Download Unit 1 Test C Name_____________________

Unit 1 Test C
Name_____________________
1. The senior class is organizing a graduation party. They estimate the expenses for the party will be
$5,000. This $5,000 cost will need to be equally divided among all seniors attending the party. The rule
𝟓𝟎𝟎𝟎
relating cost per senior C and number of seniors N who attend the party is 𝑪 =
𝒏
a. Complete the sentence:
The cost per senior is ______________________ proportional to the number of seniors attending the
party with constant of proportionality ______________________.
b. Rewrite the equation 𝑪 =
𝟓𝟎𝟎𝟎
𝒏
so n is a function of C.
c. If 500 seniors attend the party, how much will each senior have to pay?
d. If the cost per senior was $25, how many seniors attended the party?
e. As the number of seniors attending the party decreases, how does the amount each senior will have
to pay change? Be as specific as possible.
f. As the number of seniors attending the party increases, how does the amount each senior will have to
pay change? Be as specific as possible.
2. The length of a spring (in cm) is related to the mass (in gm) of the object attached to the spring by
the formula L = 0.25m
Complete the sentence: The length of a spring, L is ______________________ proportional to the mass
of the object, m, with constant of proportionality ______________________.
a.
If a spring has a mass of 10 gm, use the function L = 0.25m to determine how long the spring
would be in centimeters.
b.
If a spring is 50 cm long, use the function L = 0.25m to determine what the mass of the spring
would be in gm's.
3. The distance D (in feet) a bicycle travels with one revolution of the pedals is related to the size of the
wheel, the number of teeth on the front sprocket F, and the number of teeth on the rear sprocket R. For a
6.8𝐹
bicycle with a 26-inch rear wheel, the rule is 𝑑 =
𝑅
a. If the value of F is constant and the value of R decreases, what happens to the value of d?
b. If the value of F is constant and the value of R increases, what happens to the value of d?
c. If the value of R is constant and the value of F increases, what happens to the value of d?
d. If the value of R is constant and the value of F decreases, what happens to the value of d?
e. Rewrite the rule 𝑑 =
6.8𝐹
f. Rewrite the rule 𝑑 =
6.8𝐹
𝑅
𝑅
to express F as a function of d and r.
to express R as a function of F and d.
4.
Match each equation with the appropriate graph.
A. y = 7x
B. y=8/x
Then determine if the graph is direct or inverse variation and give the value of k.
Equation:
5.
Equation:
c. y = 9/x 2
Equation:
Use substitution or elimination to determine if the two lines below intersect. (Your
answer should be one of the following: infinitely many solutions, no solution, or one
solution). Show the work/evidence that leads to your answer.
-4x + y = 3
-8x + 2y = -6
6.
Use substitution or elimination to determine if the two lines below intersect. (Your
answer should be one of the following: infinitely many solutions, no solution, or one
solution). Show the work/evidence that leads to your answer.
-2x + y = 1
2x + y = 2
7.
Use substitution or elimination to determine if the two lines below intersect. (Your
answer should be one of the following: infinitely many solutions, no solution, or one
solution). Show the work/evidence that leads to your answer.
-6x + 3y = -9
-4x + 2y = -6
8.
Use the graphing method to solve the system of equations.
-3x + y = 8
-x + y = -2
Benchmark Assessment C:
1)
A local business has decided to give away T-shirts and hats to advertise for business. The T-shirts cost the
business $6 each, and the hats $10 each.
a. The promotional cost C for the business depends on the number of shirts x and hats y given
away. Write a rule expressing C as a function of x and y.
b. How will the business' cost change as the number of shirts given
away increases?
c. How will the business' cost change as the number of hats given away increases?
d. Suppose the business has budgeted $1800 for the promotion. Write an equation that represents the
question "How many shirts and hats can the business give away for $1800?"
e.
Rewrite your equation from Part d to express y as a function of x.
2)
Kris deposited 279 coins into a coin-counting machine and received $56.70. All of the coins she had
saved were dimes and quarters.
a. Write a system of linear equations in which one equation expresses the condition about the number
of coins that Kris deposited, and the other relates the numbers of dimes and quarters to the total value of
the money deposited.
b. Solve the system using the substitution method. Clearly show each step and describe what your
answer means in context.
c. Solve the system using the elimination method. Clearly show each step, and describe how your answer
would be seen in the graph of the system.