Derivative formula for power functions and polynomials:
6/23 s 5
Definition: the function of the form of: (x) " 3 X l' x " l
f(x) = anx@+ an_1x"1 + + ax + b
is called polynomial function and in particular f(x) = cx" is called
M119 Study Guide Test 2: Chapters 2 and 3
Understand that the derivatve at a point, f (a) gives the instantaneous rate of change of the
functon at the point x = a, while the slope of a line that connects two points gives the average rate
4.1 Essential Practice Problems
For each function below (#1-11), analyze the sign of the first derivative and use your analysis to
find intervals where the function is increasing, intervals where the function is decreasing,
critical points (include x and
Chapter 3 Short-Cuts to Differentiation
In this chapter, we learn rules for finding the derivatives of
functions and combinations of functions.
Be sure to work many practice problems from the text in this
chapter for all sections: 3.1, 3.2, 3.3, 3.4.
Chapter 4 Probability
In this chapter, we get an introduction to the terminology, notation and procedures of
We will use what we learned about sets (Chapter 2) and counting techniques (Chapter 3).
Basic Concepts of Probability
Math M118 Chapter 2 Basic Practice Questions
1. Given U cfw_1,2,3,4,5,6,7,8,9 and subsets A cfw_1,3,5,7,9 , B cfw_1,2,3,4,5 , and C cfw_1,2,5,8,9
g. A A
h. B C
i. ( A B )
j. ( B C )
m. B C
n. ( A B C )
o. A B C
p. (C A) B
Counting Techniques and Combinatorics
Combinatorics is the science of counting. It is an area of mathematics in which we study
sets (usually finite) and try to count the number or ways we can arrange their elements or the
elements for particula
C: ANSWERS TO SELECTED PROBLEMS
Chapter 2.1, Sets and Subsets
Washington, West Virginia, Wisconsin, Wyoming.
This is not a well-defined set.
All students with blue eyes. All students who are male. All students who own a dog.
Section 5.2 Expected Values, Standard Deviations and Probability
Suppose the students in a math class are asked to toss a fair coin 100 times each and record the
number of times heads comes up. Will each student in the class observe the same number of
Our goal in this chapter is to become familiar with the terminology, notation and basic
operation of sets.
Sets provide a useful tool in helping us to understand many topics in mathematics. In
particular, they will be helpful when w
Test #2 Review
1. Given events A and B, with Pr(A) = 0.20 and Pr(B) = 0.60, nd
a. Pr(A U B) if A and B are independent. b. Pr(A (W B) if A and B are disjoint.
.1 , ._-':
c. Pr(A F) B) if A and B are independent. d. Pr(A U B)
M118 Test #1 Review (Chapters 2 and 3) .6 (:5
1. A urn contains 6 red, 5 white and 4 blue marbles. You reach in and randomly choose 3 marbles. In how many
ways can the 3 marbles be selected so that:
a. all 3 marbles are red? V b. none of the s
Exam #ZB Name '
Math M1 18
Score / 60 = %
1. Given events A and B, with Pr(A) = 0.70 and Pr(B) = 010, nd Pr(A U B) if
a. A and B are disjoint. b. A and B are independent.
47+1z 7+év'7[z) a._"_(2)
3. If events A, B, and C form a artition of the univers
Practice Test Chapter 2
Let A = cfw_1, 2, 3, 4, 5 and B = cfw_1, 2, 3
1. Find n(A x B)
2. Find n(A B)
3. Find n(A U B)
4. How many subsets can be constructed from a set containing 6 elements?
5. At Garfield High, 11 students take Algebra but not
Chapter 3 Essential Practice Questions Group A
1. A class consists of 10 students (5 boys and 5 girls) and one teacher. In how many ways can the students:
sit in a row of chairs if there are no restrictions?
stand in a line, if a boy must b