algebra - Citrus Grove Middle School

ALGEBRA I
2014 SPRING BREAK PACKET [This page left intentionally blank] ETO Math Spring Break Packet – Algebra I 2013‐2014 ETO Math Spring Break Packet – Algebra I 2013‐2014 ETO Math Spring Break Packet – Algebra I 2013‐2014 Algebra 1 – Spring Break Packet
b) What is the y-intercept?
Slope and Intercepts (A.3.9)
c) What is the x-intercept?
Part I – Guided Practice w/ Video Explanations
1. Use the graph below to answer the following:
4. The design of a wheelchair ramp for a new high
school must meet the slope requirement that is
specified in the Americans with Disabilities Act
(ADA) of 1990. The relationship between the
height of the ramp (y) and the length of the ramp
(x) is modeled by the equation below.
6x  72y  0
What is slope of the equation?
5. Look at the graph below.
a) What is the slope of the line?
b) What is the y-intercept?
c) What is the x-intercept?
2. Use the equation below to answer the following:
y  3x  6
a) What is the slope of the line?
b) What is the y-intercept?
a) What is the slope of the line?
c) What is the x-intercept?
b) What is the y-intercept?
c) What is the x-intercept?
3. Use the equation below to answer the following:
3x  4y  12 6. Samuel plotted the two points (-9, -5) and (3, -2)
on a graph. What is the x-coordinate of the x-
a) What is the slope of the line?
ETO Math Spring Break Packet – Algebra I 2013‐2014 Name:
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intercept of the line that contains these two
points?
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Part II – Independent Practice
10. In order for a Miami t-shirt company to make a
profit, the company must sell a certain number
of shirts in order to cover the cost of buying the
materials. The relationship between the profit
(y) and the number of t-shirts sold (x) is
modeled by the equation below.
7. Use the graph below to answer the following:
24x 16y  1600
What is the slope of this equation?
11. Look at the graph below.
a) What is the slope of the line?
b) What is the y-intercept?
c) What is the x-intercept?
8. Use the equation below to answer the following:
1
y   x3
2
a) What is the slope of the line?
b) What is the y-intercept?
c) What is the x-intercept?
a) What is the slope of the line?
b) What is the x-intercept?
c) What is the y-intercept?
9. Use the equation below to answer the following:
8x  2y  16 a) What is the slope of the line?
12. What is the x-coordinate of the x-intercept of the
line that passes through (-2, 6) and (3, 21)?
b) What is the y-intercept?
c) What is the x-intercept?
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4. Write the equation of the line below.
Writing Equations & Parallel/Perpendicular
Lines (A.3.10)
Part I – Guided Practice w/ Video Explanations
1. Write the equation of the line shown below.
1
5. Given the following equation: y   x  5
2
a) What is the slope of a line parallel to the
given line?
b) What is the slope of a line perpendicular to
the given line?
6. Use the graph below to answer the following:
2. Write the equation of a line in slope-intercept
form that contains (1, -4) and has a slope of -2.
3. Write the equation of the linear inequality
shown below.

a) What is the slope of a line parallel to GH ?
b) What
 is the slope of a line perpendicular to
GH ?
c) Write the equation of a line that passes

through point F and is parallel to GH .
d) Write the equation of a line that passes 
through point F and is perpendicular to GH .
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Part II – Independent Practice
11. Write the equation of the line below.
7. Write the equation of the line shown below.
3
12. Given the following equation: y  x  2
5
a) What is the slope of a line parallel to the
given line?
b) What is the slope of a line perpendicular to
the given line?
8. Write the equation of a line in slope-intercept
1
form that contains (-6, 2) and has a slope of .
3
13. Use the graph below to answer the following:
9. Write the equation of a line that passes through
the points (-1, 7) and (2, 1).
10. Write the equation of the linear inequality
shown below.

a) What is the slope of a line parallel to QR ?
b) What
 is the slope of a line perpendicular to
QR ?
c) Write the equation of a line that passes

through (0, 5) and is parallel to QR .
d) Write the equation of a line that passes 
through point Q and is perpendicular to QR .
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e) What is the x-intercept of the line that is
perpendicular to line QR at point Q?
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What is the value of the exponent on w?
Part II – Independent Practice
Simplifying Monomials (A.4.1)
Part I – Guided Practice w/ Video Explanations
6. Simplify the following:
a) x 3  x 3
b) (2 pq 2 r 3 )(5q3r 4 s)
1. Simplify the following:
a) y10  y 5
2
c) (7a 2 b)(7bc 2 )
3
b) (2x )(4x )
d) (a 2 )(a 10 )
c) (x 2 y8 )(x 4 y 2 )
d) (a 5 )(a 2 )
7. Simplify the following:
2. Simplify the following:
x11
x9
x 4 y3
b) 3 4
x y
64w 2 x 5
c)
4w 4 x 2
5x 3 y
d)
10x 7
a)
10
x
x2
a3
b) 7
a
10x 2 y 4
c)
2x 3 y
12w 9 y3
d)
3w 3 y 3
a)
8. Simplify the following:
3. Simplify the following:
a) (x 2 )4
a) (x 3 )3
b) (x 4 y 3 )2
b) (a 2 b3 )7
c) (8x 5 )2
c) (3x 2 )3
d) (4xy 2 )3
d) (2x 4 y)3
9. Simplify the following expression.
4. Martin simplified the expression shown below.
(a 5b 5 )(a11b1 )
(a 4 b3 )(a 5b10 )
What is the exponent on a?
His final answer was in the form a m b n . If he
simplified the expression correctly, what is the
value of n, the exponent on b?
10. Simplify the following expression.
5. Jasmine simplified the expression below.
(3x 2 y)3
18x
(2w 3 )5
8w
What is the value of the exponent on x?
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Adding, Subtracting, & Multiplying
Polynomials (A.4.2)
5. New photo-imaging techniques on computers
allow artists to distort an image from its original
shape. Figure 1 is a square image of the
Facebook logo. Figure 2 is the logo shrunk 6
units narrower and stretched 6 units taller than
Figure 1.
Part I – Guided Practice w/ Video Explanations
1. A concert hall is in the shape of a trapezoid and
has the dimensions shown in the diagram below.
How many square units greater is the area of
Figure 1 than the area of Figure 2?
Write an expression that is equivalent to the
perimeter of the concert hall.
2. Use the expression below.
Part II – Independent Practice
(4x 2  3x 1)  (x 2  2x  7)
6. A rectangular swimming pool has the
measurements shown.
a) Simplify the expression.
b) What is the coefficient of the x term in the
simplified expression?
3. Simplify the expressions below.
a) Write an expression that is equivalent to the
perimeter of the pool.
a) 2x 4 (3x 3  x 2  5x)
b) What is the value of x if the perimeter is 68
meters?
b) 7(x  2)  5(3 x)  4x
4. What is the product of the following binomials?
7. Use the expression below.
a) (x 10)(x  2)
(3x 2  x  3)  (4x 2  5x 10)
b) (3x 1)(4x 1)
a) Simplify the expression.
b) What is the coefficient of the x term?
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b) Write an expression that represents the area
of the rectangle.
8. Use the expression below.
12. Write an expression the represents the perimeter
of the figure below.
(8x  6x 12)  (3x  9x  2)
2
2
c) Simplify the expression.
d) What is the coefficient of the x term?
9. Simplify the expressions below.
a) 4x(2x 2  x  3)
b) 2(7x  2y)  6x  7(x  3y)
c) 4x 2 (2x 3  5x  6)
10. Simplify the following expressions.
a) (x  4)(x  2)
b) (3x  4)(6x  7)
c) (x  5)(x  5)
11. Use the following diagram to answer the
questions below.
a) Write an expression that represents the
perimeter of the rectangle.
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