Exam 4 Review-Chpts. 7,8&9 MTH 140 Precalculus
Name_____________________
1) Solve the system by the substitution
method.
a) 
b) 
2) Solve the system by the addition
method.
a) 
b) 
3) A vendor sells hot dogs and bags of potato
chips. A customer buys 4 hot dogs and 3
bags of chips for $12.25. Another
customer buys 2 hot dogs and 5 bags of chips for $8.75. Find the cost of each item.
4) A chemist needs 110 milliliters of a
21% solution but only has 1% and 56% solutions available. Find how many milliliters of each that should
be mixed to get the desired solution.
5) A company that manufactures bicycles
has a fixed cost of $100,000. It costs
$100 to produce each bicycle. The
selling price is $300 per bike. Let x represent the number of bicycles
produced and sold.
a) Write
the cost function, C.
b) Write
the revenue function, R.
c) Determine
the break-even point. Describe what this
means.
6) Solve using substitution: 
7) A rectangular piece of tin has an area
of 722 square inches. A square of 5
inches is cut from each corner, and an open box is made by turning up the ends
and the sides. If the volume of the box is
1260 cubic inches, what were the original dimensions of the piece of tin?
8) Write the system of linear equations
represented by the following augmented matrix.
Use x, y, z, and if necessary, w for the
variables.
9) Solve the system of equations using
matrices.
a) 
b) 
c) 
10) Write a system of linear equations in
three variables, and then use matrices to solve the
system.
a) A furniture company produces 3 types of
desks: a children’s model, an office model, and a deluxe model. Each desk is manufactured in three stages:
cutting, construction, and finishing.
The time requirements for each model and manufacturing stage are given
in the following table.
|
|
Children’s
Model |
Office Model |
Deluxe Model |
|
Cutting |
2
hr |
3
hr |
2
hr |
|
Construction |
2
hr |
1
hr |
3
hr |
|
Finishing |
1
hr |
1
hr |
2
hr |
Each week the company
has available a maximum of 100 hours for cutting, 100 hours for construction, and
65 hours for finishing. If all available
time must be used, how many of each type of desk should be produced each week?
b) A
basketball player scored 33 points in game.
The number of three-point field goals the player made was 11 less than three
times the number of free throws (each worth 1 point). Twice the number of two-point field goals the
player made was 12 more than the number of three-point field goals made. Find the number of free throws, two-point
field goals, and three-point field goals that the player made in the game.
c) The
11) Sketch the graph of the following
equations.
a) 
b) 
12) Find the standard form of the equation of
the following ellipse.
13) Sketch the graph of the following
equations.
a) 
b) 
14) Sketch the graph of the following
equations.
a) 
b) 
15) Find the standard form of the equation of
the following hyperbola.
16) Eliminate the parameter and graph the
plane curve represented by the parametric equations. Use arrows to show the orientation of each
plane curve.
a) 
b) 
c) 
Key
