Algebra 1
Review Open Response #1
Name ________________________________
1) Justify each step for solving this equation.
2x + 64 = 6
Justification:
2x = -58
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x = -29
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2) Use the rectangle to the right to answer the following questions.
a) Write 2 different expressions to describe the area of the rectangle.
One expression should represent the entire picture as one rectangle
and the second expression should represent the picture as the
combination of 2 smaller rectangles.
Expression #1: ________________________________________
Expression #2: ________________________________________
b) What property could be used to prove, algebraically, that the two expression are equivalent?
Property: ___________________________
3) A checking account is set up with an initial balance of $9400. $800 is removed from the account each month for rent (no other
transactions occur on the account.)
a) Complete the table of values to display the balance in the checking account after a given month
b) Write and equation to represent the number of months, m, it takes for the account balance to reach to $3800.
Equation: ___________________________________________
4. The scatter plot shows the number of CDs that Disc-O CD factory produced in different months.
a) What are the coordinates of Point Q? ( ________, _________)
b) Describe what you know about point Q using the labels.
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c) Explain the relationship between months and number of CD’s
produced. Is the trend in the graph a positive correlation,
negative correlation, or no correlation?
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d) John claims, “The more months a store is in business, the more CD’s they will sell.” Is John’s claim true for all stores. EXPLAIN
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e) Write an equation for the trend line using the points (1, 2400) and (4, 3900).
f) Using the equation from Part E, describe what the slope of the line means in the context of the problem.
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g) Using the equation from Part E, describe the meaning of the y-intercept in the context of this problem.
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5) Max is planning on going to some concerts this summer. He is deciding if he should become a member of the concert
organization.
Non Members
$ 6 per concert
Let:
Members
$9 initial fee + $3 per concert
x = Number of Concerts
y = Total Cost in Dollars
a) Write the system of equations that models this situation.
Non Members: ____________________________________
Members: ____________________________________
b) Find the solution of the system by graphing on the grid below. Be sure to title and label your graph.
Solution ___________
c) Explain the meaning of the solution to this system of equation in the context of the problem.
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e) Max wants to attend 4 concerts this summer. Should he become a member? Explain.
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Review – Group Open Response #2
1) A winter blow out sale. Caps are on sale for $8 and gloves are on sale for $4. You can spend at most $40
and want to buy at least 2 caps.
Let:
x = number of caps
Y = number of gloves
a) Write the system of inequalities that model this situation.
#1) _______________________________________________
#2) _______________________________________________
b) Graph the system of inequalities. (Be sure to title and label your graph.)
c) Give an ordered pair that is in the solution set to the system of inequalities: ( ________, _________)
d) Using substitution, show that the ordered pair from Part C is a solution both of the inequalities.
e) What does your solution mean in the contex of the problem? ________________________________________________
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2) Use the following functions to perform the indicated operations.
f ( x)  3x  4
a)
c)
g ( x)  x  8
f ( x)  g ( x)
b)
f ( x)  g ( x)
f ( x)  g ( x)
3) Student council has $50 in their bank account. They throw a pizza party and charge $4 per pizza. The amount of money in their
account can be represented by the function
.
a) Find
.
b) What does your solution mean in the context of the problem?
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4) Use the function
f ( x)  x 2  2 x  8 to answer the following question:
a) Find the axis of symmetry.
b) Find the vertex.
c) Is the vertex a maximum or minimum? Explain how you know.
d) Factor and use the zero-product property to find the roots.
e) Find the y-intercept.
f) Using the points you found above, graph the quadratic function.
5) The following graph models the path of a rocket.
a) What is the y-intercept and what does it mean in the context of the problem? ____________________________________
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b) What is the positive x-intercept and what does I mean in the context of the problem? ____________________________
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c) What is the maximum point of the function? _____________
Describe what the maximum point means in the context of the problem.
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d) Examine the graph from 0 to 2. Is the graph increasing, decreasing, or constant? _____________________________
e) Explain why the domain of this function is restricted from 0 to 4.2. __________________________________________
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f) Calculate the average rate of change (slope) between the y-intercept and the vertex.