

1.

Solve the system by the method of
substitution.


2.

Solve the system graphically.


3.

Solve the system by the method of elimination and
check any solutions algebraically.


4.

Solve the system by the method of
elimination.
a.   b.  (dependent)  c.   d.  inconsistent  e.  


5.

Find the least squares regression line for the points
by solving the system for a and
b.
Points:
a.  y = 3.93x
–4.21  b.  y =
2.80x –3.20  c.  y =
–2.66x +2.80  d.  y =
–3.47x –4.21  e.  y =
–3.20x +2.80 


6.

Use backsubstitution to solve the system of linear
equations.


7.

Find the equation of the circle
that passes through the points.


8.

Find values of x, y, and that satisfy the system. These systems arise in certain optimization problems in
calculus, and is called a Lagrange multiplier.


9.

A chemist needs 10 liters of a 25% acid solution.
The solution is to be mixed from three solutions whose concentrations are 10%, 20%, and 50%. How
many liters of each solution will satisfy each condition? Use 2 liters of the 50%
solution.
a.  2 L of 10%, 7 L of 20%, 1 L of 50%
 b.  7 L of 10%, 7 L of 20%, 2 L of 50%
 c.  7 L of 10%, 1 L of 20%, 2 L of 50%
 d.  1 L of 10%, 2 L of 20%, 7 L of
50%  e.  1 L of 10%, 7 L of 20%, 2 L of 50%



10.

Write the form of the partial fraction
decomposition of the rational expression. Do not solve for the constants.


11.

Write the partial fraction decomposition of the
rational expression. Check your result algebraically.


12.

Write the partial fraction decomposition of the
rational expression. Check your result algebraically.


13.

Write the partial fraction decomposition of the
rational expression.


14.

Select the correct graph of the
inequality.


15.

Find the consumer surplus and producer
surplus.
Demand
Supply


16.

Find the minimum value of the objective function
and where they occur, subject to the indicated constraints.
Objective function:
Constraints:
a.  Minimum at  b.  Minimum at  c.  Minimum at  d.  Minimum at  e.  Minimum at 


17.

Select the region determined by the constraints.
Then find the minimum value of the objective function (if possible) and where they occur, subject to
the indicated constraints.
Objective function:
Constraints:


18.

Find the maximum value of the objective function
and where they occur, subject to the constraints:
Objective function:
Constraints:
a.  Maximum at 80  b.  Maximum at  c.  No maximum  d.  Maximum at  e.  Maximum at 


19.

The linear programming problem has an unusual
characteristic. Select a graph of the solution region for the problem and describe the unusual
characteristic. Find the maximum value of the objective function (if possible) and where they
occur.
Objective function:
Constraints:


20.

An accounting firm has 780 hours of staff time and
272 hours of reviewing time available each week. The firm charges for an audit
and for a tax return. Each audit requires 60
hours of staff time and 16 hours of review time. Each tax return requires 10 hours of staff time and
4 hours of review time. What numbers of audits and tax returns will yield an optimal revenue? What is
the optimal revenue?
a.  0 audit 16 tax returns Optimal revenue:  b.  13 audits 0 tax
return Optimal revenue:  c.  16 audits 0 tax return Optimal revenue:  d.  0 audit 13 tax
returns Optimal revenue:  e.  10 audits 10 tax returns Optimal revenue: 
