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
f g 2 x 3 4 x 1
4 x 2 x 4
terms & put in
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
Free powerpoints at http:/www.worldofteaching.com
Its just Division!
The polynomial we divide with is called
The polynomial we divide by is called
The answer is called
Free From www.analyzemath.com
Math Worksheet: Polynomials
Match the polynomial functions to the graphs:
( 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
(x + 1)(x - 2)(x - 4)
The Integral Zero Theorem
a) Define the integral zero theorem. How is this theorem useful
Activity 1.2.4 Circuit Calculations (ver. 2016)
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
Bharat Kumar Shivani
University of Jamshoro
31 May, 2016.
Mr. Pawan Kumar Malani
Latifabad Unit No. 9, Hyderabad
Subject: REQUEST FOR SEEKING OUT INFORMATION.
Dear Mr. Malani:
I am writing to request further information
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
To: Surhan Fatima, Instructor Business Communication
From: Bharat Kumar, Student/
Subject: Demonstrated Leadership Memorandum About Business Communication
Date: 25 June, 2016.
Every year more than 80%
Al Rahim Plaza, VIP Road, Gujranwala
1 June, 2016.
Mr. Khadam Hussian
Manufacturing Plant, Site Area, Alipur
Subject: ANNOUNCEMENT NEW ORDER RECEIVED.
Dear Mr. Hussain
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
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
Demonstrated leadership file
Miss Surhan Fatima
o Information Seeking letters
o Response Letters
Order Placement Letters
1. Economists use the term money to refer to:
C) assets used for transactions.
D) earnings from labor.
2. Macroeconomists call assets used to make transactions:
A) real income.
B) nominal income.
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
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
Bank clerk: our interest rates are low, but very few customers are borrowing money and even fewer are depositing
Head of central bank: we cant really cut our interest rate any further because its already very l
The herb is usually used as
a supplement in diets, and
it is commonly used for
The herb offers medication
for the chronic fatigue
syndrome (CFS) and it also
fights the infections
Running head: RESEARCH METHODS
Advantages of a Qualitative Study over a Quantitative Study
Both the quantitative and the qualitative methods of study have a very
Statement of Cash Flows
Prime Sports Gear, Inc.
Work Sheet for Statement of Cash Flows
For Year Ended December 31, 2013
Week 13 Tutorial Exercise
Revision Chapters 10,24,18
Part B: Multiple Choice
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
Practice Preprogrammed Problem
Sales growth rate
Selling expense ratio