September 24th Lecture
2.1 Linear Functions and Lines
the slope of the line through (x, y) and (x, y) x=x is
m= y-y/x-x= rise/run
any point (x, y) on the line through (x, y) with slope m, satisfies y-y/x-x=m
point slope form
(y-y)=m(x-x)
if you plug
Mealky
MATH 114 FIRST MIDTERM EXAM
Lecture 1 (afternoon)
October 9, 2013
Your name:
Circle your TAs name:
Bae Jun Park, Fan Zheng, Lalit Jain, Robin Prakash, Ethan Frost
- Circle your answers.
0 Be sure to show your work and explain what you did. You will
October 1st Lecture
2.3 Integer Exponents
x is a real number, m is a positive integer
m*x= x + x + . + x m summands
properties: suppose x, y real numbers m and n positive integers
2.4 Polynomials
a polynomial is a function p of the form p(x)=. n a no
October 5th Lecture
2.5 Rational Functions
Definition: a rational function r has the form r(x)= p(x)/q(x) where p, q are polynomials and
q(x) does not equal zero
Add/Subtract rational functions
Division of Polynomials
Theorem: if p and q are polynomi
October 10th Lecture
Problem: Complete z4 where z=square root of 2/2 all times (1+i)=-1
Fundamental Theorem of Algebra (Lauss)
suppose p is a polynomial of degree n > 1, then there exist complex numbers r, . , r and a
constant c are all real numbers su
October 19th Lecture
Quiz Solutions
The common logarithm: log 10 or log
Note: the common log of an n-digit number is in [n-1, n]
Example: suppose log m = 12.6, log n = 3.2
How many digits does m/n have?
Theorem: if b and y are positive numbers, b does n
October 24th Lecture
4.2 Areas of Simple Regions
the area of a square of side length l or l squared
the area of a rectangle with base b and height h is bh
the area of a parallelogram with base b and height h is bh
the area of a triangle with base b and he
October 31st Lecture
4.4 Approximations with e and natural log (ln)
Remember: ln c = area (1/x, 1, c) = area under graph of y = 1/x between x=1 and x=c
We can approximate ln (1+t) by the area of rectangle t*1=t
if t is close to 0, then ln (1+t)=t
if
MATH 114 FINAL EXAM
December 16, 2013
Your name:
Circle your TAs name:
Sid Kiblawi, Konstantinos Mavrakakis, Michael Mostek, Sowmya Acharya
Bae Jun Park, Fan Zheng, Lalit Jain, Robin Prakash, Ethan Frost
0 Be sure to show your work and explain What you di
M. at ital/4y
MATH 114 - FINAL EXAM
May 13, 2013
Your name:
Circle your TAs name: Rui Wang Sid Kiblawi
0 Be sure to show your work and explain what you did. You. will receive
reduced or zero credit for unsubstantiated answers.
0 No books or calculators. Y
6i (W k?
MATH 114 SECOND MIDTERM EXAM
April 10, 2013
Your name:
Circle your TAs name:
Rui Wang Sid Kiblawi
0 Be sure to show your work and explain what you did. You will receive
reduced or zero credit for unsubstantiated answers.
9 No books or calculators
Name: _
Score: _ / _
Algebra I Quarter 1 Exam
Answer the questions below. Make sure to show your work and justify all of your answers
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Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Review Midterm #1
1. Find the domain of the following. Write your answer in interval notation.
(a) 2x 3
(b)
3
2x 3
(c)
p
|x + 4| + 2
(d)
p
|x + 4| 2
(e)
2x+1
x3
2. Solve. Write
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Sections 6.1-6.3
1. For the following functions, sketch the graph and nd the range, amplitude, and period.
(a) g(x) = sin(5x) on the interval [, ]
Solution
The range o
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Section 3.1
1. Evaluate the indicated expression. Do not use a calculator.
(a) log2 64
(b) log2
1
16
(c) log8 2
(d) log 100
1
(e) log 100
(f) log
10000
(g) log8 26.3
2
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Sections 3.2-3.4
1. Suppose x is such that log6 x = 23.41. Evaluate log6 (x10 ).
2. Suppose log a = 203.4 and log b = 205.4, evaluate
3. Evaluate the given quantities
Department of Mathematics, University of Wisconsin-Madison
Math 114 Fall 2014
Worksheet Sections 3.5-3.7
1. Find a number c such that
(a) ln c = 5
Solution
c = e5
(b) ln c = 3
Solution
c = e3
(c) ln(3c 2) = 5
Solution
3c 2 = e5 3c = e5 + 2 c =
1
e5 + 2
3