Download Algebra 1 EOC Recovery Activities

Algebra 1 EOC Recovery Activities
Unit I – Solving Linear Equations
(MA.912.A.3.1, MA.912.A.3.2, MA.912.A.3.3, MA.912.A.3.5, MA.912.A.5.4)
Properties of real numbers
Solve Equations (with one variable)
Solve algebraic proportions
Solve literal equations
Solve an equation from a real-world application





Example 1
Solve 5x + 3 = 23
5x + 3 = 23
Original equation
5x + 3 – 3 = 23 -3 Additive Inverse
(Subtract 3 from each side )
5x = 20
Simplify
5x/5 = 20/5
Divide each side by 5
X=4
Simplify
Example 2
The formula C = πd represents the circumference of a circle,
or the distance around the circle, where d is the diameter. If
an airplane could fly around Earth at the equator without
stopping, it would have traveled about 24,900 miles. Find the
diameter of Earth.
Example 3
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Algebra 1 EOC Recovery Activities
Example 4:
Example 5:
=
Practice
1. What is the value of x in the equation below?
(
A.
)
B. 1
(
)
C. 2
D.
2. What is the value of x in the equation below?
6(4x + 5) = 3(x + 8) + 3
A.
B.
C. 2
D. 7
3. An airline company charges $200 per flight, regardless of the destination. The company also charges $25
dollars for every piece of luggage. In addition, they charge $0.02 for every mile of the flight. With only one
piece of luggage, the total cost of the trip can be calculated using the equation below, where x represents the
number of miles in the flight.
If a trip costs $325, how many miles long is the flight?
Trip Cost = 200 + 25 + .02x
A. 5,000
B. 6,250
C. 15,000
D. 27,500
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Algebra 1 EOC Recovery Activities
4. The formula below shows how to calculate body mass index (B), using weight (w) and height (h).
Which of the following shows this equation correctly solved for w?
A.
w = Bh2 − 703
C.
B.
w = B + h2 − 703
D.
5. Marilyn spent a total of $52.34 on two new outfits. She bought two shirts for $12.99, a pair of pants of
$18.50, and a skirt. If the sales tax rate was 7.5%, how much did she pay for the skirt?
A. $4.21
B. $7.86
C. $17.20
D. $20.84
6. On Friday, Auriel had $45 in her wallet. That night, she went to the movies and spent $9.50 on a
ticket, $3.25 on a soda, and $2.75 on a box of chocolate-covered raisins. On Saturday, she bought two
used books, each for the same price. When Auriel got home from the bookstore, she had only $2 left
in her wallet.
If Auriel did not make any other purchases, and sales tax rate on the books was 7.5%, what was the
price of each book before tax?
A. $12.79
B. $13.75
C. $25.58
D. $27.50
7. There is an equal number of boys and girls in a 9th grade class. The ratio of the average heights of
boys to girls is 12 to 11. If the average height of the girls in the class is 66 inches, what is the average
height, in inches, of the boys in the class?
A. 55
B. 60
C. 72
D. 77
8. In a box of graham crackers, 2 unbroken sheets of crackers contain 120 calories and make up one
serving. Hans used the proportion below to determine the number of calories that are in 7 unbroken
sheets of crackers.
A. 14
B. 42
C. 210
D. 420
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Algebra 1 EOC Recovery Activities
Unit II – Functions and Relations
(MA.912.A.2.3, MA.912.A.2.4, MA.912.A.2.13)





Determine whether a relation is a function
Use function notation
Link equations to functions
Domain and range of a function
Solve real-world problems involving relations and functions
Example 1
Solve the equation 2x – 2 = –4 by graphing.
First set the equation equal to 0. Then replace 0 with f(x). Make a table of ordered pair solutions. Graph the function
and locate the x-intercept.
Example 2 Write an equation in functional notation for the relation shown in the graph.
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Algebra 1 EOC Recovery Activities
Example 3:
a. Express the relation {(1, 1), (0, 2), (3, -2)} as a table, a graph, and mapping.
b. Determine the domain and the range of the relation.
The domain for this relation is {0, 1, 3}. The range for this relation is {–2, 1, 2}.
1. Given the function f(x) = 5 − 2x, what is the value of x if f(x) = 3?
A. X = 3
2.
B. X= 1
Given the function
C. X = -1
for
{
D.
X = 11
}, find the range.
3. The cost of a New York City taxi fare can be described by the function f(x) = $3 + $0.50x, where x represents the
number of miles the taxi drives. What is the value of f(x) for a 12-mile taxi ride?
A. $3.50
4.
B. $9.00
What is the domain of the relation?
F {
}
H {
G {
}
I {
}
C. $15.50
D.
$38.40
}
5.
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Algebra 1 EOC Recovery Activities
Unit III – Graphing Linear Equations
(MA.912.A.3.7, MA.912.A.3.8, MA.912.A.3.9., MA.912.G.1.4)



Slope and x & y intercepts
Rewrite linear equations
Graph a line given a variety of information
Example
Example
Practice
1. What is the equation in slope-intercept form that describes the graphed line?
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Algebra 1 EOC Recovery Activities
2. Which is the graph of 3x – 4y = 6?
3.
3. Which is the graph of y - 2 = 4(x + 5)?
B.
A.
C.
D.
4. Which pair of x- and y-intercepts was used to graph the line given?
A.
B.
C.
D.
x-intercept: 3, y-intercept: ‒6
x-intercept: ‒3, y-intercept: ‒6
x-intercept: 6, y-intercept: 3
x-intercept: ‒6, y-intercept: 3
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Algebra 1 EOC Recovery Activities
5. Which table of values was used to graph the line given?
A.
B.
C.
D.
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Algebra 1 EOC Recovery Activities
Unit IV – Writing Linear Equations
(MA.912.A.3.10, MA.912.3.11, MA.912.A.3.12, MA.912.G.1.4)



Write an equation of a line given a variety of information
Parallel & perpendicular lines
Determine an equation of a line given a set of data
Example
The equation 4y + 2x = 660 can be used to determine the target heart rate of a person, where x
represents the target heart rate and y represents the person's age. When this equation is graphed on a coordinate
plane, where does the line intercept the y-axis?
The equation of a line is y = mx + b, where b represents the y-intercept (the point in which the line crosses the y –
axis). Therefore, solve for the y-intercept form for the given equation and the y-intercept (b) will be identified.
4y + 2x = 660
4y = -2x +660
y = -0.5x + 165
OR
Subtract 2x from both sides of the equation
Divide both sides of the equation by 4
The y-intercept = 165
Set x = 0 and solve for y because the y-intercept will be coordinate (x,b)
4y + 2(0) = 660
Set x= 0 by substituting
4y = 660
Divide both sides of the equation by 4
y = 165
The y-intercept = 165
Practice
1. Which of the following represents the linear equation 3x = 12 – 2y in standard form?
A.
B.
C.
D.
2. What is the y-coordinate of the y-intercept of the line that passes through the points (–4, –4)
and (4, 8)?
3. On a coordinate graph, Celeste places a red marble at the point (2, 2) and a green marble at the point (4, 1).
If she draws a line that passes through both of these points, which set of coordinates represents the x- and yintercepts of the line?
A. x-intercept: (0, 6)
y-intercept: (3, 0)
C. x-intercept: (0, 3)
y-intercept: (6, 0)
B. x-intercept: (6, 0)
y-intercept: (0, 3)
D. x-intercept: (3, 0)
y-intercept: (0, 6)
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Algebra 1 EOC Recovery Activities
4. In an isometric drawing, parallel edges of a three-dimensional object are represented as parallel lines
when the object is drawn in two dimensions. In the isometric drawing of the cube below, line is
drawn to form one edge of the cube. The equation y = x + 3 can be used to represent line .
Line k is then drawn to form a parallel edge of the cube, passing through (5, 4).
Which of the following shows the equation for line k?
A. y = x − 1
B.
y = −x + 1
C.
y=x+5
D. y = −x − 5
5. Line S passes through the points (2, 7) and (6, 1). Line t passes through the point (5, 2) and is perpendicular to
line S. What is the equation for line t?
A.
C.
B.
D.
6. Ten doughnuts were already made when Bill starts making doughnuts, and Bill can make 5
doughnuts per minute. The table shows the number of doughnuts made over 8 minutes.
Write the equation of the line using the data in the table?
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Algebra 1 EOC Recovery Activities
Unit V – Inequalities
(MA.912.A.3.4, MA.912.3.5, MA.912.A.3.12)
 Solve and graph simple and multi-step inequalities
 Solve and graph compound inequalities
 Solve and graph linear inequalities
 Symbolically represent and solve real-world problems involving inequalities
Example 1
Example 2
Example 3
Example 4
Example 5
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Algebra 1 EOC Recovery Activities
Example 6
Example 7
Example 8
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Algebra 1 EOC Recovery Activities
Example 9
1. Which graph represents the solution set for the inequality shown below?
5x + 7 ≤ 23x – 2
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Algebra 1 EOC Recovery Activities
2. Maria is helping Tony with his math homework. They need to find the solution for the inequality
−4(2x + 1) − 11 > 9
Each step in Maria's solution is shown below. Which of the following justifies step 1 of her solution?
A.
Commutative Property of Multiplication
B.
Distributive Property
C.
Associative Property of Multiplication
D.
Identity Property
3. Which of the following is the solution for 4x – 4 > 12?
A. x ≥ 4
B. x ≤4
C. x > 4
D. x < 4
4. Which graph represents the solution set for the compound inequality
‒3 ≤ −2 x + 1 < 11?
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Algebra 1 EOC Recovery Activities
5. Trini’s car breaks down on a highway. Trini estimates that she is 20 to 30 miles from the nearest car
repair shop. She calls a towing company that charges a fee of $80 plus $3 per mile to tow a car. If Trini uses
this towing company, which is the best estimate for the amount of money, m, she will pay for the company
to tow her car?
A. 103 ≤ m ≤ 113
B. 140 ≤ m ≤ 150
C. 140 ≤ m ≤ 170
D. 160 ≤ m ≤ 170
Use a graph to solve each inequality.
6. 4x – 20 < –16
7.
8.
9.
Determine which of the ordered pairs are a part of the solution
Set for the inequality graphed at the right.
F (2, 1)
H ( – 3, – 3)
G (1, 3)
I ( – 2, – 3)
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Algebra 1 EOC Recovery Activities
Unit VI – Systems of Equations
(MA912.A.3.13, MA912.A.3.14, MA.912.A.3.15)
 Solve systems of equations by graphing
 Solve systems by substitution
 Solve systems by elimination
 Write and solve systems of equations from real-world applications
Example 1:
Example 2:
Graph the following system and determine the solution.
Graph the following system and determine the solution.
x+y=2
y = 2x + 1
x–y=4
2y = 4x + 2
The graphs intersect. Therefore, there is one solution.
The point (3, -1) seems to lie on both lines. Check this
estimate by replacing x with 3 and y with -1 in each
equation.
x+y=2
3 + (-1) = 2
x–y=4
3 – (-1) = 3 + 1 = 4
The solution is (3, -1).
Example 3:
Graph the following system and determine the solution.
3x – y = – 2
3x – y = 0
The graphs coincide. Therefore there are infinitely many
solutions.
Example 4:
Solve the following system of equations using
elimination.
The lines are parallel. Therefore there are no solutions.
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Algebra 1 EOC Recovery Activities
Example 5:
Russ bought 3 medium and 2 large submarine
sandwiches for a total of $29.95. Stacy bought 4 medium
and 1 large submarine sandwiches for a total of $28.45.
Find the cost of each medium and each large submarine
sandwich?
Let m = the cost of each medium sandwich.
Let g = the cost of each large sandwich.
Set up a system of equations:
3m + 2g = $29.95
4m + g = $28.45
Using equation 2 we can solve for g:
g=28.45 – 4m
Substitute into equation 1:
3m + 2(28.45 – 4m) = 29.95
Use the distributive property:
3m + 56.90 – 8m = 29.95
Combine like terms:
– 5m + 56.90 = 29.95
Subtract 56.90 from both sides:
– 5m = 26.95
Divide by – 5 on both sides:
m = 5.39
Since g = 28.45 – 4m:
g = 28.45 – 4(5.39)
g = 28.45 – 21.56
g = 6.89
Example 6:
A website that sells songs for downloading increased its
price per song from $0.99 to $1.29. Macy spent $15.36
downloading songs during the month of the price
increase. She downloaded 4 more songs at $0.99 than at
$1.29. The set of equations below represents the
situation where x is the number of songs Macy
downloaded at $0.99 and y is the number of songs she
downloaded at $1.29.
x=y+4
0.99x + 1.29y = 15.36
What is the exact number of songs Macy downloaded at
the $0.99 price?
Since x = y + 4, substitute into equation 2:
0.99(y + 4) + 1.29y = 15.36
Use the distributive property:
0.99y + 3.96 +1.29y = 15.36
Combine like terms:
2.28y + 3.96 = 15.36
Subtract 3.96 from both sides:
2.28y = 11.40
Divide by 2.28 on both sides:
y=5
Since x = y + 4,
x=5+4
x=9
Macy downloaded 9 songs at the $0.99 price.
Each medium sandwich costs $5.39
Each large sandwich costs $6.89
Practice:
1. The linear equations y = 3 + 2x and y = 2 - 3x are graphed below.
Which is the approximate value of x in the solution of the system of equations?
1.
B.
C.
D.
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Algebra 1 EOC Recovery Activities
2. What is the solution to the following system of equations?
3x + 5y = 5
4x + 9y = 2
a. (
3.
)
b.
(
)
c. (
)
d.
(
)
The equations below approximate the populations of New York and Florida, where y is the population in
millions and x is the number of years since 2005. Which is the best estimate for the number of years
since 2005 in which the populations of New York and Florida will be equal? Round to the hundredths place.
4. Pizza Pizzazz sells the items shown in the table. During lunch, the restaurant sold 35 more pizza slices
than pizza pockets and made $825.50. Which system of equations could be used to find the number of
pizza slices, s, and pizza pockets, p, that were sold?
a.
c.
b.
d.
5. The solution to which system of equations has a positive y value?
a.
c.
b.
d.
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Algebra 1 EOC Recovery Activities
6. If y = 5x – 3 and 3x – y = – 1, what is the value of y?
a. 2
b. – 1
c. – 8
d. 7
7. Use elimination to solve the following system of equations for y
x - 5y = -6
x + 2y = 8
a.
b. 2
c. 4
d.
8. How many solutions are there to the system: 2y = 10x - 14
5x - y = 7
a. one
b. two
c. none
d. infinitely many
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