MTH 241 Review for test 1



MTH 241 Review for test 1

Skills you should have for test 1:

Test 1 will cover sections Ch1, Ch2 and part of Ch3 (Items from Ch3 will be announced in class)

The purpose of this test is to assess and brush-up your college algebra skills.

Go back to the corresponding sections of your textbook to review the following

topics and do the problems suggested in parentheses.

➢ CH1: Evaluate functions. (ex #1-18 p. 52). Know the basic properties of linear, quadratic and exponential functions (ex #25, 32p. 53, ex #35 p. 52)

➢ Find the linear equation of demand, revenue, cost and profit functions in terms of the number of items produced/sold (sec 1.2).

➢ Identify different types of functions from their graphs or from their equations: linear, quadratic, cubic, exponential, logarithm, rational, piece-wise defined.

➢ Know the basic properties of linear and piece-wise defined functions (sec 1.1, 1.2)

➢ Find the equation of a linear function given the slope and a point or two points. As an application, find the linear model for 2 pairs of data (sec 1.3)

➢ Use the above to find the linear equation of demand, supply, revenue, cost and profit functions in terms of the number of items produced/sold (ch 1)

➢ Using your calculator:

• Graph a function.

• Use the graph of a function to estimate zeros, y-intercept and maximum or minimum points.

• Plot a set of data. Use regression to find the equation (linear, quadratic or exponential) for that data and use this equation to predict new values.

• Find and compare the correlation coefficient r for different models.

▪ Section 2.1: Find the quadratic equation of revenue, cost and profit functions in terms of the sale price p. Find minimum cost, maximum profit and break-even point in terms of (# 37, 39, 40 p. 133).

▪ Section 2.2: Find the equation of an exponential function given a table with initial value. As an application, find the exponential model for 2 pairs of data (# 15-18, 42 p. 147).

▪ Section 2.2: Solve investment problems related to compounding interest. Find future or present values based on a given annual interest rate compounded either continuously or a fixed number of times a year.

▪ Section 2.3. Know and understand the definition of base b logarithms, natural logarithms and base 10 logarithms (ln and log). Know the change of base formula and the basic properties of logarithm functions, and use them to solve equations with unknowns in the exponent. Read p. 143-145. Use the above to solve application problems of investment (how long it takes to…?), half-life and exponential growth and decay. (# 23, 25, 27, 28, 29, 31, 44 p163).

▪ Section 2.4. Know the basic properties of logistic functions and how to interpret them in an application problem.

▪ Sections for Ch3 will be added to this later.

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