Download Algebra Review Packet Day 1 and Day 2 sessions v final

Name _________________________________________________________________
ALGEBRA REVIEW PACKET DAY 1
1) Solve the equation 3x2 + x = 2 algebraically for x.
2) On the set of axes below, solve the following system of inequalities graphically.
State the coordinates of a point in the solution set.
3) Given the graph of the function on the right:
a) On what interval(s) is the function increasing? ________________________
b) On what interval(s) is the function decreasing? ________________________
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 x 2 ,3  x  2
4) Graph the following function on the set of axes below. f ( x)  
6,2  x  7
5) Which of the following has the largest maximum?
1)
3)
2)
y  (2  x)(7  x)
4)
y  4 x 2  10 x  1
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6) The data table below shows water temperatures at various depths in an ocean. What is the value of the linear
correlation coefficient for these data? Round your answer to the nearest thousandth. Explain what the
correlation coefficient suggests in the context of this problem.
The state the equation of the regression line (line of best fit)
7) Given M = 4x2 – 7x + 5 and N = -5x2 + 3x – 2, find, in simplest form:
a) M + N
b) M – N
8) Christine is hiring a photographer for her wedding. She narrowed her choices down to two companies. Pretty
Pictures charges a flat rate of $80 per hour, which can be represented by P(x) = 80x, where x represents the number of
hours of the event. Fabulous Photos charges $50 per hour plus a $300 equipment fee, which can be represented by
F(x) = 50x + 300, where x represents the number of hours of the event. Determine, algebraically, the number of hours, x,
that will make both photographers cost the same. Verify you algebraic solution using your graphing calculator. Explain
what you would look for using your graphing calculator.
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9) Fifteen students were surveyed to find out how many songs they downloaded on their iPhones. The results are as
follows:
120, 124, 132, 145, 200, 255, 260, 292, 308, 314, 342, 407, 421, 435, 452
Using an appropriate scale, construct a box plot for the 15 values.
Then find the Range and the Inter-quartile Range
10) On the given axes, graph f ( x)  2 x .
If g(x) = f(x) + 5, how is the graph of
translated to form the graph of
?
If h(x) = f(x + 1), how is the graph of
translated to form the graph of
?
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11) Which function has the same y-intercept as the given graph?
1) y 


8  6x
4
2) 5y  x  20
3) 16  4 y  3x

4) y  4  x

12) Jennifer deposited $600 in an account in the Monopoly Bank, earning 5.7% interest, compounded annually. She
made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years.
13) Use the data below to write the linear regression equation for the raw test score based on the hours tutored. Round
all values to the nearest hundredth.
a) Equation: ____________________________________
b) Create a residual plot on the given
axes, using the residual scores
in the table.
c) Based on the residual plot, state whether the
equation is a good fit for the data. Justify your answer.
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14) The accompanying graph shows the heart rate, in beats per minute, of a jogger during a 4-minute interval. What is
the domain and range of the function?
15) Determine if the following statements are always true, sometimes true, or never true:
a) The sum of two integers is an integer.
b) The sum of two irrational numbers is rational.
c) The product of two irrational numbers is irrational.
d) The product of two rational numbers is irrational.
___________________________
___________________________
___________________________
___________________________
16) Is the point (5,30) on the graph represented by y = x2 + 2x – 5? Explain how you know.
17) Tim has two less quarters than dimes in his wallet, for a total of $3.00. Write and solve an equation to determine
how many dimes and how many quarters Tim has.
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18) The formula for the area of a semi-circle is
A
1 2
r .
2
What is r, in terms of A and π?
19) What is the product of (7x – 1) and (3x – 4), expressed in simplest form?
20) Write a quadratic equation, in simplest standard form, that has roots of
and 3.
21) What is a formula for the nth term of sequence B shown below?
1)
3)
2)
4)
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Name _________________________________________________________________
ALGEBRA REVIEW PACKET DAY 2
22) The diagrams below represent the first three terms of a sequence.
Assuming the pattern continues, which formula determines
23) If
1)
3)
2)
4)
and
1)
2)21
, the number of shaded squares in the nth term?
, then
3) 11
4) 43
24) What is the value of x in the equation
?
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25) A gym charges a one-time initial fee and a monthly membership charge. The total cost is modeled by the function
y = 30 + 19.99x. Which statement represents the meaning of each part of the function?
1) y is the total cost, x is the number of months of membership, $30 is the initial fee, and $19.99 is the membership
charge per month.
2) y is the total cost, x is the number of months of membership, $19.99 is the initial fee, and $30 is the membership
charge per month.
3) x is the total cost, y is the number of months of membership, $30 is the initial fee, and $19.99 is the membership
charge per month.
4) x is the total cost, y is the number of months of membership, $19.99 is the initial fee, and $30 is the membership
charge per month.
26) Factor Completely:
x 4  x 2  12
27) What are the zeros of the function f(x) = (x – 3)2 – 36?
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28) Given the following tables, determine if they represent linear, quadratic, or exponential functions. Explain your
choices.
a)
b)
c)
29) The owner of a men's clothing store bought six belts and eight hats for $140. A week later, at the same prices, he
bought nine belts and 6 hats for $132. Write a system of equations that can be used to find the price of one belt and one
hat. Using these equations, determine and state the price of one belt and one hat.
30) A student was given the equation x2 + 12x = –22 to solve by completing the square.
The step in the student’s process was x2 + 12x + c = –22 + c.
State the value of c that creates a perfect square trinomial.
Explain how the value of c is determined.
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31) Solve the inequality below to determine and state the smallest possible value for x in the solution set.
3(x + 3) < 5x – 3
32) Solve the equation 4x2 + 8x – 5 = 0 algebraically for x.
33) A local business was looking for a cleaning service to work on their property. They narrowed their choices down to
two companies. Molly Maids company charges a flat rate of $100 per hour. Sparkly Clean Company charges $80 per
hour plus a $260 equipment fee.
a) Write an equation, M(x), that represents the total cost of hiring Molly Maids for x hours. Write an equation,
S(x), that represents the total cost of hiring Sparkly Clean Company for x hours.
b) Determine and state the number of hours that must be worked for the cost of both companies to be the same.
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34) Let f be the function represented by the graph below. Let g be the function such that g ( x)  
1 2
x  3x  1 .
2
Determine which function has the larger maximum value. Justify your answer.
35) Frank bought hamburgers and hot dogs for a BBQ at his house. He spent $2.25 for each hamburger and $1.30 for
each hot dog. Frank spent a total of $98.70 on hamburgers and hot dogs and bought a total of 54 hamburgers and hot
dogs.
a) Write a system of equations that can be used to find how many hot dogs and how many hamburgers Frank
purchased.
b) Using these equations, determine and state how many hot dogs and how many hamburgers Frank purchased
for the BBQ.
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36) Solve the following system of inequalities graphically on the set of axes below.
3x  y  1
y
State the coordinates of a point in the solution set.
2
x4
3
37) The price of an Apple increases according to the equation A(x) = 6x2, where x equals the number of months. The
price of a Samsung stock increases according to the equation S(x) = 8x + 8. Graph both equations on the accompanying
grid and label them A(x) and S(x).
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37 continued
State all price(s) when both stock values were the same. Explain how you determined your answer.
If Robert only wants to invest in the stock for 3 months, should he invest in Apple or Samsung? Justify your
answer.
38) Hailey deposited $6550 in an account in Johnson’s National Bank, earning 3.4% interest, compounded annually. She
made no deposits or withdrawals.
a) Write an equation that can be used to find B, her account balance after t years.
b) Using the equation from part a, determine, to the nearest dollar, how much money Hailey will have in
the account after 10 years.
39) Graph the following function on the set of axes below.
 x, x  2
f ( x)  
 x  3, x  2
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40) Is the equation
change per time period?
a model of exponential growth or exponential decay, and what is the rate (percent) of
1) exponential growth and 12%
2) exponential decay and 12%
3) exponential growth and 88%
4) exponential decay and 88%
41) A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this population
growth?
1)
2)
3)
4)
42) The box plot below represents a set of grades in a college statistics class.
Which interval contains exactly 50% of the grades?
1) 63-88
2) 75-81
3) 63-95
4) 75-88
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