Download Week of July 5th

HONORS PRECALCULUS SUMMER 2013
Week of July 5th
4.
22 in.
Problem of the week:
Suppose a group of people is purchasing merchandise. If each
person contributes six coins, there is an excess of two coins. If
each person contributes five coins, there is a deficit of one
coin. How many people are in the group? What is the price of
the merchandise?
Skill Practice
15 in.
18 in.
44 in.
Solve.
1.
Not drawn to scale
a.
5.
a. 98
b. 100
c. 9
b.
c.
d.
b.
c.
d.
c.
d.
d. 11
Simplify the expression.
2.
J
2.
4 in.
a. –19
b. –1
c. 15
d. 9
a.
Find the area of the figure
Find the volume of the figure.
3.
7.6 cm
5m
2.7 cm
a.
Not drawn to scale
b.
4m
6.
c.
d.
a.
Not drawn to scale
b.
HONORS PRECALCULUS SUMMER 2013
Find the slope of the line.
Simplify the expression.
9. 9.
y
8
a.
b.
c.
d.
Simplify. Write the answer in standard form.
10. 10. (3g2 – 8g – 4) – (6g2 + 4g – 5)
a. 9g2 – 12g + 9
c. –3g2 – 12g + 1
b. 9g2 + 12g – 1
d. –3g2 + 12g + 1
11. 11.
a.
c.
b.
d.
12. Factor the expression..
a. (x + 2)(x + 7)
c. (x – 2)(x + 7)
b. (x + 2)(x – 7)
d. (x – 2)(x – 7)
6
4
2
7.
–8 –6 –4 –2
–2
2
4
6
8
x
–4
–6
–8
a. 1
b. 2
c. 1
d. 6

2
6
8. Find the midpoint M of the segment with the endpoints shown.
y
(–6, 7)
8
4
–8
–4
(2, 3)
4
8
x
–4
–8
a. M(–4, 5 )
b. M(2 , 10)
c. M(2 , 5 )
d. M(–4, 10)
Week of July 12th
Problem of the Week:
The word “ABRACADABRA” means something like
“complicated nonsense.” We use the word contemptuously today,
but there was a time when it was a magic word, engraved on
amulets in mysterious forms, like that below. In how many ways
can you trace the word “ABRACADABRA” in the figure below?
A
B
B
R
R
R
A
A
A
A
C
C
C
C
C
A
A
A
A
A
A
C
C
C
C
C
A
A
A
A
R
R
R
B
B
A
HONORS PRECALCULUS SUMMER 2013
5.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
5. A leaky valve on the water meter overcharges the residents for one gallon
1. Make a mapping diagram for the relation.
{(–3, 1), (0, 6), (3, 2), (5, –1)}
time t. Find the equation that models this direct variation. How many
months it will take for the residents to be overcharged for 9 gallons of water?
a.
of water every
a.
c.
–3
0
3
5
–1
1
2
6
b.
–3
1
3
2
0
6
5
–1
–3
0
3
5
1
6
2
–1
d.
–3
0
3
5
–1
2
6
1
months. The overcharged amount w varies directly with
; 2
b.
c.
7
months
10
d.
7
months
10
6. What is the slope of the line that passes through the given points?
6. (8, 7) and (5, 7)
a. 0
c. undefined
b. 13
d. 14
14
13
7. What is an equation of the line in slope intercept form?
; 30 months
y
2. 2. For
a. 0
,
b. –12
.
c. 9
8
d. 12
4
3. Specialty t-shirts are being sold online for $15 each, plus a one-time handling
fee of $2.25. The total cost is a function of the number of t-shirts bought.
What function rule models the cost of the t-shirts ( )? Evaluate the function
for 3 t-shirts.
–8
–4
4
8
x
–4
a.
c.
; $21.75
; $47.25
b.
d.
; $47.25
; $21.75
Determine whether y varies directly with x. If so, find the constant of
variation k.
4. y + 2x = – 19
a. yes; 2
b. yes; 2
c. yes; 1
d. no
; 30 months
–8
7.
a.
b.
c.
d.
; 2
HONORS PRECALCULUS SUMMER 2013
What is the graph of the equation?
8.
a.
11. What are the intercepts of the equation? Graph the equation.
11. You are trying to compare the Fahrenheit and Celsius scales and you have two
examples: Temperature A is –20 degrees Celsius and –4 degrees Fahrenheit.
Temperature B is 60 degrees Celsius and 140 degrees Fahrenheit. What graph
models the relationship between the Fahrenheit and Celsius scales? What is
an equation of the line in slope-intercept form?
c.
y
–8
y
8
8
4
4
–4
4
8
–8
x
–4
4
–4
–4
–8
–8
b.
8
x
a.
Fahrein.
d.
y
y
100
100
8
4
4
–8
–4
200
200
8
–8
Fahrein.
c.
4
8
x
–80
–4
4
8
–80
x
–40
40
Celsius
–200
–8
9. Write an equation of the line, in point-slope form, that passes through
the two given points.
9. points:
,
b.
1
2
–2

c.
d.
c.
d.
b.
d.
Fahrein.
Fahrein.
200
200
100
100
–2

1
2
10. What is the equation of the given line in standard form? Use
integer coefficients.
5
10.
7
a.
b.
Celsius
–200
–8
a.
40
–100
–100
–4
–4
–40
–80
–40
40
Celsius
–80
–40
–100
–100
–200
–200
40
Celsius
HONORS PRECALCULUS SUMMER 2013
What is the equation of the line in slope-intercept form?
12. the line parallel to
a.
through (5, 2)
c.
b.
13.

1
8
Study the patterns and then write the next two lines. Once this is
accomplished find the sum of each row.
Is there a pattern?
Solve the system by graphing.
d.
What is the equation of the absolute value function?
1. 1.
a.
13.
c.
y
y
4
4
20
y
2
2
16
12
–4
–2
8
–6
–4
–2
2
4
–2
x
O
2
4
x
2
4
x
–2
–2
–4
4
–12 –10 –8
–4
O
–4
x
–4
(3, –1)
–8
a. y =
b. y =
(–1, 3)
b
.
d
.
y
c. y =
d. y =
4
4
2
2
WEEK of July 19th
–4
Problem of the week:
Consider Pascal’s triangle:
1
1
1
2
1
1
3
3
1
1
4
6
4
1
1
5
10
10
5
1
–2
y
O
2
4
x
–4
O
–2
–2
–4
–4
(1, 3)
–2
(3, 1)
HONORS PRECALCULUS SUMMER 2013
3. 3.
2.
a
.
c
.
y
–4
–2
4
4
2
2
O
2
4
a. (2, 1)
b. (1, 2)
y
x
–4
–2
O
–2
–2
–4
–4
2
4
4. 4. A rental car agency charges a flat fee of $138.00 plus $27.00 per day to rent
a certain car. Another agency charges a fee of $47.00 plus $40.00 per day to
rent the same car.
Using a graphing calculator, find the number of days for which the costs are
the same. Round your answer to the nearest whole number of days..
x a. 11
c. 7
b. 10
d. 3
What are the solutions of the following systems?
5. 5.
a. (5, –6)
b. no solutions
(0, –3)
(–3, 0)
b
.
d
.
y
y
4
4
2
2
–2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
(3, 0)
(0, 3)
c. (–5, 6)
d. infinitely many solutions
6. 6.
a. infinitely many solutions
c. no solutions
b. (–5, 2)
d. (5, –2)
7. The length of a rectangle is 6.7 cm more than 2 times the width. If the
perimeter of the rectangle is 57.2 cm, what are its dimensions?
7.
–4
c. (–1, –2)
d. (–2, –1)
2
4
x
a. length = 21.3 cm; width = 7.3 cm c. length = 7.3 cm; width = 21.3 cm
b. length = 21.3 cm; width = 14 cm d. length = 7.9 cm; width = 14 cm
Solve the system by elimination.
8.
8.
Solve the system by using a table.
a. (2, 2, –2)
b. (–2, –2, –2)
c. (2, –2, –2)
d. (2, –2, 2)
HONORS PRECALCULUS SUMMER 2013
b.
d.
y
y
What is the solution of the system?
9.
6
6
4
4
2
2
a. (7, –4)
b. (–7, 4)
c. (7, 4)
d. (4, –7)
–6
–4
–2
2
4
6
–6
x
–4
–2
2
4
6
x
–2
–2
–4
10.
–4
–6
a. (4, 5)
b. (–4, –5)
–6
c. (5, 4)
d. (–4, 5)
WEEK of July 26th
2.
2.
a
.
Problem of the week:
Verify that the sum of the series:
1 + 2 + 3 + 4 + 5 + ⋯ . +(𝑛 − 1) + 𝑛 =
Show that the sum of the series:
3
3
3
3
3
3
1 + 2 + 3 + 4 + ⋯ (𝑛 − 1) + 𝑛 =
𝑛(𝑛+1)
2
y
if n=10
𝑛2 (𝑛+1)2
4
c
.
for n=7
y
6
6
4
4
2
2
What is the graph of the function?
–6
1.
a.
–4
–2
2
4
6
x –6
–4
–2
2
–2
–2
–4
–4
–6
–6
y
c.
6
y
6
4
4
2
2
–6
–4
translated to the left 5 unit(s)
–6
–2
2
4
6
x
–2
2
–2
–2
–4
–4
–6
–4
–6
4
4
6
x
translated down 5 unit(s)
4
6
x
HONORS PRECALCULUS SUMMER 2013
b
.
d
.
y
6
–6
–4
.
y
y
6
6
4
4
4
4
2
2
2
2
–2
2
4
6
x –6
–4
–2
2
4
6
–6
x
–4
–2
2
4
6
x –6
–4
–2
2
–2
–2
–2
–2
–4
–4
–4
–4
–6
–6
–6
–6
translated up 5 unit(s)
translated to the right 5 unit(s)
3.
4.
a
.
.
y
6
c
.
y
6
translated to the left 2 unit(s)
4
6
translated up 2 unit(s)
4.
c.
y
a.
6
y
6
y
4
4
6
2
2
4
4
2
–6
–4
–2
2
4
6
x
a.
–2
–6
–4
–2
2
4
6
2
x
–2
–4
–4
–6
–6
translated down 2 unit(s)
translated to the right 2 unit(s)
–6
–6
–4
–2
2
4
6
x
–2
d
2
4
6
–4
–4
–6
translated down 4 unit(s) and
translated to the right 3 unit(s)
translated down 4 unit(s) and
translated to the left 3 unit(s)
b
–2
–2
–6
b.
–4
d.
x
x
HONORS PRECALCULUS SUMMER 2013
–6
–4
b
.
y
y
d
.
y
y
6
6
4
4
6
6
2
2
4
4
2
2
–2
2
4
6
–6
x
–4
–2
2
–2
–2
–4
–4
4
6
–8 –6 –4 –2 O
–2
translated up 4 unit(s) and
translated to the right 3 unit(s)
translated up 4 unit(s) and
translated to the left 3 unit(s).
5. 5. Identify the vertex and the axis of symmetry of the graph of the function
.
a. vertex: (–2, 4);axis of symmetry:
b. vertex: (2, –4);axis of symmetry:
c. vertex: (–2, –4);axis of symmetry:
d. vertex: (2, 4);axis of symmetry:
6. Which is the graph of
a
8
.
c
.
y
6
4
4
2
2
–8 –6 –4 –2 O
–2
x –8 –6 –4 –2 O
–2
4
6
8
x –8 –6 –4 –2 O
–2
–4
–4
–6
–6
–8
–8
8.8. 8. (–2, –16), (0, –4), (4, –28)
a.
b.
c.
d.
What is the expression in factored form?
2
4
6
8
–4
–4
–6
–6
–8
–8
2
4
6
What is the equation, in standard form, of a parabola that contains the
following points?
8
6
2
7. Suppose a parabola has an axis of symmetry at
, a maximum height of 1
and also passes through the point (9, –1). Write the equation of the parabola in
vertex form.
a.
c.
b.
d.
?
y
8
x
–6
–6
8
2
4
6
8
x
9. 9.
a.
b.
c.
d.
10. 10.
a.
b.
c.
d.
8
x
HONORS PRECALCULUS SUMMER 2013
11.
17.
a.
b.
c.
d.
a
.
12.
a.
b.
c.
d.
13.
a.
b.
c.
d.
14.
a. 2, 4
b. –2, 2
15.
a.
b.
7
6
7

3
–6
–4
c.
d.

6
4
4
2
2
2
4
6
x –6
–4
–2
–2
–2
–4
–4
–6
–6
2
4
6
x
2
4
6
x
(–4, –3)
(–2, –1)
(–5, 3)
(–1, –1)
b
.
7
3
y
6
–2
=0
c. 5
,2
2
d.
5
2,
2
c
.
y
d
.
y
7
6
y
6
6
4
4
2
2
Use the Quadratic Formula to solve the equation.
–6
16.
a.
1
4
d.
–2
2
4
6
x –6
–4
–2
–2
–2
8
–4
–4
1
8
–6
–6
c.
8
b.
–4
(–5, –3)
(–1, 1)
(–4, 3)
(–2, 1)
HONORS PRECALCULUS SUMMER 2013
What is the solution of the linear-quadratic system of equations?
18.
a.
(–4, 1)
(–2, 3)
b. (1, –4)
(3, 2)
c.
(–4, 1)
(2, 3)
d. (1, –4)
(3, –2)
c. The leading term is
. Since n is odd and a is negative, the end
behavior is up and down.
d. The leading term is
. Since n is odd and a is negative, the end
behavior is down and up.
3. 3. What is the graph of
y
a
.
WEEK of August 2nd
Problem of the Week:
The figure
–4
The figure
consists of 5 triangles (4 that are 1X1X1 AND 1 that is 2X2X2)
many are there in the figure?
Multiple Choice
the choice that best completes the statement or answers the question.
1. Classify –2x4 – x3 + 8x2 + 12 by degree.
a. quartic
c. quadratic
b. quintic
d. cubic
Consider the leading term of each polynomial function. What is the end
behavior of the graph?
2.
a. The leading term is
. Since n is odd and a is negative, the end
behavior is down and down.
b. The leading term is
. Since n is odd and a is negative, the end
behavior is up and up.
4
2
2
2
4
x
–4
–2
–2
–2
–4
–4
b
.
d
.
y
–4
y
4
–2
Obviously consists of 1 triangle.
c
.
4
2
2
2
4
4
x
2
4
x
y
4
–2
2
x
–4
–2
–2
–2
–4
–4
HONORS PRECALCULUS SUMMER 2013
4. Graph
a
.
y
y
and describe the end behavior.
y
c
.
y
4
12
24
8
16
4
8
4
2
2
–6
–4
–6
–2
2
4
6
–4
–2
–4
–4
–2
2
4
x
–4
–2
2
–2
–2
–4
–4
4
b
.
b. 0, –2, 5
d. 2, –5, –2
The end behavior is down and up.
d
.
y
24
4
2
2
16
16
y
4
8
8
–6
–6
–4
–2
2
4
6
–4
–2
x
–8
–16
2
4
6
–8
–16
–24
–24
–4
–2
2
4
x
–4
–2
2
–2
–2
–4
–4
4
x
What are the zeros of the function? What are their multiplicities?
The end behavior is down and up.
The end behavior is up and down.
What is the degree of the polynomial that generates the given data?
What are the zeros of the function? Graph the function.
5.
a. 2, –5
c. 0, 2, –5
x
–24
24
y
6
–12
y
The end behavior is up and down.
4
–16
–8
x
2
–8
x
6. 6.
a.
b.
c.
d.
the numbers 1, –4, and 0 are zeros of multiplicity 2
the numbers –1, 4, and 0 are zeros of multiplicity 2
the numbers –1, 4, and 0 are zeros of multiplicity 1
the numbers 1, –4, and 0 are zeros of multiplicity 1
x
HONORS PRECALCULUS SUMMER 2013
7. The design of a digital box camera maximizes the volume while keeping the
sum of the dimensions at 4.5 inches. If the length must be 1.5 times the
height, what should each dimension be?
a. height: 1.2 in., length: 1.8 in., width: 1.5 in.
b. height: 1.2 in., length: 1.5 in., width: 1.8 in.
c. height: 1.8 in., length: 1.2 in., width: 1.5 in.
d. height: 1.5 in., length: 1.8 in., width: 1.2 in.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. 1. Find all the real square roots of 0.0004.
a. 0.00632 and –0.00632
c. 0.0002 and –0.0002
b. 0.06325 and –0.06325
d. 0.02 and –0.02
2. 2. Find all the real square roots of
What are the real or imaginary solutions of each polynomial equation?
.
a. no real root
c.
b.
d.
8.
a. 6, –6, 2, –2
b. 6, –2
c. 6, –6
d. no solution
What are the real or imaginary solutions of the polynomial equation?
and
3. Find the real-number root.
3.
9.
a.
b. 2,
c. 2,
d. 2,
and
, and
, and
, and
a. 1.3
b. 2.86
c. 0.85
d. no real number root
4. 4.
Divide using synthetic division.
10. Divide
a.
b.
by (
a.
b.
c.
d.
).
c.
d.
WEEK of August 9th
Problem of the week:
Compute the product
(1 − 𝑥)(1 + 𝑥 + 𝑥 2 + 𝑥 3 + ⋯ + 𝑥 𝑛 + ⋯
, R –20
, R 20
What is a simpler form of the radical expression?
5. 5.
a.
b.
c.
d.
6. 6.
a.
b.
c.
d.
7. 7. The formula for the volume of a sphere is
. Find the radius, to
the nearest hundredth, of a sphere with a volume of 15 in.3.
a. 3.58 in.
b. 258.01 in.
c. 1.53 in.
d. 1.85 in.
HONORS PRECALCULUS SUMMER 2013
14. 14.
a. 1
Multiply and simplify if possible.
8. 8.
a.
b.
c.
1 and 
2
5
c. 1
d.

2
5
d. not possible
15. 15.
a. –9
b. 9 and –4
c. –4
d. –9 and –4
===============================================================
What is the simplest form of the expression?
WEEK of August 16th
Problem of the week:
The Fibonacci numbers begin with the sequence 0, 1, 2, 3, 5, 8, 13, …
Find the next three Fibonacci numbers.
9.
a.
b.
b.
c.
d. none of these
The
Graph the exponential function.
What is the simplest form of the quotient?
1.1. 1.
a
.
10.
a.
b.
c.
y
16
d.
–6
11.
c
.
y
4
A garden has width
and length
. What is the perimeter of the
garden in simplest radical form?
a.
c. 91 units
units
b.
d.
units
units
What is the simplest form of the number?
–4
–2
2
4
6
x
12
–4
8
–8
4
–12
–16
–6
–4
–2
2
–4
12.
–20
c. –28
d. –18
a. 9
b. 57
What is the solution of the equation?
13.
a. 14
b. –8
c. 4
d. –6
What is the solution of the equation? Eliminate any extraneous solutions.
4
6
x
HONORS PRECALCULUS SUMMER 2013
b
.
d
.
y
b
.
y
20
d
.
y
12
y
12
16
16
8
8
12
4
4
12
8
8
–6
4
4
–6
–4
–2
2
4
6
x
–6
–4
–4
–2
2
4
6
–4
–2
2
4
x –6
6
–4
–2
2
–4
–4
–8
–8
–12
–12
4
x
–4
4.
2. Find the annual percent increase or decrease that
a. 230% increase
c. 35% decrease
b. 135% increase
d. 65% decrease
models.
4.
4. Use the graph of
to evaluate
to four decimal places.
a. 5.4739
b. 4.6211
c. 2.7183
d. 0.1827
5.
5. Suppose you invest $1600 at an annual interest rate of 4.6% compounded
continuously. How much will you have in the account after 4 years?
a. $800.26
b. $6,701.28
c. $10,138.07
d. $1,923.23
6.
6. You open a savings account and deposit $1,000. After 1 year of earning
continuously compounded interest, your balance is $1,018.16. After 2 years,
the balance is $1,036.66. Assuming you make no deposits or withdrawals,
find the equation for the best-fitting exponential function to represent the
balance of the account after x years. How much money will be in the account
after 10 years?
Graph the function.
3. 3.
a
.
c
.
y
12
–6
–4
y
12
8
8
4
4
–2
2
–4
4
6
x –6
–4
–2
2
4
6
x
–4
–8
–8
–12
–12
a.
b.
, $6,049.65
, $1,001.20
c.
d.
7. Write the equation in logarithmic form.
7.
a.
b.
c.
d.
, $1,197.22
, $1,001.20
6
x
HONORS PRECALCULUS SUMMER 2013
y
b.
8.
a.
c.
–6
b.
–4
y
d.
12
12
8
8
4
4
–2
2
4
6
–6
x
–4
d.
–2
2
4
6
x
–4
–4
–8
–8
–12
–12
Evaluate the logarithm.
9.
a. –3
10.
a.
c. –4
b. 5
y
d. 4
y
c.
12
12
8
8
4
4
–6
–6
–4
–2
2
–4
–8
–12
4
6
x
–4
–2
2
–4
–8
–12
4
6
x
11.
Write the expression as a single logarithm.
11.
a.
b.
c.
d.
Solve the exponential equation.
12. 12.
a. 3
4
b. 8
3
c. 3
8
d. 2
Solve the logarithmic equation. Round to the nearest ten-thousandth if
necessary.
13. 13.
a.
Solve
7

4
.
b. 495
2
c. 250
d. 990
HONORS PRECALCULUS SUMMER 2013
WEEK of August 23rd
Problem of the week:
The Babylonians considered 6 the devil’s number because it had
the somewhat unique property that the sum of its factors equaled
itself. That is, 1 + 2 + 3 = 6. There is one two digit number
and at least one three digit number with the same magic property.
Find these numbers.
𝟒
𝒚=𝒙
Graph the function.
4.
a.
y
c.
y
10
10
5
5
–10
–10
–5
Is the relationship between the variables in the table a direct variation, an
inverse variation, or neither? If it is a direct or inverse variation, write a
function to model it.
5
–5
5
10 x
10 x
–5
–5
–10
1.
–10
x
9
11
13
15
y
–17
–1
6
27
y
y
a.
10
10
5
5
inverse variation;
b.
17
direct variation; y =  x
9
c. neither
2. Suppose that y varies directly with x and inversely with z, and y = 28 when x =
32 and z = 8. Write the equation that models the relationship. Then find y when
x = 12 and z = 3.
a.
c.
7
2
4
b.
d.
32
28
3. Designer Dolls, Inc. found that the number N of dolls sold varies directly with
their advertising budget A and inversely with the price P of each doll. The
company sold 5200 dolls when $26,000 was spent on advertising and the price
of a doll was set at $30. Determine the number of dolls sold when the amount
spent on advertising is increased to $52,000. Round to the nearest whole
number.
a. 5,200 dolls
c. 3,447 dolls
b. 1,723 dolls
d. 10,400 dolls
–10
–5
5
10 x
–10
–5
5
–5
–5
–10
–10
10 x
HONORS PRECALCULUS SUMMER 2013
5. This graph of a function is a translation of
. What is an equation for the
function?
What is the product in simplest form? State any restrictions on the
variable.
9. 9.
y
10
8
6
a.
c.
b.
d.
4
2
–10 –8 –6 –4 –2
–2
2
4
6
8 10 x
–4
3
100
–6
–8
–10
10.
a.
c.
b.
d.
Find any points of discontinuity for the rational function.
a.
c.
b.
d.
11.
Suppose that y and x vary inversely and that
a. What does the graph of this function look like?
6.
a. x = 1, x = 4
b. x = –1, x = –4
c. x = 3, x = –5, x = 7
d. x = –3, x = 5, x = –7
a. x = –2, x = –7
b. x = 2, x = –7
c. x = –8
d. x = 2, x = 7
7.
What is the graph of the rational function?
8.
b. What is x when y = –2?
when
.