Algebra 2 Study Island 3d, f, j l-n, 4a-b, 6c-d
Directions: Show ALL of you work to find the best answer for the following questions.
Algebraic Expressions
1.
x1/2
Which of the following expressions is equivalent to the expression above?
A. 1/2x
B.
(x)
C. (x)
D. x-2
Quantitative Relationships
2. Pam invested money into a small stock market account. After several years of continued
growth, the table below shows how much her investment earned.
Investment Earnings
Years
1
2
3
4
$500 $2,000
Money Earned $31.25 $125
Which of the following functions would best model the data above?
A. exponential function
B. constant function
C. quadratic function
D. linear function
5
$8,000
Change in Parameters
3.
The curve given by the equation y = 3x2 - 2 is graphed above. How will the graph of the equation
be affected if the equation is changed to y = -3x2 - 2?
A. The graph will be shifted down.
B. The graph will be wider.
C. The graph will open down.
D. The graph will be the same.
Inverse & Composition of Functions
4. If f(x) and g(x) are defined as below, what is f(g(x))?
A.
C.
B.
D.
Change in Parameters
5.
The curve given by the equation y = 4x - 3 is graphed above. How will the graph of the equation be affected if
the equation is changed to y = 4x - 1?
The graph of the equation will increase at the same rate, but the graph and y-intercept will be shifted up.
A.
B.
C.
The graph will not change.
The graph of the function will increase at a faster rate.
The graph of the equation will increase at the same rate, but the graph and y-intercept will be shifted
D. down.
Nonlinear Systems of Equations
6. Which is the apparent solution set to the system of equations shown on the graph?
A.
B.
C.
D.
Inverse & Composition of Functions
7.
A.
C.
B.
D.
Transformations
8. The graph of f(x) = 5x3 is a ____________ of the graph of
g(x) = x3.
A. translation
B. dilation
C. reflection
D. rotation
Transformations
9. The equation y = -1/2x + 2 is graphed below.
If the graph is reflected across the x-axis, then which equation below represents the new graph?
A. y = -1/2x - 2
B. y = 1/2x + 2
C. y = 1/2x - 2
D. y = -1/2x + 2
Scatter Plots
10. Choose the equation below which would be the line of best fit for the scatter plot.
A. y = 2/5x + 5
B. y = 3/4x + 2
C. y = 1/2x + 5
D. y = 1/2x + 2
Probability
11. Jodie is conducting an experiment and has to make a free throw and throw a dart for a bullseye. The
probability of accomplishing both is 4 out of 7. The probability of making the free throw is 13 out of 18. Given
the free throw is made, what is the probability of hitting the bullseye?
A.
B.
C.
D.
Scatter Plots
12.
The graph above shows a line of best fit for data collected on the number of tickets sold at a year-round
waterpark as a function of the daily high temperature. What is the equation of the line of best fit?
A.
B.
C.
D.
Exponential & Logarithmic Functions
13. Which statement describes the rate of change of the following function?
f(x) = (1/4)x
A.
B.
C.
D.
The function decreases for all x, decreasing faster when x > -4 than it does when x < -4.
The function decreases for all x, decreasing faster when x < 1 than it does when x > 1.
The function increases for all x, increasing faster when x < 1 than it does when x > 1.
The function has a constant rate of change, decreasing for all x at a rate of 1/4.
Transformations
14. Changing the equation y = (x - 4)3 - 2 to y = -(x - 4)3 - 2 will change the graph by reflecting it across the
A. line y = -2.
C. y-axis.
B. line x = -4.
D. x-axis.
Change in Parameters
15. Each of the following statements describes a transformation of the graph y = |x|.
Which statement describes the graph of y = |x + 11| - 11?
A.
B.
C.
D.
It is the graph of |x| shifted 11 units right and 11 units up.
It is the graph of |x| shifted 11 units left and 11 units down.
It is the graph of |x| shifted 11 units left and 11 units up.
It is the graph of |x| shifted 11 units right and 11 units down.
Nonlinear Systems of Equations
16. What is the solution set to the following system of quadratic equations?
y = x2 - 2x - 4
y = 2x2 - 9x + 6
A. {(2,2);(5,11)}
B. {(2,31);(5,4)}
C. {(2,-4);(5,11)}
D. {(-2,-4);(-5,11)}
Trigonometry
17.
If x = 32.5 cm and z = 39.2 cm, what is the measure of angle ?
A. 50°
B. 34°
C. 56°
D. 40°
Probability
18. Kevin went to the store to rent a DVD. There are 23 copies of the DVD he wants to rent and 4 of them are
scratched to the point that they will skip. Given one person came in right before Kevin and grabbed a copy that
does not skip, what is the probability that Kevin will grab a DVD that skips?
A. 2/11
B. 3/22
C. 3/23
D. 4/23
Algebraic Expressions
19. Evaluate the expression below for x = 1 and y = -1.
A. -7
B. -5
C. 9
D. -1
Trigonometry
20.
If
= 65° and h = 5 mm, what is the value of k to the nearest tenth of a millimeter?
A. 11.8 mm
B. 11.3 mm
C. 5.5 mm
D. 10.7 mm
Inverse & Composition of Functions
21.
A.
B.
C.
D.
Nonlinear Systems of Equations
22. Solve the following system of equations.
y = x2 - 4x + 18
y = 3x + 6
A. (4,18) and (9,63)
B. (3,15) and (4,18)
C. (-3,-3) and (-4,-6)
D. (3,15) and (-4,-6)
Scatter Plots
23.
The graph above shows a line of best fit for the data collected at a batting cage for the number of hits in relation
to the speed of the pitch. What is the equation of the line of best fit?
A.
B.
C.
D.
Quantitative Relationships
24. Look at the data in the table below.
x
0
1
2
3
4
5
-1
4
30 214 1,291 7,775
y
Which of the following models would do the best job of modeling the data above?
A. constant model
B. exponential model
C. quadratic model
D. linear model
Algebraic Expressions
25. Rewrite the following expression with only positive exponents.
x-6y-5z-6
x6y10z-3
1
A.
x12y15z3
z3
B.
x12y15
1
C.
x12y15z9
1
D.
y5z3
Probability
26. Which of the following statements best describes probability distribution?
A.
B.
C.
D.
The occurrence of one event does not affect the probability of another event.
A function that displays each outcome of a random event with its probability.
The set of all possible outcomes of an experiment.
The probability that one event leads to another event.
Exponential & Logarithmic Functions
27. What is the x-intercept of the following function?
A. 1
C. The function does not have an x-intercept.
B. 0
D. 7
Quantitative Relationships
28. Look at the data in the table below.
x
1
2
3
4
5
y
0
7
14
21
28
Which of the following models would do the best job of modeling the data above?
A.
exponential
model
B. quadratic model
C. linear model
D. constant model
Exponential & Logarithmic Functions
29. Between
?
and
, which function has an average rate of change that is less than that of
A.
C.
B.
D.
Trigonometry
30.
If n = 44 mm and p = 67 mm, what is the measure of angle ?
A. 33°
C. 41°
B. 57°
D. 49°