Name: _____________________
Class: _________________
AU10: Notes & HW – Lesson 2
Date: _________________
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1. Which ordered pair is not in the solution set of y   x  5 and y  3 x  2 ? (FS 1 – AU4)
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(1) (5, 3)
(3) (4, 3)
(2) (3, 4)
(4) (4, 4)
2. The equation y  x 2  3x  18 is graphed on the set of axes below. (RJu09#24 – AU9)
Based on this graph, what are the roots of the equation x 2  3x  18  0 ?
(1) -3 and 6
(2) 0 and -18
(3) 3 and -6
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(4) 3 and -18
3. The graphs below represent functions defined by polynomials. (SS2 – AU9)
For which function are the zeros of the polynomials 2 and –3?
(1)
(3)
(2)
(4)
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4. The table below, created in 1996, shows a history of transit fares from 1955 to 1995. On the
grid below, construct a scatter plot where the independent variable is years. State the
exponential regression equation with the coefficient and base rounded to the nearest
thousandth. Using this equation, determine the prediction that should have been made for the
year 1998, to the nearest cent. (GC 3 – AU5/6)
y
x
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5. Max purchased a box of green tea mints. The nutrition label on the box stated that a serving of
three mints contains a total of 10 Calories. (FS 8 – AU3)
On the axes below, graph the function, C, where C (x) represents the number of Calories in
x mints.
Write an equation that represents C (x).
A full box of mints contains 180 Calories. Use the equation to determine the total number of
mints in the box.
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6. The table below lists the total cost for parking for a period of time on a street in Albany, N.Y.
The total cost is for any length of time up to and including the hours parked. For example,
parking for up to and including 1 hour would cost $1.25; parking for 3.5 hours would cost
$5.75. (FS 11 – AU2)
Graph the step function that represents the cost for the number of hours parked.
Explain how the cost per hour to park changes over the six-hour period.
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7. The diagram below, when completed, shows all possible ways to build equivalent expressions
of 3x2 using multiplication. The equivalent expressions are connected by labeled segments
stating which property of operations, A for Associative and C for Commutative Property,
justifies why the two expressions are equivalent. (M1:MM#6 – AU1)
a) Fill in the empty circles with A or C and the empty rectangle with the missing expression
to complete the diagram.
b) Using the diagram above to help guide you, give two different proofs that
x  x  3  3  x  x .
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8. A father divided his land so that he could give each of his two sons a plot of his own and keep
a larger plot for himself. The sons’ plots are represented by squares #1 and #2 in the figure
below. All three shapes are squares. The area of square #1 equals that of square #2 and each can
be represented by the expression 4 x 2  8 x  4 .
(M4:MM#2 – AU7)
a. Find the side length of the father’s plot, square #3, and show or explain how you found it.
b. Find the area of the father’s plot and show or explain how you found it.
c. Find the total area of all three plots by adding the three areas and verify your answer by
multiplying the outside dimensions. Show your work.
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