Math 201-02 - Review Sheet Test 2



Math 201-01 – Review Sheet Test 2

1. Understand and be able to work with each of the following:

a. Slope of a line: the ratio of vertical change to horizontal change between any two points on a given line. Slope is positive when increasing from left to right, negative when decreasing from left to right, zero for a horizontal line and undefined for a vertical line. The slope ratio is represented by the letter m.

b. Recognize that the equation of a straight line is the algebraic description of all points which are tied to a specific point (x1, y1) with a given slope relationship. That is, the line is the set of all points (x, y) such that [pic].

c. Be able to write the equation of a line when given appropriate information. Be able to convert the form shown in 1b above to point slope form , slope intercept form or general linear form.

d. Recognize that parallel lines have equal slopes and that perpendicular lines have slopes that multiply to yield a product of –1.

e. When the equation of a straight line is in slope-intercept form, that is y = mx + b form, be able to use the slope m and y-intercept b to sketch the line.

2. Understand and be able to work with quadratic functions recognizing that such functions graph as parabolas and will have either a maximum ( ( ) or a minimum ( ( ) at the vertex.

a. Be able to use formula [pic] to find the equation of the axis of symmetry of a parabola. Recognize that the vertex of the parabola falls on this axis and hence the equation [pic] gives the x coordinate of the vertex as well. Be able to substitute this value into the original function to find the y coordinate of the vertex, then use intercepts and other points to graph.

3. Be able to represent practical situations presented in the text with functions that are either linear or quadratic and be able to work with those resulting functions.

4. Be able to solve systems of linear equations. Be able to work with parameters in simple situations. Be able to solve application problems that may be represented by such systems.

5. Be able to solve systems of equations that may be non-linear. Be able to solve application problems that may be represented by such systems.

6. Understand and be able to work with equilibrium between supply and demand functions.

7. Understand and be able to work with break even between Total Revenue and Total Cost functions. Be able to use

these functions to work with Profit

Chapter 4

1. Understand and be able to work with exponential functions with base larger than 0. (b ≠ 1)

a. Be able to graph such exponential functions.

b. Be able to work with application problems which may be represented by exponential functions.

2. Understand and be able to work with logarithmic functions as defined on page 175.

a. Be able to graph such logarithmic functions.

b. Be able to work with application problems which may be represented by logarithmic functions.

3. Recognize special notation used for log base 10 (log x ) and log base e (ln x).

4. Be able to work with the rules and properties of logs summarized below. In addition, review and be able to work with rules for exponents stated on page 163.

Rule 1: log b (mn) = log b m + log b n

Rule 2: log b [pic] = log b m – log b n

Rule 3: log b mr = r log b m

Rule 4: log b [pic] = – log m

Rule 5: log b 1 = 0

Rule 6: log b b = 1

Rule 7: log b br = r

Rule 8: b log b m = m

Rule 9: log b m = [pic]

Concept 1: If m = n, then log b m = log b n

Concept 2: If m = n, then bm = bn .

5. Be able to solve exponential and logarithmic equations. Be able to solve application problems that may be represented by exponential or logarithmic equations.

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