# MATH 105 Sample Mastery Exam

- Factor 4
*x*^{2} - 9*y*^{2}.
- Expand (3
*x* + 2)^{2}.
- Simplify (2
*x*/*y*^{2})^{3}.
- Simplify (2
*x*^{2} - *x* - 3)/(*x*^{2}
- 1).
- Solve the system
- Solve 2
*x* + 1/3 = *x*/2* *- 1.
- Solve |
*x* - 1| ≤ 10
- Simplify .
- Find the equation of the graph given below.

- Find the equation of the line parallel to 2
*x* - *y*
= 2 that passes through (1,4).
- Find the zeros of
*f* where *f*(*x*) = (*x*^{2}
- 4)(2*x* + 8).
- Use the graph of
*g*(*x*) = *x*^{3}
+ *x*^{2} - 2*x* shown below to find
the solution set of *x*^{3} + *x*^{2}
> 2*x*.

- Find the distance between (2,3) and (1,-6).
- Solve 2/
*x* + 3/*x* = 5/3.
- Find the
*x*-intercepts of the parabola *y* = *x*^{2}
- 6*x* - 7.
- Sketch the graph of
*x*^{2} + *y*^{2}
- 4*x* + 2*y* - 4 = 0.
- Solve 2
*x*^{2} + 6*x* - 3 = 0.
- Find the domain of
*f*(*x*) = (*x* + 4)/(2*x*
- 6).
- Given that
*f*(*x*) = 2/*x* and *g*(*s*)
= 3*s* - 5, compute *f*(*g*(*t*)).
- Find the inverse
*f *^{-}^{1}(*x*)
where *f*(*x*) = *x*^{3} + 1.
- Solve 3
^{2x + 1} = 1/3.
- Which of the following statements are true
- Every natural number is an integer.
- Some integers are irrational numbers.
- Some complex numbers are real.

- Use the graph of
*y* = *x*^{3} - 7*x*^{2}
+ 17*x* - 14 shown below to find the solution of *x*^{3}
- 7*x*^{2} = 14 - 17*x*.

- The graph of a function
*f*(*x*) is shown
below. Sketch the graph of *h*(*x*) = *f*(*x*
+ 1) - 4.

- Sketch the graph of
- The function
*C*(*x*) = 10*x*^{2}
+ 40*x* + 90 gives the cost (in dollars) of
producing *x* units of product. Find the cost for
producing 4 units.
- Find the vertical asymptotes of
*f*(*x*) = 1/(*x*^{2}
- 2*x* - 3).
- Sketch the graph of
*f*(*x*) = *e*^{x
+ 2}.
- Evaluate log
_{2} 16.
- Express 5 log
*x* - 6 log *y* + 3 log *z*
as a single logarithm.
- The fastest growing city in the United States between the
years 1980 and 1990 was Moreno Valley, California. The
population was approximately 30,000 in 1980 and 120,000
in 1990. Assuming exponential growth (i.e. the population
*P* as a function of the time *t* in years is *P*
= *P*_{0}*e*^{kt}), what
will the population be in the year 1998?
- Graph the system of inequalities
*y* ≤ 1, *x*
≥ *y*/2.
- A budding numismatist (coin collector) has a total of 15
silver dollars and quarters; the total face value of the
silver dollars and the quarters is $9.75. How many of
each does he have?