Transcript PPT Advanced Algebra 1 Midterm Exam Review

Advanced Algebra 1
Midterm Exam Review
Equations
CHAPTER 1
Lesson Quiz: Part I
Give two ways to write each algebraic
expression in words.
1. j – 3
2. 4p
The difference of j and 3; 3 less than j.
4 times p; The product of 4 and p.
3. Mark is 5 years older than Juan, who is y years
old. Write an expression for Mark’s age.
y+5
Lesson Quiz: Part II
Evaluate each expression for c = 6, d = 5, and
e = 10.
1
11
4. d
5. c + d
2
e
Shemika practices basketball for 2 hours each
day.
6. Write an expression for the number of hours she
practices in d days. 2d
7. Find the number of hours she practices in 5, 12,
and 20 days.
10 hours; 24 hours; 40 hours
Lesson Quiz
Solve each equation.
1.
2.
3.
4.
5.
6.
r – 4 = –8 –4
m + 13 = 58 45
0.75 = n + 0.6 0.15
–5 + c = 22 27
This year a high school had 578 sophomores
enrolled. This is 89 less than the number enrolled
last year. Write and solve an equation to find the
number of sophomores enrolled last year.
s – 89 = 578; s = 667
Lesson Quiz: Part 1
Solve each equation.
1.
2.
21
2.8
3. 8y = 4
4. 126 = 9q
5.
6.
40
–14
Lesson Quiz: Part 2
9
7. A person's weight on Venus is about
10
his or
her weight on Earth. Write and solve an equation
to find how much a person weighs on Earth if he
or she weighs 108 pounds on Venus.
Lesson Quiz: Part 1
Solve each equation.
1. 4y + 8 = 2
2.
–8
3. 2y + 29 – 8y = 5 4
4. 3(x – 9) = 30 19
5. x – (12 – x) = 38
6.
9
25
Lesson Quiz: Part 2
7. If 3b – (6 – b) = –22, find the value of 7b. –28
8. Josie bought 4 cases of sports drinks for an
upcoming meet. After talking to her coach,
she bought 3 more cases and spent an
additional $6.95 on other items. Her receipts
totaled $74.15. Write and solve an equation
to find how much each case of sports drinks
cost.
4c + 3c + 6.95 = 74.15; $9.60
Lesson Quiz
Solve each equation.
1. 7x + 2 = 5x + 8 3
2. 4(2x – 5) = 5x + 4
3. 6 – 7(a + 1) = –3(2 – a)
4. 4(3x + 1) – 7x = 6 + 5x – 2 all real numbers
5.
1
6. A painting company charges $250 base plus $16
per hour. Another painting company charges $210
base plus $18 per hour. How long is a job for which
the two companies costs are the same?
20 hours
8
Lesson Quiz: Part 1
Solve for the indicated variable.
for h
1.
2. P = R – C for C
C=R–P
3. 2x + 7y = 14 for y
4.
5.
for m
for C
m = x(k – 6 )
C = Rt + S
Lesson Quiz: Part 2
Euler’s formula, V – E + F = 2, relates the
number of vertices V, the number of edges E,
and the number of faces F of a polyhedron.
6. Solve Euler’s formula for F. F = 2 – V + E
7. How many faces does a polyhedron with 8
vertices and 12 edges have? 6
Lesson Quiz
Solve each equation.
1. 15 = |x| –15, 15
2. 2|x – 7| = 14 0, 14
3. |x + 1|– 9 = –9 –1 4. |5 + x| – 3 = –2 –6, –4
5. 7 + |x – 8| = 6
no solution
6. Inline skates typically have wheels with a
diameter of 74 mm. The wheels are
manufactured so that the diameters vary from
this value by at most 0.1 mm. Write and solve an
absolute-value equation to find the minimum and
maximum diameters of the wheels.
|x – 74| = 0.1; 73.9 mm; 74.1 mm
Lesson Quiz: Part 1
1. In a school, the ratio of boys to girls is 4:3.
There are 216 boys. How many girls are there?
162
Find each unit rate. Round to the nearest hundredth if
necessary.
2. Nuts cost $10.75 for 3 pounds.
$3.58/lb
3. Sue washes 25 cars in 5 hours.
5 cars/h
4. A car travels 180 miles in 4 hours. What is the
car’s speed in feet per minute?3960 ft/min
Lesson Quiz: Part 2
Solve each proportion.
5.
6.
6
16
7. A scale model of a car is 9 inches long. The
scale is 1:18. How many inches long is the car
it represents? 162 in.
Lesson Quiz: Part 1
Solve for the indicated variable.
for h
1.
2. P = R – C for C
C=R–P
3. 2x + 7y = 14 for y
4.
for m
5.
for C
m = x(k – 6 )
C = Rt + S
Lesson Quiz: Part 2
Euler’s formula, V – E + F = 2, relates the number of
vertices V, the number of edges E, and the number of faces
F of a polyhedron.
6. Solve Euler’s formula for F.
F=2–V+E
7. How many faces does a polyhedron with 8
vertices and 12 edges have? 6
Inequalities
CHAPTER 2
Lesson Quiz: Part I
1. Describe the solutions of 7 < x + 4.
all real numbers greater than 3
2. Graph h ≥ –4.75
–5
–4.75
–4.5
Write the inequality shown by each graph.
3.
4.
x≥3
x < –5.5
Lesson Quiz: Part II
5. A cell phone plan offers free minutes for no more
than 250 minutes per month. Define a variable
and write an inequality for the possible number of
free minutes. Graph the solution.
Let m = number of minutes
0 ≤ m ≤ 250
0
250
Lesson Quiz: Part I
Solve each inequality and graph the solutions.
1. 13 < x + 7
x>6
2. –6 + h ≥ 15
h ≥ 21
3. 6.7 + y ≤ –2.1
y ≤ –8.8
Lesson Quiz: Part II
4. A certain restaurant has room for 120
customers. On one night, there are 72
customers dining. Write and solve an
inequality to show how many more people
can eat at the restaurant.
x + 72 ≤ 120; x ≤ 48, where x is a natural
number
Lesson Quiz
Solve each inequality and graph the solutions.
1. 8x < –24 x < –3
2. –5x ≥ 30
x ≤ –6
3.
4.
x≥6
x > 20
5. A soccer coach plans to order more shirts for
her team. Each shirt costs $9.85. She has $77
left in her uniform budget. What are the
possible number of shirts she can buy?
0, 1, 2, 3, 4, 5, 6, or 7 shirts
Lesson Quiz: Part I
Solve each inequality and graph the solutions.
1. 13 – 2x ≥ 21 x ≤ –4
2. –11 + 2 < 3p
p > –3
3. 23 < –2(3 – t)
t>7
4.
Lesson Quiz: Part II
5. A video store has two movie rental plans. Plan
A includes a $25 membership fee plus $1.25 for
each movie rental. Plan B costs $40 for
unlimited movie rentals. For what number of
movie rentals is plan B less than plan A?
more than 12 movies
Lesson Quiz: Part I
Solve each inequality and graph the solutions.
1. t < 5t + 24 t > –6
2. 5x – 9 ≤ 4.1x – 81 x ≤ –80
3. 4b + 4(1 – b) > b – 9
b < 13
Lesson Quiz: Part II
4. Rick bought a photo printer and supplies for
$186.90, which will allow him to print photos
for $0.29 each. A photo store charges $0.55
to print each photo. How many photos must
Rick print before his total cost is less than
getting prints made at the photo store?
Rick must print more than 718 photos.
Lesson Quiz: Part III
Solve each inequality.
5. 2y – 2 ≥ 2(y + 7)
no solutions
6. 2(–6r – 5) < –3(4r + 2)
all real numbers
Lesson Quiz: Part I
1. The target heart rate during exercise for a 15
year-old is between 154 and 174 beats per
minute inclusive. Write a compound inequality to
show the heart rates that are within the target
range. Graph the solutions.
154 ≤ h ≤ 174
Lesson Quiz: Part II
Solve each compound inequality and graph
the solutions.
2. 2 ≤ 2w + 4 ≤ 12
–1 ≤ w ≤ 4
3. 3 + r > −2 OR 3 + r < −7
r > –5 OR r < –10
Lesson Quiz: Part III
Write the compound inequality shown by
each graph.
4.
x < −7 OR x ≥ 0
5.
−2 ≤ a < 4
Functions
CHAPTER 3
Lesson Quiz: Part I
1. Write a possible situation for the given graph.
Possible Situation: The level of water in a bucket stays
constant. A steady rain raises the level. The rain slows
down. Someone dumps the bucket.
Lesson Quiz: Part II
2. A pet store is selling puppies for $50 each. It has 8
puppies to sell. Sketch a graph for this situation.
Lesson Quiz: Part I
1. Express the relation {(–2, 5), (–1, 4), (1, 3),
(2, 4)} as a table, as a graph, and as a
mapping diagram.
Lesson Quiz: Part II
2. Give the domain and range of the relation.
D: –3 ≤ x ≤ 2: R: –2 ≤ y ≤ 4
Lesson Quiz: Part III
3. Give the domain and range of the
relation. Tell whether the relation is a
function. Explain.
D: {5, 10, 15};
R: {2, 4, 6, 8};
The relation is not a function
since 5 is paired with 2 and 4.
Lesson Quiz: Part I
Identify the independent and dependent variables. Write a rule in function
notation for each situation.
1. A buffet charges $8.95 per person.
independent:
number of people
dependent: cost
f(p) = 8.95p
2. A moving company charges $130 for weekly
truck rental plus $1.50 per mile.
independent:
miles
dependent: cost
f(m) = 130 + 1.50m
Lesson Quiz: Part II
Evaluate each function for the given input values.
3. For g(t) =
, find g(t) when t = 20 and
when t = –12.
g(20) = 2
g(–12) = –6
4. For f(x) = 6x – 1, find f(x) when x = 3.5 and
when x = –5.
f(3.5) = 20
f(–5) = –31
Lesson Quiz: Part III
Write a function to describe the situation. Find a reasonable domain and
range for the function.
5. A theater can be rented for exactly 2, 3, or 4
hours. The cost is a $100 deposit plus $200
per hour.
f(h) = 200h + 100
Domain: {2, 3, 4}
Range: {$500, $700, $900}
Lesson Quiz: Part I
1. Graph the function for the given domain.
3x + y = 4
D: {–1, 0, 1, 2}
2. Graph the function y = |x + 3|.
Lesson Quiz: Part II
3. The function y = 3x
describes the
distance (in inches)
a giant tortoise
walks in x seconds.
Graph the function.
Use the graph to
estimate how many
inches the tortoise
will walk in 5.5
seconds.
About 16.5 in.
Lesson Quiz: Part I
For Items 1 and 2, identify the correlation you would expect to see
between each pair of data sets. Explain.
1. The outside temperature in the summer and
the cost of the electric bill
Positive correlation; as the outside temperature increases, the electric bill
increases because of the use of the air conditioner.
2. The price of a car and the number of
passengers it seats
No correlation; a very expensive car could seat only 2 passengers.
Lesson Quiz: Part II
3. The scatter plot shows the number of orders
placed for flowers before Valentine’s Day at one
shop. Based on this relationship, predict the
number of flower orders placed on February 12.
about 45
Lesson Quiz: Part I
Determine whether each sequence appears to be an arithmetic sequence.
If so, find the common difference and the next three terms in the
sequence.
1. 3, 9, 27, 81,…
not arithmetic
2. 5, 6.5, 8, 9.5,…
arithmetic;
1.5; 11, 12.5, 14
Lesson Quiz: Part II
Find the indicated term of each arithmetic sequence.
3. 23rd term: –4, –7, –10, –13, …
–70
4. 40th term: 2, 7, 12, 17, …
197
5. 7th term: a1 = –12, d = 2
0
6. 34th term: a1 = 3.2, d = 2.6
89
7. Zelle has knitted 61 rows of a scarf. Each
day she adds 17 more rows. How many
rows total has Zelle knitted 16 days later?
333 rows
Linear Functions
CHAPTER 4
Lesson Quiz: Part I
Tell whether each set of ordered pairs satisfies a linear function.
Explain.
1. {(–3, 10), (–1, 9), (1, 7), (3, 4), (5, 0)}
No; a constant change of +2 in x corresponds to different changes in y.
2. {(3, 4), (5, 7), (7, 10), (9, 13), (11, 16)}
Yes; a constant change of +2 in x corresponds to a constant change of
+3 in y.
Lesson Quiz: Part II
Tell whether each function is linear. If so, graph the function.
3. y = 3 – 2x
4. 3y = 12
no
yes
Lesson Quiz: Part III
5. The cost of a can of iced-tea mix at Save More
Grocery is $4.75. The function f(x) = 4.75x
gives the cost of x cans of iced-tea mix. Graph
this function and give its domain and range.
D: {0, 1, 2, 3, …}
R: {0, 4.75, 9.50,
14.25,…}
Lesson Quiz: Part I
1. An amateur filmmaker has $6000 to make a film
that costs $75/h to produce. The function f(x) =
6000 – 75x gives the amount of money left to
make the film after x hours of production. Graph
this function and find the intercepts. What does
each intercept represent?
x-int.: 80; number of hours it takes to spend all
the money
y-int.: 6000; the initial amount of money
available.
Lesson Quiz: Part II
2. Use intercepts to graph the line described by
Lesson Quiz: Part I
Name each of the following.
1. The table shows the number of bikes made
by a company for certain years. Find the rate
of change for each time period. During which
time period did the number of bikes increase
at the fastest rate?
1 to 2: 3; 2 to 5: 4; 5 to 7: 0; 7 to 11: 3.5;
from years 2 to 5
Lesson Quiz: Part II
Find the slope of each line.
2.
3.
undefined
Lesson Quiz
1. Find the slope of the line that contains (5, 3)
and (–1, 4).
2. Find the slope of the line. Then tell what the
slope represents.
50; speed of bus is 50 mi/h
3. Find the slope of the line described by x + 2y = 8.
Lesson Quiz: Part I
Tell whether each equation represents a direct variation. If so, identify
the constant of variation.
1. 2y = 6x
2. 3x = 4y – 7
yes; 3
no
Tell whether each relationship is a direct variation. Explain.
3.
4.
Lesson Quiz: Part II
5. The value of y varies directly with x, and
y = –8 when x = 20. Find y when x = –4.
1.6
6. Apples cost $0.80 per pound. The equation
y = 0.8x describes the cost y of x pounds
of apples. Graph this direct variation.
6
4
2
Lesson Quiz: Part I
Write the equation that describes each line in the slope-intercept form.
1. slope = 3, y-intercept = –2
y = 3x – 2
2. slope = 0, y-intercept =
y=
3. slope = , (2, 7) is on the line
y=
x+4
Lesson Quiz: Part II
Write each equation in slope-intercept form. Then graph the line described
by the equation.
4. 6x + 2y = 10
y = –3x + 5
5. x – y = 6
y=x–6
Lesson Quiz: Part I
Write an equation in slope-intercept form for the line with the given slope
that contains the given point.
1. Slope = –1; (0, 9)
2. Slope =
; (3, –6)
y = –x + 9
y=
x–5
Write an equation in slope-intercept form for the line through the two
points.
3. (–1, 7) and (2, 1)
y = –2x + 5
4. (0, 4) and (–7, 2)
y=
x+4
Lesson Quiz: Part II
5. The cost to take a taxi from the airport is a linear
function of the distance driven. The cost for 5,
10, and 20 miles are shown in the table. Write
an equation in slope-intercept form that
represents the function.
y = 1.6x + 6
Lesson Quiz: Part I
Write an equation is slope-intercept form for the line described.
1. contains the point (8, –12) and is parallel to
2. contains the point (4, –3) and is perpendicular
to y = 4x + 5
Lesson Quiz: Part II
3. Show that WXYZ is a rectangle.
slope of
=XY
slope of YZ = 4
slope of
=WZ
slope of XW = 4
The product of the slopes of adjacent sides is –1.
Therefore, all angles are right angles, and WXYZ
is a rectangle.
Lesson Quiz: Part I
Describe the transformation from the graph of f(x) to the graph of g(x).
1. f(x)
= 4x, about
g(x) = (0,
x 0) (less steep)
rotated
2.
f(x) = x – 1, g(x) = x + 6
3.
translated 7 units up
4.
f(x) =
x, g(x) = 2x
rotated about (0, 0) (steeper)
f(x) = 5x, g(x) = –5x
reflected across the y-axis, rot. about (0, 0)
Lesson Quiz: Part II
5. f(x) = x, g(x) = x – 4
6. translated 4 units down
f(x) = –3x, g(x) = –x + 1
rotated about (0, 0) (less steep), translated 1 unit up
7. A cashier gets a $50 bonus for working on a
holiday plus $9/h. The total holiday salary is given
by the function f(x) = 9x + 50. How will the graph
change if the bonus is raised to $75? if the hourly
rate is raised to $12/h?
translate 25 units up; rotated about (0, 50) (steeper)
System of Equations and Inequalities
CHAPTER 5
Lesson Quiz: Part I
Tell whether the ordered pair is a solution of
the given system.
1. (–3, 1);
no
2. (2, –4);
yes
Lesson Quiz: Part II
Solve the system by graphing.
3.
y + 2x = 9
(2, 5)
y = 4x – 3
4. Joy has 5 collectable stamps and will buy 2
more each month. Ronald has 25 collectable
stamps and will sell 3 each month. After how
many months will they have the same number
of stamps? 4 months How many will that be?
13 stamps
Lesson Quiz: Part I
Solve each system by substitution.
1.
2.
3.
y = 2x
(–2, –4)
x = 6y – 11
3x – 2y = –1
–3x + y = –1
x–y=4
(1, 2)
Lesson Quiz: Part II
4. Plumber A charges $60 an hour. Plumber B
charges $40 to visit your home plus $55 for
each hour. For how many hours will the total
cost for each plumber be the same? How much
will that cost be? If a customer thinks they will
need a plumber for 5 hours, which plumber
should the customer hire? Explain.
8 hours; $480; plumber A: plumber A is
cheaper for less than 8 hours.
Lesson Quiz
Solve each system by elimination.
1.
2x + y = 25
3y = 2x – 13
2.
–3x + 4y = –18
x = –2y – 4
(2, –3)
3.
–2x + 3y = –15
3x + 2y = –23
(–3, –7)
(11, 3)
4. Harlan has $44 to buy 7 pairs of socks. Athletic
socks cost $5 per pair. Dress socks cost $8 per
pair. How many pairs of each can Harlan buy?
4 pairs of athletic socks and 3 pairs of dress socks
Lesson Quiz: Part I
Solve and classify each system.
1.
y = 5x – 1
5x – y – 1 = 0
infinitely many solutions;
consistent, dependent
2.
y=4+x
–x + y = 1
no solutions; inconsistent
3.
y = 3(x + 1)
y=x–2
consistent,
independent
Lesson Quiz: Part II
4. If the pattern in the table continues, when will
the sales for Hats Off equal sales for Tops?
never
Lesson Quiz: Part I
1. You can spend at most $12.00
for drinks at a picnic. Iced tea
costs $1.50 a gallon, and
lemonade costs $2.00 per
gallon. Write an inequality to
describe the situation. Graph
the solutions, describe
reasonable solutions, and then
give two possible
combinations of drinks you
could buy.
1.50x + 2.00y ≤ 12.00
Lesson Quiz: Part I
1.50x + 2.00y ≤ 12.00
Only whole number solutions are
reasonable. Possible answer:
(2 gal tea, 3 gal lemonade) and
(4 gal tea, 1 gal lemonde)
Lesson Quiz: Part II
2. Write an inequality to represent the graph.
1. Graph
Lesson Quiz: Part I
y<x+2
.
5x + 2y ≥ 10
Give two ordered pairs that are solutions and
two that are not solutions.
Possible answer:
solutions: (4, 4), (8, 6);
not solutions: (0, 0), (–2, 3)
Lesson Quiz: Part II
2. Dee has at most $150 to spend on restocking
dolls and trains at her toy store. Dolls cost $7.50
and trains cost $5.00. Dee needs no more than
10 trains and she needs at least 8 dolls. Show
and describe all possible combinations of dolls
and trains that Dee can buy. List two possible
combinations.
Lesson Quiz: Part II Continued
Reasonable answers must
be whole numbers.
Possible answer:
(12 dolls, 6 trains) and
(16 dolls, 4 trains)
Solutions