Download Unit 1 Post Test A Answers

Unit 1 Post-Test
Modeling Functions
NAME: ______________________________ DATE: ________ Period : ______
REVIEW SHEET
SCORE:
Solve a system of equations
Solve a system of inequalities
Solve for a specific variable
Graph linear, absolute value, and quadratic functions
Write linear, absolute value, and quadratic functions
Evaluate and apply various functions
ALGEBRA: ______ / _______ = _______%
FUNCTIONS: ______ / _______ = _______%
ALGEBRA
1. Two brothers are saving money to buy tickets to a concert. Their combined savings is $75. One brother has $35 more
than the other. How much has each saved?
X + y = 75, x + 35 = y; x + (x + 35) = y; x = 20, y = 35
2. Solve for h:
V   r 2h
v/∏r2 = h
3. Last year the volleyball team paid $5 per pair of socks and $17 per pair of shorts on a total purchase of $315. This
year they spent $342 to buy the same number of socks and shorts because the socks now cost $6 and the shorts now
cost $18. How many pair of socks and shorts did the team buy each year?
5x + 17y = 315, 6x + 18y = 342; x = 15, y = 14
4. Solve the system:
 2x – y = 2

 2x – 2 y = 4
(0, -2)
5. Your candy factory is making chocolate-covered peanuts and chocolate-covered pretzels. For each case of peanuts,
you make $40 profit. For each case of pretzels you make $55 profit. The table below shows your conditions.
Production Hours
Peanuts
Pretzels
Maximum Hours
Machine Hours
2
6
150
Man Hours
5
4
155
a. Write a system of inequalities to represent the situation.
b. Graph the system of inequalities and Label your vertices.
c. How many cases of each product should you make to maximize profit? What is the profit you will make?
________ peanuts
________ pretzels
Profit: _______________
FUNCTIONS
Voting in Presidential Election Years
The table shows the percent of people of
voting age who reported they voted in
presidential election years.
Year
% who voted
1988
57
1992
61
1996
54
2000
55
2004
58
SOURCE: HTTP://WWW.CENSUS.GOV/POPULATION/WWW/SOCDEMO/VOTING.HTML#HIST
6. Represent the data using each of the following:
a. a mapping diagram
1988
54
1992
55
1996
57
2000
58
2004
61
b. ordered pairs
c. graph on coordinate plane
(1988, 57), (1992, 61), (1996, 54),
(2000, 55), (2004, 58)
7. Write a function to model the cost of renting a truck for one day. Then evaluate the function for the given
number of miles.
Daily rental: $39.95
Rate per mile: $.60 per mile
Miles traveled: 48 miles
8. Evaluate the function for the given value of x, and write the input x and the output f (x) as an ordered pair.
a. f(x) = ½ x – 1 for x = -2
f(-2) = -2
b. Find the Error:
Evaluate
f(x) = 3x2 – 4x + 1
for x = -5
f( -5) = 3(-5)2 – 4(-5) + 1
f( -5) = 3(10) – 4(-5) + 1
f( -5) = 51
9. Given (2, -3) and (-4, -5) find the following:
a. Calculate the slope between the points
b. Write the equation of the line passing through those points
c. Write the equation of the line parallel to the one you found in part (b) passing through (6, 1)
d. Write the equation of the line perpendicular to the one you found in part (b) passing through (6, 1)
e. Graph the equation of the line you found in part (b).
10. A company in Greensboro manufactures piston rings that are to be 5.25 inches in diameter. A ring is rejected if its
diameter, d, is off by more than 0.0125 inch.
a. Write an absolute value inequality that represents this situation. |d – 5.25| ≤ .0125
b. Solve. State the meaning of the answer in the context of the problem. The diameter can be between
5.2625 and 5.2375
11. Write the function represented in each graph. Then state the domain and range of each.
a.
b.
y = 2(x + 1)2 – 4
Y < 1/3x + 1
c.
y = 4|x| + 1/2
12. Use the function, f ( x)  2 x 1  3 answer the following:
a. Graph the function (label the vertex)
Vertex: (1, 3)
b. State the transformations to the parent graph
Right 1, Up 3, Stretched by factor of 2
c. State the domain and range of the function
D = All real numbers; R = All real numbers greater than or equal to 3
1
3
13. Use the function, f ( x)   x 2  4 x  16 answer the following:
a. Graph the function (label the vertex, axis of symmetry, and y-intercept)
A of S: x = -6; Vertex: (-6, -4); y-intercept = -16
b. Write the function in vertex form
y = -1/3(x + 6)2 – 4
c. State the transformations to the parent graph
Left 6, down 4, compressed by factor of 1/3, reflected across the x-axis
d. State the domain and range of the function. D = all real numbers; R = All real #’s ≤ -4
14. A player hits a tennis ball across the court and records the height of the ball at different times, as
shown in the table.
Time(s) Height (ft)
a. Find a quadratic model for the data. -1/2x2 + x + 5.5
0
5.5
1
6.0
b. Use the model to estimate the height of the ball at 4 seconds. 1.5 feet
2
5.5
c. What is the ball’s maximum height? 6 ft
3
4.0
15. A small independent motion picture company determines the profit P for producing n DVD copies of a
recent release is P = 0.02n2 + 3.40n  16. P is the profit in thousands of dollars and n is in thousands
of units.
a. How many DVDs should the company produce to maximize the profit? 85 thousand DVDs
b. What will the maximize profit be? $128,500
Performance Tasks:
ALGEBRA
16. Given the inequality │x + 2│ ≤ k , find a value of k, if possible, that satisfies each condition. In each case, explain
your choice.
a. Find a value of k such that the inequality has no solution.
b. Find a value of k such that the inequality has exactly one solution.
c. Find a value of k (different from your value in part b) for which a solution exists but for which the solution set
does NOT include 5.
FUNCTIONS
17. Write a short paragraph about the similarities and differences of the types of functions covered in this unit (linear,
absolute value, quadratic). Reference which functions are even and which are odd and justify your choice. Be sure to
thoroughly answer in vivid detail.
(BONUS) Given the data below: Find the recursive and explicit equations: