### Math 1050 (College Algebra) - Final Review

This is the final review for Math 1050.  It covers almost everything found in the course outline.  To reveal the answers click on the problem's number or scroll down.

1) Functions in Equations (Sec 1.1, 1.5, 5.4). Solve the equation.

2) Quadratic Function (Sec 4.1). Find standard form, vertex, and graph.

3) Inverse Function (Sec 3.7). Find the inverse of a one-to-one function and state domain and range for both the function and its inverse.

4) Polynomial Function (Sec 4.4). Use the Rational Zeros Theorem and Descartes' Rules of Signs to set up the problem, factor using synthetic division, and graph.

5) Rational Function (Sec 4.6). Using a sign chart as an aid, find and label all asymptotes and x- intercepts, and graph a rational function.

6) Radioactive Decay (Sec 5.5). Determine time based on radioactive decay. No number crunching required. Using log properties, simplify answer to form provided.

Polonium-210 (10Po) has a half-life of 140 days. Suppose a sample of this substance has a mass of 300 mg.
(a) Find a function that models the amount of the sample remaining at time t.
(b) Find the mass remaining after one year.
(c ) How long will it take for the sample to decay to a mass of 200 mg?
(d) Draw a graph of the sample mass as a function of time.

7) Ellipse (Sec 8.4). Find standard form, locate center, vertices, foci, and graph.

8) Partial Fraction Decomposition (Sec 6.4). Rewrite a rational function as the sum of partial fractions.

9) Linear Programming. Maximize the profit with a given set of constraints. Focus on Modeling.

A small shoe manufacturer makes two styles of shoes: oxfords and loafers. Two machines are used in the process: a cutting machine and a sewing machine. Each type of shoe requires 15 min per pair on the cutting machine. Oxfords require 10 min of sewing per pair, and loafers require 20 min of sewing per pair. Because the manufacturer can hire only one operator for each machine, each process is available for just 8 hours per day. If the profit is \$15 on each pair of oxfords and \$20 on each pair of loafers, how many pairs of each type should be produced per day for maximum profit?

10) System of Equations. Solve a 3x3 system of equations.

Gauss-Jordan Elimination (Sec 7.1).

Inverse Matrix Method (Sec 7.3).

Cramer's Rule (7.4).

11) Matrix Operations (Sec 7.2). Perform matrix operations.

12) Arithmetic Series (Sec 9.2). Find the sum of the first 200 terms of an arithmetic sequence.

3, 7, 11, 15, ...

13) Infinite Geometric Series (Sec 9.3). Find the sum of infinitely many terms of a geometric sequence.

14) Binomial Theorem (Sec 9.6). Use the Binomial Theorem to find a binomial expansion.

Solutions