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 tw
Practice problems for Midterm 2 (Math 4C-F2017)
Exercise (1)
Suppose you deposit 5000 dollars in a bank:
(i) Assuming the bank applies a continuously compounded interest,
what interest rate is requir
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 o
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)
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
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 a
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
(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 2
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)
Practice problems for Midterm 1 (Math 4C-F2017)
Exercise (1)
Consider the functions f (x) =
p
|x| and g(x) =
1
.
x3
Let h be the com-
position g f and k = f g. Let u(x) = 3f (x 1).
(i) Find the domain