2.2 Solving Quadratic Equation
A quadratic equation can be solved by using:
1. Factorization
i) Arrange the unknowns in general form (ax2+bx+c=0) and factorize it 2. Completing the square
i) x2-6x+4=0
ii) x2-6x=-4
iii) x2-6x+-622=-4+-622
iv) x2-6x+-32=-4+-32
v) x-32=5
vi) x-3=±5
vii) x=3±5
viii) x=3+5 OR 3-5
ix) x=5.236/0.7369

3. Quadratic formula
x=-b±b2-4ac2a
* Forming quadratic equation from given roots
SOR=sum of roots POR=product of roots
SOR=-ba POR=ca
.x2-α+βx+αβ=0
.x2-SORx+POR=0
* Types of roots
b2-4ac>0| Two different roots| Straight line intersects a curve at two different points| b2-4ac=0| Two equal roots| Straight line touches the curve at one point/ tangent to the curve| b2-4ac<0| No real roots| Straight line does not intersect the curve|

Example Questions:
1. Show that the quadratic equation x2=21-kx-9-k2 has two real roots for k≤-4. Solution:
.x2-21-kx+9+k2=0
.a=1, b=-2+2k, c=9+k2
Since it has 2 real roots,
.b2-4ac≥0 {It didn’t mention that the 2 roots are equal roots or different roots, so it can be >0/=0 that becomes ≥0} .(-2+2k)2-4(1)(9+k2)≥0
.4-8k+4k2-36-4k2≥0
.-8k-32≥0
.-8k≥32
.-k≥4
.k≤-4 (shown)

...organelle
Characteristics
Functions
1. Plasma/cell membrane
-made of_________ & phospholipids
-________ permeable
-it regulates the_______of substances_____and out of the cytoplasm
2. Cell wall
(Plant cell)
-made of _________.
- _______ to all fluids
-gives _____ to plant
-provides mechanical ________ for the plant cell
3. Cytoplasm
-jelly-like matrix
-medium which organelles are _______.
-contains organic and inorganic substances
-medium for _______ reactions in the cell.
2.1 UNDERSTANDING CELL STRUCTURE AND FUNCTION
Cell Structure : Organelle
a) Organelle
Characteristics
Function
1. Nucleus
-the largest organelle
-has _______ thread
-control all _______ of the cell
-contain _______ which determine the characteristics and cell functions.
2. Vacoule
(plant cell)
-fluid filled sac enclosed by membrane called tonoplast.
-the fluid is called __________.
-vacoule in plants store chemicals such as water,________, ________, mineral, _________.
-vacoule regulate _________ in plant cell and paramecium
-supports ___________ plants
3. Mitochondrion
-cylindrical shape
-made up of ________
membrane units
-the site of _________ production through cellular respiration.
Glucose + O2 Energy + H2O + CO2
-energy released is used for cellular _______.
4. Lysosomes
(animal cell)
-contain hydrolytic ______.
-membrane-bound sac
-release enzyme to _______ material in food vacuoles in...

...such illness. Nutritional guidelines play an important role in helping us to make informed choices about our nutrient intake. The foods that constitute a balanced diet should contain the major nutrients which include carbohydrates, proteins and lipids, as well as vitamins, minerals, water and dietary fibre. A balanced diet is essential for the healthy growth and development of the body.
The objectives of carrying out this project work are:
1 To collect data on the heights and weights of students.
2 To calculate BMI of each students.
3 To represent data using various methods.
4 To relate students’ knowledge with the data obtained.
5 To suggest ways to practice healthy lifestyle.
The methods of research are as follows:
1 To obtain the height, weight and BMI of 50 students in Form 1 and 50 students in Form 5.
2 To tabulate the data consisting the height, weight and BMI of this 100 students.
3 To convert the data and represent it using three different statistical graph.
4 To find the mean, mode and median of BMI for the 50 students from each group of students.
5 To calculate the variance and the standard deviation of BMI for this students.
Statistic :
Finding mean, mode and median of ungrouped data and grouped data.
Finding interquartile range, variance and standard deviation of ungrouped data and grouped data.
Finding gradient according to the...

...ECO 550 WEEK 2CHAPTER 3 AND CHAPTER4 PROBLEMS
download here
Chapter 3: Problems 3, 4, and 7
3. The Olde Yogurt Factory has reduced the price of its popular Mmmm Sundae from $2.25 to $1.75. As a result, the firm’s daily sales of these sundaes have increased from 1,500/day to 1,800/day. Compute the arc price elasticity of demand over this price and consumption quantity range.
4. The subway fare in your town has just been increased from a current level of 50 cents to $1.00 per ride. As a result, the transit authority notes a decline in rider-ship of 30 percent.
a. Compute the price elasticity of demand for subway rides.
b. If the transit authority reduces the fare back to 50 cents, what impact would you expect on the ridership? Why?
7. In an attempt to increase revenues and profits, a firm is considering a 4 percent increase in price and an 11 percent increase in advertising. If the price elasticity of demand is −1.5 and the advertising elasticity of demand is +0.6, would you expect an increase or decrease in total revenues?
Chapter4: Problems 5, 6, and 7
5. General Cereals is using a regression model to estimate the demand for Tweetie Sweeties, a whistle-shaped, sugar-coated breakfast cereal for children. The following (multiplicative exponential) demand function is being used:
6. The demand for haddock has been estimated...

...20
Additional Mathematics
Project Work 2
Written by: ALVIN SOO CHUN KIT I/C Num : Angka Giliran: School : Date :
Alvin Soo Chun Kit
Additional Mathematics Project Work 2
2011
TABLE OF CONTENTS
Num. 1 Part I Part II ~ Question 1 ~ Question 2 (a) ~ Question 2 (b) 2 ~ Question 2 (c) ~ Question 3 (a) ~ Question 3 (b) ~ Question 3 (c) 3 4 Part III Further Exploration Question Page
Alvin Soo Chun Kit
Additional Mathematics Project Work 2
2011
PART I History of cake baking and decorating Although clear examples of the difference between cake and bread are easy to find, the precise classification has always been elusive. For example, banana bread may be properly considered either a quick bread or a cake.The Greeks invented beer as a leavener, frying fritters in olive oil, and cheesecakes using goat's milk. In ancient Rome, basic bread dough was sometimes enriched with butter, eggs, and honey, which produced a sweet and cake-like baked good. Latin poet Ovid refers to the birthday of him and his brother with party and cake in his first book of exile, Tristia.Early cakes in England were also essentially bread: the most obvious differences between a "cake" and "bread" were the round, flat shape of the cakes, and the cooking method, which turned cakes over once while cooking, while bread was left upright throughout the baking process. Sponge...

...Case # 4Chapter2.
Issue: There are two parties involved in the case dispute the one is called plaintiff, according to Kubasek. , Browne, , Herron, , Giampetro-Meyer, , Barkacs, , Dhooge, , & Williamson, (2012) the definition of plaintiff is, “ the person or party who initiates a lawsuit (an action) before a court by filing a complaint with the clerk of the court against the defendant(s). Also known as claimant or complainant,” (page, G22). In this case Jarold Daniel Friedman is plaintiff; he is the one who initiates the lawsuit before the court against the pharmaceutical warehouse, so warehouse is defendant, as according to Kubasek. , Browne, , Herron, , Giampetro-Meyer, , Barkacs, , Dhooge, , & Williamson, (2012) , “The person , party , or entity against whom a civil or criminal lawsuit is filed in a court of law,” (Page G-7). The issue of this case is discrimination on the base of religion as the condition for giving permanent job is to get vaccination which is against the religion practice of the plaintiff, so he raised this issue in the court against the defendant who is employers.
Rule of Law: the rule of law in this case is about religious discrimination, as According to (U.S Equal Employment, 2014), “religious discrimination involves treating a person, an applicant or employee, unfavorably because of his or her religious belief. The law forbids discrimination when it comes to any aspect of employment, including...

...ID: 22087885
Exam: 986093RR - Business Math, Part 2
1. Ann works 51/2 hours, Mary works 61/3 hours, and John works 41/4 hours. How many combined hours
have they worked?
A. 165/12
*B. 161/12
C. 151/12
D. 155/12
2. You pay the following for supplies: $19.36 for pens; $21.75 for notepads; and $32.26 for computer
paper. What is your total?
A. $73.73
B. $77.37
C. $77.73
*D. $73.37
3. How many liters will a U.S. 6-quart container hold? Round your answer to the nearest hundredth.
A. 6.11 liters
*B. 5.68 liters
C. 5.97 liters
D. 6.37 liters
4. If your paycheck indicates that you worked 7.5 hours each day in an 8-day pay period, how many hours
did you work in all?
A. 40 hours
*B. 60 hours
C. 54 hours
D. 45 hours
5. If the price of upholstery fabric is $12.49 per yard, how much will 16 yards cost?
*A. $199.84
B. $189.84
C. $201.04
D. $199.94
6. Reduce 24/40 to its lowest terms.
A. 2/5
*B. 3/5
C. 4/5
D. 12/20
7. It takes you approximately 1/3 hour to type a memo. If you plan to work for 6 hours, how many memos
can you type?
A. 2
B. 6
C. 9
*D. 18
8. Paul earned a salary of $926.35 and a commission of $136.15. How much did he earn in all?
*A. $1,062.50
B. $780.20
C. $1,052.50
D. $790.20
9. What is 51/4 ÷ 22/7 ?
A. 12
B. 2
C. 1219/64
*D. 219/64
10. To get to a job site, you must travel 45 kilometers. How many miles will you travel?...

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