158 Understanding Pure Mathematics: Chapter 5
16. Find the real values of k for which the equation x2 + (k + 1)x + k2 = 0
has (a) real roots, (b) one root double the other. (A.E.B.)
17. The roots of the quadratic equation
(x + 2)2 2kx = 0,
where k is a no
The sum f + g
f g x f x g x
This just says that to find the sum of two functions, add
them together. You should simplify by finding like terms.
f x 2 x 3
g x 4 x 1
2
3
2
3
f g 2 x 3 4 x 1
3
2
4 x 2 x 4
Combine like
terms & put in
descending
order
The di
Polynomial functions
mc-TY-polynomial-2009-1
Many common functions are polynomial functions. In this unit we describe polynomial functions
and look at some of their properties.
In order to master the techniques explained here it is vital that you undertak
Polynomial
Long
Division
Polynomial Long Division
Free powerpoints at http:/www.worldofteaching.com
Its just Division!
The polynomial we divide with is called
The Dividend
The
Divisor
The polynomial we divide by is called
The answer is called
The Quotie
Free From www.analyzemath.com
Math Worksheet: Polynomials
Match the polynomial functions to the graphs:
1.
2.
3.
4.
( x + 1)( x 1) 2 ( x + 2) 2
( x + 1) 2 ( x 1)2 ( x 3)
( x + 1)( x 1)4
( x + 1)( x 1)3 ( x 3)
5. ( x + 1) 2 ( x 1)3
6. ( x + 1)2 (1 x)( x
x3 - 5x2 + 2x + 8
Polynomial, Radical, and Rational Functions
LESSON THREE - Polynomial Factoring
Lesson Notes
(x + 1)(x - 2)(x - 4)
Example 1
The Integral Zero Theorem
Integral Zero
Theorem
a) Define the integral zero theorem. How is this theorem useful
PC 3 Unit Graphing Polynomials Worksheet
Directions: Graph the following polynomials. Identify the end behavior.
1. p(x) = (x 4)2
2. p(x) = (x + 5)2
As , () _ and
as , () _
3.
Activity 1.2.4 Circuit Calculations (ver. 2016)
Introduction
Regardless of circuit complexity, circuit designers as well as users need to be able to
apply basic electrical theories to circuits in order to verify safe operation and
troubleshoot unexpected
Bharat Kumar Shivani
University of Jamshoro
PAKISTAN
31 May, 2016.
Mr. Pawan Kumar Malani
Municipal Engineer
Latifabad Unit No. 9, Hyderabad
PAKISAN
Subject: REQUEST FOR SEEKING OUT INFORMATION.
Dear Mr. Malani:
I am writing to request further information
Practice Questions
Claim and Adjustment Letters
Q. 1. (a) Incorrectly Personalized Product
You are the Marketing Manager for Statewide Telemarketing, a company that conducts
telemarketing campaigns on behalf of local banks, department stores, and insuranc
Demonstrated Leadership Memorandum
Memorandum
To: Surhan Fatima, Instructor Business Communication
From: Bharat Kumar, Student/
Shivani
Subject: Demonstrated Leadership Memorandum About Business Communication
Date: 25 June, 2016.
Every year more than 80%
Marked Assignment-04
Jannat Plastics
Al Rahim Plaza, VIP Road, Gujranwala
PAKISTAN
1 June, 2016.
Mr. Khadam Hussian
Field Supervisor
Jannat Plastics
Manufacturing Plant, Site Area, Alipur
PAKISTAN
Subject: ANNOUNCEMENT NEW ORDER RECEIVED.
Dear Mr. Hussain
Question-01
The task is "You and a friend want to be volunteers in the World Support Programme. Write a
letter asking for information and details". Write an information seeking letter to WSP for
providing necessary information. Also assume all necessary i
Business Communication Practice Questions
Situation-01
You are the Head of Stitching Department of Mod Garments Limited. Work on an important export order
for Mens Suits amounting to Rs 25 million is in process. While coming to work, 30 workers i.e. 20 pe
Business
Communicat
ion
Demonstrated leadership file
Instructor
Miss Surhan Fatima
Submitted By
Shama Lashari
Letter
s
Direct letter
o Information Seeking letters
o Response Letters
o
o
o
o
Order Placement Letters
Claim Letters
Adjustment Letters
Good Ne
1. Economists use the term money to refer to:
A) income.
B) profits.
C) assets used for transactions.
D) earnings from labor.
2. Macroeconomists call assets used to make transactions:
A) real income.
B) nominal income.
C) money.
D) consumption.
3. All of
1. The rate of inflation is the:
A) median level of prices.
B) average level of prices.
C) percentage change in the level of prices.
D) measure of the overall level of prices.
2. The definition of the transactions velocity of money is:
A) money multiplied
20160921
ch3
Chapter3PracticeQuestions
1. Themarginalpropensitytoconsumeis:
A. normallyexpectedtobebetweenzeroandone.
B. equaltoconsumptiondividedbydisposableincome.
C. normallyassumedtodecreaseasdisposableincomeincreases.
D. normallyassumedtoincreaseasdi
1. The circular flow model shows that households use income for:
A) consumption, saving, and factor payments.
B) consumption, taxes, and factor payments.
C) taxes, saving, and factor payments.
D) consumption, taxes, and saving.
2. In the circular flow dia
DEFLATION
FINANCIAL DISTRICT:
Bank clerk: our interest rates are low, but very few customers are borrowing money and even fewer are depositing
their savings.
Head of central bank: we cant really cut our interest rate any further because its already very l
Name of
Herb
Therapeutic use
Glucosamine
The herb is usually used as
a supplement in diets, and
it is commonly used for
arthritis.
Echinacea
The herb offers medication
for the chronic fatigue
syndrome (CFS) and it also
fights the infections
including the
Running head: RESEARCH METHODS
1
Research Methods
Authors Name
Institutional Affiliation
RESEARCH METHODS
2
Research Methods
Advantages of a Qualitative Study over a Quantitative Study
Both the quantitative and the qualitative methods of study have a very
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
B
C
D
E
F
G
CASHFLOW
Statement of Cash Flows
Prime Sports Gear, Inc.
Work Sheet for Statement of Cash Flows
For Year Ended December 31, 2013
Analysis of
Transactions for
Week 13 Tutorial Exercise
Revision Chapters 10,24,18
Part B: Multiple Choice
Dishonoured cheques:
a.
b.
Must be listed in the bank reconciliation
Are cheques from debtors that were deposited into the firm's bank
account but were not paid due to lack of fu
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
B
C
D
E
F
ESTIMATOR
Practice Preprogrammed Problem
Data Section
January sales
Sales growth rate
Selling expense ratio
General expenses
$100,000
2%
60%
$19,000
Answer Section
Sales
Expenses
Selling ex