Math 1314 Lesson 1:
Prerequisites
Prerequisites are topics you should have mastered before you enter this class.
Because of the emphasis on technology in this course, there are only a few
computations that you will still have to do by hand. This lesson is intended as a
quick review of these topics.
1. Using scientific notation
Example 1: Write in decimal form:
3.56 106
Example 2: Write in decimal form: 1.625E 5
Recall:
“E” means" times 10 to the power given
See
See
http://www.nyu.edu/pages/mathmol/textbook/scinot.html
http://www.usna.edu/ChemDept/plebeChem/manual/apdxA.pdf
2. Exponents
Example 3: Simplify and write the answer without using negative
exponents: 5x 3
Recall:
xn 
1
xn
Evaluate for x = 2
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Example 4: Simplify and write the answer without using negative exponents:
A.
3x 2
B.
(3x)2
Evaluate both using x = 2
Example 5: Write using rational exponents:
x
3
5
m
n
Recall: x  n x m
Evaluate using x = 2
Example 6: Write using a radical sign:
See
See
7
x2
http://www.youtube.com/watch?v=j_Eb5FsgJLY
http://www.sparknotes.com/math/prealgebra/powersexponentsroots/section3.rhtml
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3. Writing equations of lines
Example 7:
Suppose the slope of a line is
1
3
and the line passes
through the point (-3,7).
Write the equation of the line in slope-intercept form ( y = mx+ b).
Recall: y  y0  m( x  x0 )
This is the point-slope formula! Know it by heart!
Example 8: Write an equation of the line that passes
through the points (-1, 6) and (3, -4)
Recall: m 
See
y2  y1
x2  x1
http://www.youtube.com/watch?v=oG19cFGRFeA
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4. Simplifying an algebraic expression
Example 9:
Simplify:
22  4 x2  4 x  4
WARNING: VICIOUS and CRUEL
5. Multiplying Binomials and Factoring
Example 10:
Multiply: (4x2 —1)(2x +3)
RECALL FOIL
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Example 11:
Multiply: ( x  3) 2
Example 12:
Factor:
x 2  3x  2
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6. Domain
Example 13:
Find the domain:
f ( x)  x 2  5 x  6
Example 14:
Find the domain:
f ( x)  5 x  4
Example 15:
Find the domain:
Example 16:
Find the domain:
See
3x  12
x5
2x  6
www.youtube.com/watch?v=pUAv94BH7y4
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7. Asymptotes
Vertical Asymptotes:
Factor the numerator and denominator. Look at each factor in the denominator.
If a factor cancels with a factor in the numerator, then there is a hole where that
factor equals zero.
If a factor does not cancel, then there is a vertical asymptote where that factor
equals zero.
Horizontal Asymptotes
Let f ( x) 
p ( x)
q ( x)
Shorthand: degree of f = deg(f), numerator = N, denominator = D
1. If deg(N) > deg(D) then there is no horizontal asymptote.
2. If deg(N) < deg(D) then there is a horizontal asymptote and it is y = 0 (x-axis).
3. If deg(N) = deg(D) then there is a horizontal asymptote and it is a/b
where a is the leading coefficient of the numerator. b is the leading coefficient
of the denominator.
Google this for videos and reviews!
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Example 17:
f ( x) 
Find any vertical and/or horizontal asymptotes:
4x  2
2x 1
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Example 18:
f ( x) 
Find any vertical and/or horizontal asymptotes and holes:
( x  2)( x  3)
( x  2)2
What is the domain?
What does the graph look like?
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8. Using functional notation
Example 19 A
If f ( x)  x 2  5x find:
A.
f (-2)
B.
f (4+h)
19B For the given function, find f (− 1 + h)
See
f ( x)  x 2  2 x  12
http://answers.yahoo.com/question/index?qid=20080916204806AAqMQBN
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Example 20:
A Use the piecewise-defined function below to find f (5), f(10) and f (− 3) .
 x 3  1 x  5
f ( x)  
2
3  x x  5
B.
Use the piece-wise defined function below to find the
y-intercept and f (−2).
3 x 2  1
f ( x)  
5  x  3
x0
x0
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Example 21:
Given the following graph of a function f state:
A
Domain
B
Range
C
f(−2)
D
all asymptotes
E
x = ____ when f(x) = 0
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9. Solving an equation for a variable x
Example 22:
Solve for s:
ys – 6s = 12
10. Solve the Systems of Equations
Example 23:
See
Solve the system:
x  5y  8
x  2y 1
www.youtube.com/watch?v=xB-oXaCoJoc
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Example 24:
Solve the system:
4 x2  5 y  0
8 x  5 y  12
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Interval Notation – On your own. See, for example:
http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation01.htm
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Information about the class:
Assignments:
Lectures
15 weeks of these, 24 + test reviews
Tests
Test 1 online, 8%, 2 attempts….70% boundary…prerequisite
material. Can be made up
Tests 2 – 4, 12 % each, in CASA by appointment
Test 2 – Lessons 1 – 8
Test 3 – Lessons 9 – 15
Test 4 – Lessons 16 – 24
DO NOT SCHEDULE your tests during the lecture time!
Cannot be made up – you will have to take the final if you miss
your appointment. 10 minute rule. Their clock.
Final
cumulative 24%
Can opt out (80.000000 grade after Test 4)
Can count twice…no makeups!
In our classroom, on a popper form
Quizzes
12 of these … close on Sundays. 12%. No second chances.
Homework 24 of these, due 48 hours after the lecture
(Thursdays and Sundays)
10 questions each. 10% of your grade. Drop the lowest 15%.
No makeups.
Poppers
start the third week of class, daily,
sit by people who want the same grade that you want!
10% of your grade. Drop the lowest 15%. No makeups
Resist the urge to email me if you’re missing one.
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