Math 141 Exam 2

Sections 3.1-3.3, 5.1-5.3, 6.1-6.4

Be sure to review the following:

  1. Setting up a linear programming word problem.
  1. Solving a linear programming problem by graphical methods.
  1. Interpreting the solution to a linear programming problem.
  1. Solve finance problems involving simple and compound interest, including continuous compounding and effective interest rates.
  1. Solve finance problems involving present and future value, including annuities and sinking funds.
  1. Solve finance problems involving amortization, and create amortization tables.
  1. Writing sets in roster notation and set builder notation.
  1. Finding unions, intersections, complements and subsets of sets algebraically and graphically.
  1. Understanding the difference between elements of sets, subsets, and proper subsets.
  1. Drawing Venn diagrams.
  1. Find the number of elements in a set through Venn diagrams, algebraic techniques, and counting techniques.
  1. Using the multiplication principle to find the number of ways an event can happen.
  1. Drawing tree diagrams.
  1. Working problems involving permutations and/or combinations

Chapter 3 Formulas

A standard maximization problem is one in which

1) The objective function is to be maximized.

2) All the variables involved in the problem are nonnegative.

3) Each linear constraint may be written so that the expression involving the variables is less than or equal to a nonnegative constant.

Chapter 5 Formulas

Simple Interest

I = Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

A = P(1 + rt), where A is the accumulated amount, P is the principal, r is the interest rate, and t is the time in years.

Compound Interest

, where A is the accumulated amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.

, where A is the accumulated amount, P is the principal, r is the annual interest rate compounded continuously, and t is the time in years.

, where is the effective rate of interest, r is the annual interest rate, and n is the number of compounding periods per year.

Chapter 6 Formulas

De Morgan’s Laws

Let A and B be sets. Then, and

n(AB) = n(A) + n(B) – n(AB)

n(ABC) = n(A) + n(B) + n(C) – n(AB) – n(AC) – n(BC) + n(ABC)

The number of permutations of n distinct objects taken n at a time:

P(n, n) = n!

The number of permutations of n distinct objects taken r at a time:

P(n, r) =

Permutations of n Objects, Not All Distinct:

Given a set of n objects in which objects are alike and of one kind, objects are alike and of another kind,…, and, finally, objects are alike and of yet another kind so that

then the number of permutations of these n objects taken n at a time is given by

The number of combinations of n distinct objects taken r at a time is given by

C(n, r) = (where rn)

P(E F) = P(E) + P(F) – P(EF)

P() = 1 – P(E)