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Precalculus I Lecture Notes

Fri 10 Oct — Review for Exam 2 on A.8, A.10, Cpt 1, and Cpt 2

A.8 Word Problems

Simple Interest Problems

Mixture Problems

Uniform Motion Problems

Constant Rate Job Problems

One train leaves for Mpls from Chicago at 9 pm traveling 50 mph. One hour later, another train leaves
Mpls for Chicago traveling at 40 mph. The distance along the track is 410 miles. At what time do they
meet?



Let t = time for fast train

Then, time for slow train is t - 1 since it left one hour later.


410 = 50t + 40(t !1)
410 = 50t + 40t ! 40
450 = 90t
5 = t

So, the time for the fast train is 5 hours. Since it left at 9 pm, it meets the slow train
at 9 pm + 5 hours = 2 am.

Tickets to a show cost $5 for adults and $2 for kids. If 200 tickets were sold and
$589 was collected, how many of each type of ticket was sold?

x = # kid tickets

200 - x = # adult tickets

Total Money = Money from kids + Money from Adults

589 = 2•x + 5•(200 - x)
589 = 2x + 1000 - 5x
-411 = -3x
137 = x

So, there are 137 kid tickets and 200 - 137 = 63 adult tickets sold.

A.10 Roots

Simplify radicals
Add and subtract radicals
Rationalize denominators of radicals
Solve radical equations
Rational exponents

Simplify:

Simplify:

1.1 Lecture on Distance and Midpoint Formulas , which includes:

Rectangular (x-y) coordinates
Distance formula
Midpoint formula

1.2 Lecture on Graphs of Equations in Two Variables , which includes:

Graph equation by plotting points
Intercepts of a graph
Test for symmetry with respect to x-axis, y-axis, and origin
Graph y = x^3, x = y^2, and y = 1/x

1.3 Lecture on Lines, which includes:

Calculate and inter pret the slope of a line
Graph lines given a point and the slope
Equation of a vertical line
Equation of a horizontal line
Point-slope form of a line
Find equation of a line given two points
Slope-intercept form of a line
Identify slope and y-intercept of a line given its equation
General form of a line
Parallel lines
Perpendicular lines

1.4 Lecture on Circles , which includes:

Standard form
Graph a circle
General form and completing the square

2.1 Lecture on Functions, which includes:

Relations
Value of a function
Implicit form of a function
Domain of a function
Sums , differences , products , and quotients of functions

2.2 Lecture on Graph of a Function, which includes:

Identify the graph of a function
Obtain information from the graph of a function

2.3 Lecture on Properties of Functions, which includes:

De termine even and odd functions from a graph
Identify even and odd functions from the equation
Use a graph to determine where a function is increasing, decreasing, or constant
Local maxima and local minima
Average rate of change of a function
Secant line

2.4 Lecture on Library of Functions & Piecewise-defined Functions, which includes:

Square root , cube root, absolute value, square, cube, reciprocal , greatest integer
Piecewise-defined functions

2.5 Lecture on Graphing Techniques & Transformations, which includes:

Vertical shifts
Horizontal shifts
Compressions
Stretches
Reflections about x-axis and y-axis

2.6 Lecture on Mathematical Models & Building Functions, which includes:
Word problems on building and analyzing functions

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