Math 4C Fall 2007 Midterm 1 Reference Sheet Distance between two points Linear equations
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d = ( x 2 " x1 ) 2 + ( y 2 " y1 ) 2 Midpoint between two points x +x y +y ( 1 2 , 1 2) 2 2
Slope between two points m =
General form Slope-intercept form Po
The Complex Plane and Eulers Formula
Any complex number can be written in the form
x + yi
for real numbers, x and y . We call x the real part and y the imaginary part
of the complex number. Examples of complex numbers include 1 + 4i and
2
3i. Real number
Math 4C
Midterm Exam 1 Solutions
1. Consider the intervals
A = (1, 7]
B = (4, )
Draw each on the number line provided. Be sure to indicate whether each endpoint is included.
Solution.
(a) A
(b) B
(c) A B
(d) A B
2. (a) Write the equation of a line paralle
Summary of Graph Transformations
Consider a complicated (new) function y = f (x) written in terms of a simple (old)
function b = g (a).
Vertical transformations mess with g s output and so they go on the outside.
Horizontal transformations mess with g s
Math 4C
Practice Final
Please note: the Final Exam will be cumulative. That is, it will cover all of the course material.
However, this Practice Exam only covers material since Midterm 2. You should also review the
Practice Midterms, and the actual Midter
Math 4C
Practice Exam 2
This practice exam is provided as a study aid. The actual exam problems should be of a similar
diculty. Note, however, that the exam problems may cover material not covered by this practice.
Also, the exam problems will not just be
(1) Suppose f is an exponential function and that
f (3) = 2
f (4) = 7
Find f (5).
Solution. One solution would be to plug in y = 2 for t = 3 and y = 7 for t = 4
into the exponential equation:
y = y0 2t/d
to get two equations. By manipulating these equatio
Math 4C Fall 2007 Midterm 2 Reference Sheet Trigonometric functions sin " = opp hyp, cos " = adj hyp, tan " = opp adj Of acute angles sin " = y r , cos " = x r , tan " = y x ( x # 0) (circle radius r) Of any angle sin t = y, cos t = x, tan t = y x (