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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

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



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 interpret 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:

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:

Determine 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
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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