is
stretched vertically. Stretched up when x is positive and
stretched down when x is negative.
original
y
( 1 2 , 3), (3, 0), (1, 0), (4 1 2 , 3)
image
x
a, b. See graph at right.
c.
It is a horizontal shearing. Students many say that it is
stretched horizontally. Stretched to the right when y is
positive and to the left when y is negative.
5.
a.
Any vector of the form   .
 4n 
6.
a.
Any vector of the form   .
n 
 n 
n 
n 
b.
Any vector of the form   .
n 
b.
Any vector of the form   .
 n 
 n 
Lesson 13.1.1 Circles
1.
2.
Find the equation of the circle(s) described below.
a.
C  (3, 6), r  12
b.
C  (2, 7), r  5 3
c.
C  (4, 2) and goes through (3, 1)
d.
C  (5, 1) and goes through (–2, 3)
e.
Diameter with endpoints (–5, –7) and (7, 7)
f.
Diameter with endpoints (2, 0) and (5, –3)
g.
C  (3,1) and tangent to the line x  8
h.
C  (8, 9) and tangent to the line y  1
Find the center and radius of the given circle.
a.
(x  2)2  (y  8)2  4
b.
(y  1)2  (x  3)2  48
c.
x 2  y2  16x  12y  88
d.
x 2  y2  12x  6y  53
3.
A circle is centered at (4, 8) and has an area of 294 . Find the equation of the circle.
4.
A circle is centered at (3, –7) and tangent to the line y  x  4 . Find the equation of the circle.
5.
A circle containing the point (8, 1) is tangent to the y-axis at the point (0, –3). Find the equation of
the circle.
Lesson 13.1.2 Ellipses
1.
For the given ellipse(s), find the center, the lengths of the major and minor axes, the coordinates of
the foci, and sketch the graph.
a.
(x3)2
16
c.
(y2)2
25
b.
(x4)2
8
9x 2  16y2  144
d.
12x 2  9y2  108
e.
4x 2  9y2  16x  20  0
f.
x 2  6y2  4x  60y  136  0
g.
12x 2  5y2  24x  30y  39  0
h.
1
36

1

(x2)2
4
1
1 y2  1 x  9 y  153  1
x 2  25
2
25
50
2.
Find the equation of the ellipse with foci at (3, 7) and (3, –1) and a minor radius of 3.
3.
Find the equation of the ellipse with vertices at (5, 2) and (–7, 2) and focal point (4, 2).
4.
Find the equation of the ellipse that has a center at (–2, –5), a focal point of (2, –5), and a major
axis of length 7.
5.
An ellipse is tangent to the x- and y-axes. The length of the major axis is 10 and a focal point is
(8, –4). Find the equation of the ellipse.
Lesson 13.1.3 Hyperbolas
1.
2.
For the given hyperbola(s), find the center, the equations of the asymptotes, the coordinates of the
foci, and sketch the graph.
b.
(y1)2
36
4x 2  8x  12  4y2
d.
4x 2  y2  8x  6y  21  0
e.
x 2  4y2  2x  16y  51
f.
y2  4x 2  2y  16x  19
g.
2y2  4x 2  12y  8x  6  0
h.
x 2  16y2  4x  160y  400  0
a.
(x2)2
9
c.

(y2)2
25
1

(x3)2
16
1
Find the equation of the hyperbola opening vertically, with asymptotes of y  2x and a vertical
major axis of length 8.
3.
Find the equation of the hyperbola with vertices at (–3, 4) and (–3, 0) and focal points at
(–3, 6) and (–3, –2).
4.
Find the equation of the hyperbola with focal points at (–1, 0) and (–1, 4) on the minor axis which
is of length 2.
5.
Find the equation of the hyperbola with focal points at (–4, –4) and (4, –4) on the minor axis which
is of length 6.
Lesson 13.1.4 Parabolas
1.
For the given parabola(s), find the vertex, focus, directrix, and sketch the graph.
a.
20x  y2
b.
1 x2
y   16
c.
12(y  1)  (x  3)2
d.
16(y  3)  (x  5)2
e.
y  (x  5)2  4
f.
x  4(y  4)2  2
g.
y  x 2  2x  3
h.
x 2  4x  8y  36  0
2.
Find the equation of the parabola with the focus at (7, –1) and directrix of x  5 .
3.
Find the equation of the parabola with the vertex at (6, –2) and directrix of y  9 .
4.
Find the equation of the parabola with the vertex at (–2, –4) and the focus at (3, –4).
5.
Find the equation of the parabola with the vertex at (–4, 3), containing the point (–6, 11).
Lesson 13.1.1 Answers
1.
a.
(x  3)2  (y  6)2  144
b. (x  2)2  (y  7)2  75
2.
c.
(x  4)2  (y  2)2  58
d. (x  5)2  (y  1)2  65
e.
(x  1)2  y2  85
f.
g.
(x  3)2  (y  1)2  25
h. (x  8)2  (y  9)2  64
a.
C  (2, 8), r  2
b. C  (3, 1), r  4 3
c.
C  (8, 6), r  2 3
d. C  (6, 3), r  7 2
3.
(x  4)2  (y  8)2  294
4.
(x  3)2  (y  7)2  18
5.
(x  5)2  (y  3)2  25
x  27   y  23   92
2
2
Lesson 13.1.2 Answers
y
y
1.
a.
b. C  (4, 2)
C  (3, 2)
x
M  10, m  8
F  (3, 5), (3, 1)
M  4 2, m  4
F  (6, 2), (2, 2)
y
c.
C  (0, 0)
M  8, m  6
F  ( 7, 0), ( 7, 0)
x
y
d. C  (0, 0)
x
x
M  4 3, m  6
F  (0, 3), (0,  3)
y
x
e.
C  (2, 0)
M  6, m  4
f.
y
M  6 2, m  2 3
x
F  (2  5, 0)
g.
C  (1, 3)
M  4 3, m  2 5
F  (1, 3  7 )
C  (2, 5)
F  (2  15, 5)
y
y
h.
x
C  (9, 4.5)
M  12, m  10
F  (9  11, 4.5)
*Graph is scaled by 3’s.
x
2.
(x3)2
9

(y3)2
25
1
3.
(x1)2
36

(y2)2
11
1
4.
(x2)2
49

(y5)2
33
1
5.
(x5)2
25

(y4)2
16
1
Lesson 13.1.3 Answers
1.
a.
C  (2, 2)
y
b.
y   53 (x  2)  2
C  (3, 1)
y   23 (x  3)  1
x
F  (8, 2), (4, 2)
*Graph is scaled by 2’s.
y
y
C  (1, 0)
y  (x  1)
x
d.
F  (1  2 2, 0)
e.
C  (1, 2)
y   12 (x  1)  2
F  (1  3 5, 2)
*Graph is scaled by 2’s.
x
F  (3, 1  2 13)
*Graph is scaled by 2’s.
c.
y
C  (1, 3)
y  2(x  1)  3
x
F  (1  2 5, 3)
f.
y
x
C  (2, 1)
y  2(x  2)  1
y
x
F  (2, 1  5 )
y
C  (1, 3)
g.
h.
x
y   2(x  1)  3
y2
16
3.
(y2)2
4

(x3)2
12
1
4.
(y2)2
1

(x1)2
3
1
5.
x2
9


x2
4
y
y   14 (x  2)  5

F  (1, 3  6 )
2.
C  (2, 5)
F  2 
17
2
,5
x

1
(y4)2
7
1
Lesson 13.1.4 Answers
y
y
1.
a.
V  (0, 0)
F  (5, 0)
D : x  5
b.
V  (0, 0)
F  (0, 4)
D: y 4
x
*Graph is scaled by 2’s.
*Graph is scaled by 2’s.
y
y
c.
C  (3, 1)
F  (3, 4)
D : y  2
*Graph is scaled by 2’s.
x
d.
x
V  (5, 3)
F  (5, 7)
D: y 1
*Graph is scaled by 2’s.
x
y
y
V  (5, 4)
e.

F  5, 4
1
4
x

f.
D : y  3 43
*Graph is scaled by 2’s.
V  (2, 4)
F  (3, 4)
D : x  1
x
*Graph is scaled by 2’s.
y
y
V  (1, 2)
g.

F  1, 2
1
4

D : y  1 43
h.
x
V  (2, 4)
F  (2, 8)
D: y0
*Graph is scaled by 2’s.
2.
x
1
4
(y  1)2  6
3.
y
1
28
(x  6)2  2
4.
x
1
20
(y  4)2  2
5.
y  2(x  4)2  3
x