MTH 101 (Final Sample)
1. A survey of 850 family houses showed that 220 own Laptops, 450 own PCs, and 130 own
both Laptops and PCs.
a. How many houses in the survey own either a Laptop or a PC?
(a) 280
(b) 540
(c) 800
(d) 720
(e) None of the above
b. How
132 C H A P T E R 3 Mathematics of Finance
Now using formula (2) with A = 2,539.62,P = 2,443.02, and t = £02 2 we
h 360 9
ave
A = P(1 + rt)
2,539.62 = 2,443.02(1 + gr)
= 2,443.02 + 1,357.23r
96.60 = 1,357.23r
_ 96.60 N o '*
r 1,357.23 ~ 0.07117
8/28/2016
Section 1.2
Graphs and Lines
The Cartesian Coordinate System
Main Objectives (typical exam questions)
Be able to solve applications of linear equations
Be able to solve questions involving price-demand and
price-supply
Necessary techniques
11/7/2016
Example - Solution
Example
Solve the following system using the augmented
matrix method.
2 x3 7 x5 12
x1 2 x2 5 x3 3x4 6 x5 14
2 x1 4 x2 5 x3 6 x4 5 x5 1
Step 1. Locate the leftmost column that does not consist entirely of zeros.
Step 2. Int
10/30/2016
Section 4.3
Gauss-Jordan Elimination
Reduced Row Echelon Form
MEMORIZE
Identify reduced row echelon form
Identify number of solutions
Be able to solve systems by Gauss-Jordan elimination.
Be able to solve applications using Gauss-Jordan elimina
Solve the following liner programming problems.
Note that the feasible regions have been determined in Section 5.2.
If the region is bounded both maximum and minimum exist.
If region is unbounded maximum typically does not exist (see notes).
Example 1:
Ma
1. The cost for labor associated with fixing a washing machine is computed as
follows: There is a fixed charge of $25 for the repairman to come to the house, to
which a charge of $20 per hour is added.
(a). Find an equation that can be used to determine t
11/12/2016
Section 6.1
Linear Programming - Simplex Method
6.1 Geometric Introduction to the
Simplex Method
The geometric method of linear
programming from the previous
section is limited in that it is only
useful for problems involving two
variables and
9/27/2016
Section 3.2 - Compound Interest
Compound Interest
Unlike simple interest, compound interest on an amount
accumulates at a faster rate than simple interest.
The basic idea is that after the first interest period, the amount
of interest is added
Solve the following graphically. Indicate if the region is bounded or unbounded and
determine the coordinates of the corner points.
Example 1:
Example 2:
Example 3:
Example 4:
1. Based on the table above, how many people are males or are heavy
smokers?
2. Based on the table above, how many people are females and are heavy
smokers?
3. Based on the table above, what is the probability of randomly selecting
someone who is a male o
Linear Programming in Two
Dimensions: A Geometric Approach
Chapter 5
Linear Inequalities and Linear
Programming
Section 3
Linear Programming in Two Dimensions: A
Geometric Approach
In this section, we will explore applications which utilize
the graph of a
Example 1 Find the dual
Example 2 If the final tableau of Example 1 is given
below, find the solution to Example 1.
Example 3
Find the dual
Example 4 If the final tableau of the dual in Example
3 is given below, find the solution to Example 3.
Example 5
E
9/20/2016
Chapter 2.3 Applications
Objectives
Break-Even and Profit-Loss Analysis
Calculate the revenue function given a price function
Any business has costs and revenue
x denotes quantity
C(x) denotes cost as a function of quantity
R(x) denotes rev
11/14/2016
Learning Objectives for Section 6.3
Dual Problem: Minimization with
Problem Constraints of the Form >
Initial Matrix
Consider matrix:
1 1 3 12
2 1 1 16
A
16 9 21 1
Barnett/Ziegler/Byleen Finite Mathematics 11e
1
Barnett/Ziegler/Byleen Fini
9/25/2016
3.1 Simple Interest
Definitions
Basic idea: money in the future is worth more than today.
If we borrow some money today (denoted P), then we will
have to pay back more in the future (denoted A)
In the case of simple interest:
If we invest P, w
Formulae
[1]
fx ax 2 bx c 0
b b 2 4ac
2a
Vertex : h, k where h b and k fh
2a
Solution : x
[2]
A P1 rt
A
P
1 rt
I Prt A P
[3]
r
i m
n mt
[4]
A P1 i n
A
P
1 i n
I AP
r
APY 1 m
m
1
[5]
A Pe rt
P Art
e
I AP
APY e r 1
[6]
1 i n 1
i
FVi
PMT
1 i n 1
FV PMT
[7]
Systems of Linear Inequalities
in Two Variables
Chapter 5
Linear Inequalities and Linear
Programming
In this section, we will learn how to
graph linear inequalities in two
variables.
Section 1
Linear Inequalities in Two Variables
2
Graphs of Linear Inequa
9/18/2016
Section 2.2
Piecewise Functions
Motivation
Main Objectives (typical exam questions)
Be able to solve applications involving piecewise
functions
Note that we will only consider piecewise linear functions
Necessary techniques
Be able to fit a
10/14/2016
Example Commission
Solution
Example Commission
Many investment firms charge commissions on transactions based on the amount of the
transaction. Suppose that an investment firm charges 1% commission when an investment is
purchased and 0.5% when
10/14/2016
Present Value of an Annuity
Present Value
Present value of an annuity represents the value of n future
payments of size PMT
Payments are made at the end of the n periods
The first payment is made at the end of the first period
Ordinary annui
MTH 101 - Quiz 1
Name:
Student number:
Question 1
From collecting market data, a seller found the following information.
At a price of $1400 per diamond ring, the demand is 500 and the supply is 50.
At a price of $1800 per diamond ring, the demand is 300
MTH 101 - Quiz 2
m. SOLUTION
Student number:
Question 1 (20 points)
A shipping company charges according to the packages weight. There is a base charge of $10.
If the package weighs 20 kilograms or less, then the cost of shipping is $3 per kilogram. If th
OLULT/9/L/
MTH 101 - Quiz 3
Name:
Student number:
Question 1
A real estate developer makes three kinds of houses. A small house costs $100,000 and requires 2
working days to build. A medium house costs $200,000 and requires 6 working days to build. A larg
Math 101
Quiz 3
N ame_._ Student number
Show all work
Closed book.
Scientic calculatos allowed.
x) = at: + bx + c = 0
_ 4mm
Solution : x 7
_a
Vertex : (hJc) where h = ;_3- and k =h)
1. (Each part 4 points) Given the following price-demand and cost funct
Math 101
Quiz 6
N am_*_ Student number
Show all work!
Closed book. Alib cfw_51 Mi VG (A "
Scientic calculates allowed. TO SQIC. i F 'i' i/Q
\re Si 9 n be i o v0
1. (10 points) Maximize and minimize i '3 C 0 (tr Q C _i_ bk. SQ
P=53+10y (2.0) +0 CnCCiL
SOLMTlON
MTH 101 - Quiz 7
Name:
Student number:
Question 1 Solve the following linear system using the augmented matrix method. If there is no
solution, then state so.
:cl+2xI +3x3=6
2xI +42:z +6x3 =10
-3x, +3:2 +2x3 =3 Question 2 Solve the following line
SOLUTloN
MTH 101 - Quiz 7
Name:
Student number;
Question 1 Solve the following linear system using the augmented matrix method. If there is no
solution, then state so.
2x, +23;2 +4x3 =6
xl +2x2 +2.13: :5
3x2 +x3 =5
G I NOT REQUIRE!
] 1 2 S *1R1+R9