MATH 111 MIDTERM 2 STUDY GUIDE

Midterm 2 will he held on Tuesday March 4. You will have 50 minutes
to answer 10 questions. No notes or calculators will be permitted.

It will cover sections 4.1, 4.2, 4.4, 4.5, 4.6.A, 5.1, 5.2, 5.2.A, and 5.3.

1. STUDY TIPS

The problems on the midterm will be very similar to the homework problems
from WebAssign. Use the homework (Homework 15 to Homework
26) as a study guide. Since quizzes also came from WebAssign, it makes
sense to study those as well.

Try to do problems as you would in a testing environment. In particular,
try to do them without notes or calculators because that is how you will
have to do them on test day. Being able to do homework problems with a
calculator and notes in front of you is very different from being able to do
those problems without them.

Practice, practice, practice. You should not only understand how to do
the problems, but also be able to do them quickly. You should be able to
look at a problem and know automatically what to do. No problem should
take more than 5 minutes.

2. KNOW HOW TO DO THE FOLLOWING. . .

Homework 15
(1) Determine the vertex of a given parabola.
(2) State whether it opens upward or downward.
(3) Find the difference quotient of a quadratic function.
(4) Evaluate the difference quotient at the x- coordinate of the vertex .
(5) Apply a list of given transformations to a quadratic function.
(6) Find the rule of the quadratic function if given its vertex and a point
through which it passes.

Homework 16
(1) The bridge problem.
(2) The rocket problem.
(3) The triangle problem.
(4) The rectangular box problem.
(5) The rectangular garden problem.
(6) The salesperson problem.
(7) The vendor problem.

Note: These are really all the same type of problem. Be sure to label your
variables! This will make it easier to see what to do with x once you’ve
found it. You are given information to set up a quadratic function. You are
asked to find what values maximize the function. So you need to find the
vertex. Then, translate your answer into words.

Homework 17
(1) Determine whether a given algebraic expression is a polynomial.
(2) Given a polynomial, find the leading coefficent.
(3) Given a polynomial, find the constant term.
(4) Given a polynomial, find the degree.

Homework 18
(1) Divide two polynomials using long division.
(2) Determine whether or not a real number is a root of a polynomial.
(Use factor theorem)
(3) Find the remainder when a polynomial is divided by x−c without
doing long division. (Use remainder theorem)
(4) Use the Factor Theorem to determine whether or not x−c is a factor
of a polynomial.
(5) Given a graph of a polynomial function, find the factors of the polynomial.
(6) Find a polynomial with a given degree, a given leading coefficient,
and a given number of roots.
(7) Find a number k such that x−c is a factor of a polynomial with
some coefficients involving k. (See #15 and 16)

Homework 19
(1) Decide whether a given graph could possibly be the graph of a polynomial
function.
(2) Determine the least possible degree of a polynomial function with a
given graph.
(3) Given a graph of a polynomial function, list the roots and state
whether the multiplicity of each root is even or odd.
(4) Use your knowledge of polynomial graphs, to match a function to
its graph.
(5) Given a complete graph of a polynomial function, state whether the
function is even or odd, state whether the leading coefficient is positive
or negative , find the real roots, and find the smallest possible
degree of the function.

Homework 20/21
(1) Find the domain of a rational function.
(2) Sketch f (x) = 1/x and g(x) = 1/x² and apply transformations to
them.
(3) Given a rational function , find the vertical asymptotes, holes, and
horizontal asymptote.
(4) Find the x and y- intercepts of a rational function.
(5) Use the above information to sketch a graph of the function.
(6) Find the difference quotient of a rational function.

Note: For linear rational functions, it’s easy. Just apply the theorem for linear
rational functions.

Homework 22
(1) Solve a linear absolute value inequality algebraically.

Homework 23
(1) Simplify expressions involving exponents.
(2) Factor a given expression. (See #6)

Homework 24
(1) Sketch a complete graph of an expoential function.
(2) Apply transformations to an expoential function.
(3) Match an exponential function to its graph.
(4) Determine whether an exponential function is even, odd, or neither.
(5) Solve word problems involving exponential functions. (See #7-12)

Homework 25
(1) Solve investment problems in which interest is compounded discretely
(i.e. annually, quarterly, monthly, etc.).
(2) Solve investment problems in which interest is compounded continuously .

Homework 26
(1) Find a logarithm.
(2) Translate a given logarithmic statement into an equivalent exponential
statement.
(3) Translate a given exponential statement into an equivalent logarithmic
one.
(4) Evaluate a given expression. (See #10-14)
(5) Find the domain of a given logarithmic function.
(6) Sketch a graph of f (x) = log x and g(x) = ln x.
(7) Apply transformations to these logaritmic functions.
(8) Solve word problems involving logarthmic functions. (See #19-21)