The Spectre Of Cheating In Exams And Collusion With Other Assessment Items

The Spectre Of Cheating In Exams And Collusion With Other Assessment Items
By Richard D Boyce

We all know that cheating and/or collusion between students will always be a concern where exams and other assessments are done. Teachers need to develop a process on how it is to be handled, particularly if there is no school protocol.

Below are actions to consider when cheating is discovered during an examination:

• When you discover cheating during an exam, note the time and place in 'red' ink on the actual exam paper. Separate the individuals involved if possible. Allow them to complete the exam. You must also remove any 'cheat' page used to cheat and include it with the final exam paper when it is collected so this will be used in judging the appropriate penalties.


• Indicate on the front page of the exam what has happened and who else was involved.


• Report the incident to your up-line supervisor and the student's teachers if it is not your student.


• Follow your school's protocol on penalties in the marking of the assessment task. Here your up-line supervisor will be your guide.

When an assessment task is done outside school time, there is opportunity for collusion to take place between students or students can get others, e.g. tutors, to do the task for them. The best ways to detect if this is occurring include:

Mark one section of every student's work at a time. This will make finding the direct copying of others' work easier. Look for common and sometimes unusual errors, diagrams, spelling mistakes and setting out.

After looking at the suspect students' academic records, you may be able to conclude who copied or cheated. Both students need to be interviewed and penalised if both were involved, based on the school protocol. Sometimes a student copies the other's work without their knowledge.

1. Another scenario occurs when a student does exceptional work beyond his/her normal results. This is a cause for concern and needs to be investigated. Your first course of action is to interview the student, asking questions to test the student's knowledge of the topic to see if it reflects the student's results. If it does not, further investigation is necessary to determine if the work is from the student's own efforts. (Sometimes in non-traditional assessment, students do perform at a higher level). If there is a real doubt as to the integrity of the assessment task, ask more direct questions on how it was done, who might have helped and so on. You may get a 'confession'.


2. If you get a 'confession', follow school protocol in relation to marks, redoing the work and so on.


3. If you do not get a 'confession' and you are sure something is amiss, pass the issue on to your supervisor to deal with.


4. Document all your actions in regard to this issue. I would record it in your diary and with your student records (in pencil only so it can be removed if it proves an unwarranted assertion).


5. Mark the assessment task as you would normally and record the results until the issue is resolved one way or the other.

In these days of 'political correctness', you need to be very careful about what you say to students about these issues. Therefore, document what you say and do with the students and their work and keep your supervisor informed of what has transpired. Finally, ensure you follow exactly the school protocol.

The website http://www.realteachingsolutions.com provides an eBook that looks at all aspects of examinations and other types of assessment. The eBook is "The Exam Book". Our author, during the last 16 years of his teaching career was the Head of a Mathematics Department where he was responsible for the assessment program. He offers practical advice that works on aspects as diverse as running a class exam up to how best to mark alternative assessment tasks.

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Simple Heat Conduction

Author: nitin.p070

Heat conduction or Thermal conduction is the transfer of energy between particles in a solid.Heat can also be transferred by Thermal radiation and/or convection and it is normal that more than one of these processes happen at the same time.

In the atomic theory solids, liquids and gases are made of tiny particles called atoms. The temperature of the material measures how fast the atoms are moving and the heat measures the total amount of energy due to the vibration of the atoms.

You might imagine conduction to take place when one part of a material is heated. The atoms in this part vibrate faster and are more likely to hit their neighbours.When collisions take place, the energy is passed on to the neighbouring atoms allowing the energy to travel through the solid. ( Rather like the way energy passes along a set of tumbling dominos.)

The atomic picture also helps explain why conduction is more important in solids: in solids the atoms are close together and unable to move around. In liquids and gases the particles can move past each other, so the collisions are less common
A thermos bottle is an excellent example demonstrating how all three methods are inhibited. A thermos bottle has a double wall that creates a vacuum, and a shiny surface inside of it. We've seen that the shiny part on the inside is an example of radiation, where heat is reflected back from the walls and back to the liquid. Heat conduction is inhibited by the use of insulators such as glass and plastic. Heat does escape, through the body and the lid, but very slowly. The vacuum inhibits convective currents and also conduction.

Grilling, broiling, and cooking over an open flame when you go camping are examples of cooking by radiation. However, when you grill and place your food on the grates, conduction also comes into play. When the air becomes hot, convection currents are created between the air and the food.

When you bake a cake or pot roast, all three methods are once again involved. There are convection currents as the air becomes hot from the oven. The pan the food is in becomes hot due to conduction. The walls of the oven become hot, and this is due to radiation.

We have previously seen that when you boil or steam food, the air and the water is heated by convection. Solid food, however, is heated by conduction, as the atoms inside of it begin colliding with each other.

Aside from cooking, there are simple heat transfer experiments you can do at home.

A Simple Heat Conduction Experiment

Obtain objects of different materials. Ideally, they would be of the same geometry, such as rods made from wood, glass, aluminum, and iron. However, materials such as plastic, wooden, and metal silverware will do. You will also need a heat source such as hot water, a stove burner, a hot plate, or a candle. To make the measurements, use a watch or some other time keeping device, and a simple thermometer. To record your results, use a spreadsheet or graph paper.

For a direct measurement, use masking or electrical tape to attach the thermometer to an object. Submerge it partially in hot water, and take time and temperature readings every few seconds. Graph the temperature versus time by placing the dependent variable, temperature, on the y axis and the independent variable, time, on the x axis. Do this for every object. Compare your results.

For indirect measurements, melt a substance such as candle wax or paraffin on the object. Slowly heat the object, and record the time it takes for the substance to melt. If you are careful, the substance can also be ice, butter, or something similar. In this case, the holder would have to be a spoon.

Remember to use caution whenever doing heat transfer experiments, as the objects and sources will be hot.

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Joint Probability

Author: nitin.p070

Probability in math is defined as the chance of happening something in future. The two random variables A and B are defined on the same probability space, the joint probability distribution for A and B defines the probability of events defined in terms of both A and B. In the case of having only two random variables, this is called a bi-variate distribution, but the thought simplify to any number of random variables, giving a multivariate distribution.

Joint probability:

A numerical measure where the chance of two events happening together and at the same time are calculated. For example if the probability of event B happening at the same time event A happens, then the Joint probability has been given as follows.
Joint probability notation takes the form:

P (A `nn` B) or P (A and B)

Indicates the joint probability of A and B.

Example: The joint probability can be calculated by rolling a 2 and a 5 with two dissimilar dice.

with and without replacemant-Joint probability:

Joint probability is used in multistage testing .Joint probability can be done with replacement or without replacement.

With replacement: It indicates that the thing that are chosen on one stage are returned to the sample space before the next choice is made .For example, tossing a head on the first toss does not affect the outcome of flipping the coin a second time.

The probability that independent events A and B occur at the same time can be found by using the multiplication rule, or the product of the entity probabilities.

Example 1:

If you pick two cards from the deck without replacement, find the probability that they will both be aces.

Solution:

Total number of aces in the deck of cards = 4.

Cards picked up = 2 aces.

total number of aces* (total number of aces-1)
Hence the probability = --------------------------------------------------
total number of cards*( total number of cards-1)

P (AA) = `(4/52)*(3/51)` = `1/221` .

Without replacement:

Uses the same idea, if the first choice is not replaced only we consider the change in the sample space. Still we use the multiplication rule, but for each of the stages the numerator and/or denominator decreases

Example 2:

Find the probability of tossing a fair coin twice in a row, getting heads both times.

Solution:

While tossing a fair coin once we get head or tail.

Given that while tossing a coin head occurs,So

We know that the probability =(Number of favourable outcomes/Total number of outcomes)

Therefore probability of getting head while tossing the coin once P(H)= `1/2.`

Similarly tossing a coin next time we have probability of getting head P(H) =`1/2.`

As the question is to find the probability of tossing a fair coin twice in a row, getting heads both times it indicates that we have to find the joint probability without replacement.

As the probability of tossing a head is ` 1/2 ` each time P (H,H) =` (1/2) *(1/2) = 1/4.`

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Self-Esteem and Multiple Intelligences of Students With Dyslexia

Self-Esteem and Multiple Intelligences of Students With Dyslexia
By Susan Tan Aparejo

This study was based on the theory that the academic performance of the students is dependent or influenced by various factors such as their self-esteem and multiple intelligences. This study was anchored on the theory of West in 1997 explaining the brain hemispheric dominance of each person, by Gardner i 1993 in his MI theory, by Armstrong in his MI theory too, by Levine in 2002, by Lazear in 1993, by Shaw in 1994 and by Pollock, Waller and Pollit in 1994.The multiple intelligences includes the linguistics, logical -mathematical, bodily kinesthetics, musical, interpersonal, intrapersonal, spatial and naturist intelligences. The study hypothesized that there is a significant relationship among self-esteem, multiple intelligences and academic performance of first year students at risk with dyslexia at Gingoog City Comprehensive National High School Gingoog City for school year 2007-2008. The method used was descriptive survey.

This study was conducted at Gingoog City Comprehensive National High School, Gingoog City. The respondents were the twenty nine ( 29 ) students and twenty three ( 23 ) were males while the six ( 6 ) were females who were identified at risk with dyslexia. The three ( 3 ) sets of questionnaires were administered to gather the needed data like the test on Identifying Adult and Students with Dyslexia, Barksdale Self -Esteem Evaluation (SEI ) and Multiple Intelligence Development Series ( MIDAS ). The statistical tools used were the percentage, frequency, mean, standard deviation, and multiple regression analysis.

The findings reveals that there was a dominance among males with low self-esteem because more males were identified with dyslexia. Besides, females could handle their difficulties by being studious, diligent, obedient, patient and by trying hard in the midst of their difficulties.

The findings further reveal that majority of the respondents showed signs of mild dyslexia. Twenty ( 20 ) of 69% of the students were lack of self-esteem. Nine ( 9) or 31 % were males who suffered serious handicapped. However none among respondents had linguistic intelligence. This is understandable because of their difficulty in reading as what expert said that learning disability students affects language processing ( Wadlington, 2005 ).

It was found that the said respondents possessed different types of intelligences. Ten ( 10 ) or 34.5 percent of the students had intrapersonal skills, the ( 10 ) or 34.5 percent with interpersonal skills and musical skills too, four ( 4 ) or 13.8 percent had logical skill, and spatial skill and only one ( 10 or 3.4 percent had naturalist intelligence.

The mean of the academic performance level of the students was 75.93 percent. This shows poor result of their academic subjects. There is no significant relationship among self-esteem, multiple intelligences and academic performance.

Susan T. Aparejo, is a Ph.D. graduate at Capitol University, Cagayan de Oro City. She is a master teacher in English and adviser of SPED class for Learning Disability, Self-contained in this city.

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Algebra Lessons: 5 Steps For Success

Algebra Lessons: 5 Steps For Success
By Rob A. Jackson

Your teenager's education foundation and learning begins with algebra. The subject is relevant for growing upon other math fields as well as several other fields which include sciences, architecture, and engineering. As moms and dads, it is imperative that your youngster understands algebra from the very start to ensure that an academic foundation is built for future math disciplines. The following are five helpful strategies to help your daughter or son conquer this important subject matter.

In any standardized examinations, such as the SAT or ACT, the most common topic tested is algebra. For that reason, it is imperative that your child have a solid understanding of algebra if you want your child to be accepted into a good university. Basic sub-topics like fractions and various other functions are regularly examined. Consequently, your child will not score very well if your child does not fully grasp these concepts.

Find an algebra instructor who can guide your son or daughter with preparation and studying for assessments. A tutor will help your child pay attention as well as help with comprehension outside of the classroom. Ensure that the algebra tutor you select for tutoring is experienced, trained, and provides a background of references for teaching in algebra. Ask the tough questions. Is the tutor a college or university graduate? Does he or she have proficiency in a math or a math-intensive field?

Without a doubt, algebra will occupy much time for your youngster out of school, despite the capability or intelligence of your daughter or son. For this reason, it is really important that you command your daughter or son to invest significant time in accomplishing his or her assignments. Seek the advice of your daughter or son's instructor and inquire how long your youngster ought to be investing on his or her algebra assignments. Design study time for your teenager based on this recommendation.

Some children learn better in a private setting, so discover what setting your son or daughter learns algebra best. For that reason, the classroom surroundings may not be the most advantageous to your son or daughter's learning. While the classroom is obviously necessary, as a parent, you must understand your teenager's learning patterns and employ the services of a tutor if that is necessary. Since algebra lessons are typically not expensive, you can get the help your teenager needs while remaining in budget.

Ensure that you are familiar with your son or daughter's algebra textbook. Indeed, you likely have not opened a textbook in quite a few years; nonetheless, it's necessary that you become versed in the subject matter all over again so when your kid requests help, you can provide it. At the same time, if you do not fully grasp the concepts your child is learning, get help from your child's teacher after class or do not hesitate to retain the services of a tutor.

Unquestionably, algebra is a tricky topic area for your son or daughter to comprehend. As a result, it's a necessary facet to his or her educational background that is going to serve as a cornerstone to his or her future success. Whether for the SAT or ACT or to receive an "A" in a class, ensure your kid is competent in algebra by acquiring an algebra tutor. You will be glad, both personally and academically, you did!

Rob is a teacher, tutor, and math enthusiast. Learn more about algebra tutoring at San Diego algebra lessons.

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Bloom's Taxonomy: Conceptual Learning and Questioning

Bloom's Taxonomy: Conceptual Learning and Questioning
By Dr. Genola Johnson

Benjamin Bloom's Levels of Taxonomy was created for educators to plan effective instruction. Using the levels during lesson planning and creating assessments assists the teacher in reaching all modalities of learning.

Using Bloom's Taxonomy's helped me understand how thinking was classified. There were certain areas I wanted to reach when teaching a concept and the classifications or taxonomy helped direct my questioning techniques.

To direct the questioning of my lessons, I created questions from the verbs in the taxonomy classifications. If I wanted high, complex questioning I would use words from the analysis, synthesis and evaluation areas.

I always wanted my students to think deeper, use problem solving skills, discuss with peers and seek further information on the concept to be learned.

In my opinion, the foundational idea would be for students to learn a concept using Bloom Taxonomy's and transfer that knowledge to other concepts.

� Understand-Explain ideas/concepts

� Remember-Recall information

� Analysis-Breakdown into parts

� Evaluation-Justify thinking

� Create-New ways, ideas, products of thinking

When creating lesson plans, I would often have the taxonomy close by to ensure I am reaching all levels. Using the assigned curriculum, I would develop my lesson objectives, identify the skills the student needed to learn, and align my objective to the assessment.

All of my lessons contained critical thinking questioning. Sometimes I would build from the knowledge level with questions that were just recall. For example, list the steps in the writing process. If the student can identify the steps, they can begin the process of designing a writing piece.

Today, students need to be able to understand why the need to know a concept. Having the factual knowledge of 2 x 2=4 is essential when you need to import this factual knowledge into an algebraic or geometrical formula when calculating the area of land to build a greenhouse to build a neighborhood garden.

I would often say, "You need to know this information, in order to create or develop, this product." Letting the students know where they are going is essential in getting them to learn the curriculum you are to teach.

Teaching synthesis (creating and evaluating) after teaching the knowledge and comprehension of a concept helps the student put the recall and understanding into a whole part. Students should be able to develop or create something new with the new information they have been taught.

Using the Bloom's Taxonomy to develop your lessons, questioning and assessments helps students and the teacher focus on deeper conceptual learning.

Dr. Genola Johnson has been an educator for 21 years. She uses Bloom's Taxonomy during lesson planning and assessments. For more information about Dr. Genola Johnson, and a list of the Bloom's Taxonomy List of Verbs, visit http://www.gaelcllc.com.

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Unit of electrical energy and work

Author: Matthew David

Unit of electrical energy and work

Introduction to unit of work:

Work is a physical unit which is also called as mechanical work. Work is defined as the energy that is transferred by the force that is acting on the object through a distance. Work is a scalar quantity like energy. The work is calculated in terms of joules. Joules is the SI unit of work.

Consumers of electricity do not pay for the amount of current or unit of electrical voltage their appliances take. The cost is based on the amount of energy electrical energy consumed. However, electrical energy for this purpose is not measured in joule as it is a very small unit. Electrical energy is usually measured in a unit called a kilowatt-hour (kWh) which is the amount of electrical energy consumed when an electrical appliance with a power rating of 1 kilowatt is used for 1 hour.

1 kWh = 1 kW x 1 hour = 1000 Wx 3600 s = 3,600,000 J

The kilowatt-hour (kWh) is called the board of trade unit or simply the unit.

Calculation of energy consumption at home

The electric meter installed in every house measures the electricity

 consumption in kWh. Our electricity consumption bill is made on

the basis of the number of units consumed by us during a given

period. A sample calculation is as follows.

• A 100 W bulb consumes energy at the rate of 0.1 kWh per hour. Therefore if the bulb is used for 5 hours a day, it uses up 0.1x5 x 30 = 15 kWh energy every month.

• If 4 such bulbs are used, total consumption = 60 kWh or 60 units.

• A fan with a rating of 60 W consumes 0.06 kWh energy every hour. Therefore if 4 fans are used for 10 hours a day, the energy used up in a month is 0.06 x4xl0x30 = 72 kWh or 72 units.

• If a 250 W refrigerator works for 12 hours a day, energy consumption = 0.25x12x30 = 90 kWh or 90 units in a month.

• If a 2 kW AC works for 6 hours a day, energy consumption = 2 x 6 x 30 = 360 kWh or 360 units.

Total energy consumed every month = 60 + 72 + 90 + 360 = 562

units

If cost of electricity is Rs 4 per unit, then monthly electricity bill

will be Rs 4 x 562 = Rs 2248 .

Representation of work

According to the theorem of work and energy, When an external force act on any object it causes the kinetic energy to change from E_k1 to E_k2, then the work W is represented as

`W= Delta E_k= E_k_2 - E_k_1 = 1/2(m v_2^2- m v_1^2)`

If the resultant force F that is acting on an object when the object is displayed at a certain distance d, and force and displacement will act in parallel direction to each other, The work done on an object is represented as the product of force F multiplied by the distance d

`W=F.d`

When the force and displacement are in same direction and parallel, then the mechanical work will be positive. If the force and displacement are in opposite direction and are parallel that is anti parallel to each other then the mechanical work will be negative.

When the force and displacement are perpendicular to each other then the work done by the force will be equal to 0. There will be no work done if they are perpendicular.

The Force and the displacement are vector quantities and by using the dot product these are combined to calculate the mechanical work which will be a scalar quantity:

`W=F.d=F.d cos theta`

Where F represents the force and d represents the displacement vector and theta represents the angle between the force and displacement.

Unit of work:

Since the work that is done is represented by W=F.S, So the units of work is represented as force times the length. The SI unit of work is represented as Joule(J) or Newton-meter(Nm)

 1 J = 1 Nm

In the cgs system the unit of work is erg or dyne cm.

1 joule is equal to `10^7` ergs.

 The dimensional formula of work is represented as `[ML^2T^-2]`

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Gold Chemistry Element

Author: nitin.p070

Element gold has been called as the most beautiful element because of its beauty which has made it desirable due to its attractive color and brightness also for its art work. Gold element is a dense, yellow, lustrous precious metal which belongs to group 11(1b) and period 6 of the periodic table. Gold is found in nature in comparatively pure form. Gold is one of the good conductors of heat and electricity and it is also soft and the most malleable and ductile of the elements.

Sources of Gold chemistry element: In nature, gold is found as the free metal and in tellurides. It is widely distributed metal and associated with pyrite or quartz. Gold is found in veins and in alluvial deposits. Depending on the location of the sample it occurs in sea water in the amount of 0.1 to 2 mg/ton.

Uses of gold chemistry element: It was used in the coinage. And it is the standard for many monetary systems. It is used for jewelry, dental work, plating and reflectors and Chlorauric acid is used in photography for toning silver images.

Characteristic properties of gold chemistry element:

Physical properties of gold chemistry element:

Density (g/cc): 19.3

Melting Point (°K): 1337.58

Boiling Point (°K): 3080

Appearance: soft, malleable, yellow metal

Debye Temperature (°K): 170.00

Pauling Negativity Number: 2.54

First Ionizing Energy (kJ/mol): 889.3

Oxidation States: 3, 1

Lattice Structure: Face-Centered Cubic (FCC)

Lattice Constant (Å): 4.080

Specific Gravity (20°C): 18.88

Atomic Radius (pm): 146

Atomic Volume (cc/mol): 10.2

Covalent Radius (pm): 134

Ionic Radius: 85 (+3e) 137 (+1e)

Specific Heat (@20°C J/g mol): 0.129

Fusion Heat (kJ/mol): 12.68

Evaporation Heat (kJ/mol): ~340

Chemical properties of gold chemistry element:

Gold is a yellow-colored metal, it may be black, ruby, or purple in finely divided form.

Chemistry element gold is the most malleable and ductile metal.

It is well known for the good conductor of electricity and heat.

Gold is not affected by exposure to air and to most reagents.

Gold is an inert metal and a good reflector of infrared radiation.

It is usually alloyed to increase its strength.

Extraction and refining of gold chemistry element:

Extraction:

Gold can be extracted by two ways, one is amalgamation and the other is cyanidation. This ore contains a variety of impurities, including zinc, copper, silver, and iron. Ore has to be mixed with mercury metal which combines with gold in the ore to form an amalgam. Further, this amalgam becomes a mixture of two or more metals in which one is mercury. Finally the gold amalgam is removed from the ore and it is heated to drive off the mercury to obtain pure gold.

Refining:

There are two methods for purification of gold. Those are Miller process and the Wohlwill process.

In the Miller process, all the impurities present in gold combine with gaseous chlorine more readily than gold does at temperatures equal to or greater than the melting point of the gold. Further impure gold is melted and gaseous chlorine is blown into the resulting liquid. Finally impurities form chloride compounds that separate into a layer on the surface of the molten gold. Miller process is most rapid and simple, but it produces gold of only about 99.5 percent purity where as Wohlwill process increases purity to about 99.99 percent by electrolysis.

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Montessori Preschools for Nurturing the Overall Personality of a Child

Montessori Preschools for Nurturing the Overall Personality of a Child
By Roosevelt Hunt

Montessori preschool or the Montessori method of education has proved to be the best system of education for preschool kids. It is a very innovative educational system where a perfect learning environment is created for the kids so that they naturally develop an urge to learn with an eagerness for knowledge. The system gives focus on the overall physical, emotional, social and cognitive development of a child.

Characteristics of Montessori

• Multi age grouping - This facilitates peer learning as children of different age groups get a chance to interact each other. The older children impart their skills and knowledge to the younger ones. Moreover, these schools train the child to socialize with others.

• Uninterrupted blocks of work time

• Discovery model - Unlike learning a concept through instruction, here the children work with materials and learn it.

• Guided choice of work activity

• Montessori learning materials

Advantages

The early years of a child are a very crucial phase and have an influence in the development of his/her personality. The traits which he learns during the childhood stay with him throughout the life. So molding of a child must begin from this phase itself. Though parents play an integral role in the molding of a child's personality, they will not be able to impart all the necessary approaches which are essential for a child's overall development.

Moreover, due to work commitments, the parents may not be able to give the child proper attention. Montessori preschools work on the nourishment of the overall character of a child. Rather than the regular classroom sessions, here the child gets an opportunity to interact with children from different age groups. This interactive form of learning helps him develop his innate skills and talents in a healthy environment.

The cognitive powers like tasting, smelling, hearing, touching, movement and seeing is also enhanced through these sensory-motor activities. The teacher guides the child in pursuing his interest in this environment. So a close interaction between the children, teacher and the environment takes place. The children also get the freedom and independence to do the activities which are of his interest. The child develops an interest for academics and extracurricular activities here which will help him in the next stage of school. Subsequently, he will be able to have a rewarding career which is of his/her interest.

The strong academic base imparted to the child in the Montessori school will help him learn other concepts in academics as well as society. So your children must be enrolled in a top notch Montessori school for ensuring a sound overall development.

If you are looking for a good school in Gilbert and Chandler AZ, Arizona area.Visit Spondeo Preschool

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Two Linear Equations in Two Variables

Two Linear Equations in Two Variables
By Andrew Holyk

Suppose you want to solve a system of two linear equations in two variables.

I will discuss elimination method.

So, you have following general system:

ax+by=c

dx+ey=f

Elimination method works as follows: express x (or y) from first expression and plug result into second.

I will express x from first:

x=(c-by)/a

Now, plug result into second:

d(c-by)/a+ey=f

dc/a-by/a+ey=f

y(e-b/a)=f-dc/a

y=(f-dc/a)/(e-b/a)

Now, x=(c-by)/a=(c-b(f-dc/a)/(e-b/a))/a

A bit messy, right?

But on practice it is more clear.

Example 1. Solve the system

3x+2y=12

4x+5y=23

Solution.

Express x from first equation: x=(12-2y)/3

Now, plug this result into second:

4*(12-2y)/3+5y=23

Multiply both sides of equation by 3:

4(12-2y)+15y=69

48-8y+15y=69

7y+48=69

7y=21

y=3

Now, x=(12-2y)/3=(12-2*3)/3=2

Thus, x=2 and y=3

Example 2. Solve the system

x-4y=-3

y-3x=-2

Solution.

Actually it doesn't matter from which equation to express variable and what variable to express.

Let's express y from second equation:

y=3x-2

Plug this result into first:

x-4(3x-2)=-3

x-12x+8=-3

-11x=-11

x=1

Finally, y=3x-2=3*1-2=1

So, x=1 and y=1.

Probably, you know that system of two linear equations in two variables has either one solution or no solution or infinitely many solutions.

Let's see how elimination method works when we have two special cases: no solution or infinitely many solutions.

Example 3. Solve the system

2x+3y=2

4x+6y=4

Solution.

From first equation x=(2-3y)/2

Plugging this in first yields:

4(2-3y)/2+6y=4

2(2-3y)+6y=4

4-6y+6y=4

4=4

Wow! All variables have canceled out.

Since 4=4 is correct equality then this system has infinitely many solutions.

Example 4. Solve the system

2x+3y=1

4x+6y=4

Solution.

From first equation x=(1-3y)/2

Plugging this in first yields:

4(1-3y)/2+6y=4

2(1-3y)+6y=4

2-6y+6y=4

2=4

Again all variables have canceled out.

But, since 2=4 is incorrect equality then this system has no solution.

Geometrically all above three cases have following meaning:

1. System has one solution: lines intersect at one point.
2. System has no solution: lines are parallel and don't coincide.
3. System has infinitely many solutions: lines coincide.

More math notes at http://www.emathhelp.net

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Assessing Students Becoming Sick During Exams

Assessing Students Becoming Sick During Exams
By Richard D Boyce

There will always be conscientious students who are sick but will come to school to do an examination. Teachers should discourage this practice both to the student and their parents as most, if not all schools, have protocols to overcome initial absences from examinations.

Encourage your students to tell you if they have been or are feeling sick prior to an examination. Then, with them, you can make a decision as to whether they will attempt it or not.

If the worst does occur and the student does get sick doing the exam, here is a process you might follow.

• Note the time this occurs on the student's exam paper at the point where the illness occurs as the student may like to continue at a later time.


• Treat the ill student in accordance with school protocol.


• When the exam paper is returned to you for marking, mark the parts of the exam that have been done prior to the illness occurring and any other work separately. Compare the two sections to see if they seem to be typical of the student's results and then discuss the results with your supervisor to decide on a mark or adopt normal school policy on how to give appropriate credit.


• Check also if the child was sick before the exam. This too could be factored into your decision about a final rating/mark for the exam. It may be that the results you already have from previous assessment items, give you enough data to give a valid level of achievement for the subject. That means you can ignore this exam result. School policy may suggest how you treat this situation.


• Always encourage a student to do the exam at a later date rather than do it when they are ill. The exam can be marked and used as a guide to their achievement as well as giving the student a real idea of how he/she understood the learning tested in that exam. This would allow him/her to do remedial work if necessary before continuing the subject or starting the next unit in the subject or the next year. These marks could be recorded with an explanation and may be used later to give extra data to help decide on the final subject rating on exit from the year or from school.


• Check for serial 'sick' offenders,.i.e. students who always seem to be sick on exam days. Some may have chronic illnesses and the school may have a policy for this situation. Those who have no history of chronic illness need to be 'forced' to do the exam ASAP under exam conditions with the same time or even less.

Perhaps they might be given a different test and the tests could be in their time, not class time. Again, this is a school policy issue. It is worthwhile checking the history of these students with past teachers and referring the issue to higher authorities for further intervention, e.g. parent interviews with school administration.

It is important that no student be disadvantaged through genuine illness at exam time. Additionally, they must be seen to be treated fairly in the allocation of their final grading. Here, a teacher must use their professional judgment based on the evidence of learning in class as well as the available assessment data. Here 'like' students can be a guide to where the student lies in the class order of merit in that subject.

The website http://www.realteachingsolutions.com provides an eBook that looks at all aspects of examinations and other types of assessment. The eBook is "The Exam Book". Our author, during the last 16 years of his teaching career was the Head of a Mathematics Department where he was responsible for the assessment program. He offers practical advice that works on aspects as diverse as running a class exam up to how best to mark alternative assessment tasks.

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History of algebra 2

Author: Matthew David

History of algebra 2

Introduction to history of algebra 2:

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra 2 covers the four basic operations in algebra such as addition, subtraction, multiplication and division. The most important terms variables, constant, coefficients, exponents, terms and expressions are explained in algebra 2. We will know the symbols and alphabets in the place unknown a value by the help of algebra 2. Therefore, students are getting algebra 2 for their studies. But in this article we are going to see the history of algebra.

Type in algebra 2 questions:

In this article we discuss type in algebra 2 questions solving. In algebra 2 questions solving are easy to understand and solve. Algebra is one of the main branches of arithmetic. It explains the interaction and properties of quantity by means of letters and other signs. The basic algebra has the following subtopics are

Variables,
Expressions,
Terms,
Polynomials,
Equations

The solving type in algebra 2 questions are given below.

History of algebra 2:

The History of geometric algebra was invented by Greeks. The Greek is the father of the algebra. He worked with algebraic equations.

The History of word algebra was derived the Arabic language. The most of the algebraic method are invented by Arabic mathematician Muhammad ibn Musa al-Khwarizmi. He studied Indian mathematics addition and subtraction and introduced these operations (addition and cancellation) in algebra.

Al-Khowarizmi used the words jabr and muqubalah to point out the basic operation of the equation. The word Jabr represent the subtraction of the both sides and the word nuqubalah represented the like terms to cancel."

The solution for the cubic equation is discovered by mathematical inventor by omer. Italian mathematician and Leonardo Fibonacci proved the history of the cubic equation  by the approximated value.

The Italian mathematicians Scipione del Ferro, Niccolo Tartaglia and Gerolamo got the exact solution for general cubic equation by using constant term.

Cardano's pupil, Ludovico Ferrari were got the solution fourth degree equation.

In algebra, symbols are used which was introduced in early 16th century.

The French mathematician Rene invented analytic geometry, which reduces the steps to solve geometric and algebraic.

In 18th century, the German mathematician Carl Friedrich Gauss had proven that every polynomial equation must have at least one root in the complex. Due to this invention, algebra had got new phase. Therefore, the concentration moved to polynomial equation.

British mathematician William Rowan Hamilton discovered the History of Quaternion. He extended the arithmetic complex numbers.

Type in algebra 2 questions:

Example 1:

Solve 5x – 6 = 3x – 12

Solution:

Given expression 5x – 6 = 3x -12

Add 6 on both sides of the equation

5x -6 + 6 = 3x – 12 +6

5x = 3x -6

Subtract 3x on both sides of the equation

5x – 3x = 3x – 3x – 6

2x = -6

Divide 2 on both sides of the equation

`(2x)/2` = `-6/2`

x = `-6/2`

x = -3

Solution is x = -3

Example 2:

Solve the equation: x+2y+3z =14; 3x+y+2z = 11; 2x+3y+z = 11.

Solution:

x+2y+3z = 14 Equation (1)

3x+y+2z = 11 Equation (2)

2x+3y+z = 11 Equation (3)

Consider the equations (1) and (3)

Equation (1)          x+2y+3z = 14

Equation (3)   *3=6x+9y+3z = 33

Subtracting the equation (1) and equation (3) = -5x -7y = -19

                                                                        = 5x+7y = 19    Equation (4)

Consider the equation (2) and (3)

Equation (1)                3x+y+2z = 11

Equation (3)                 4x+6y+2z = 22

Subtracting equation (1) and equation (3) = -x -5y = -11

                                                                   = x+5y = 11   Equation (5)

Consider the equation (4) and (5)

Equation (4)                5x+7y = 19

Equation (5)         * 3=5x+25y = 55

Subtracting equation (4) and (5)   = -18y = -36

Divide -18 on both sides of the equation

`(-18y)/-18` = `(-36)/-18`

y = 2

Substitute y = 2 in (5) we get

x+5(2)+z = 11

x+10 = 11

Subtract 10 on both sides of the equation

x+10 -10 = 11-10

x = 1

Substitute x = 1, y = 2 in (3) we get

2(1)+3(2)+z = 11

 2+6+z = 11

8+z = 11

Subtract 8 on both sides of the equation

8 – 8 + z = 11 – 8

z = 3

The solution is x = 1, y = 2, z = 3.

Type in algebra 2 questions Practice problems and solutions:

Problem 1: Solve 5x+6 = 3x-6

Solution: -6

Problem 2: Solve 3x – 3y +4z = 14; -9x -6y +2z = 1; 6x+3y+z = 5

Solution: x = 1, y = -1, z = 2.

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Newton's laws

Author: Matthew David

NEWTON'S LAWS

NEWTON'S LAWS OF MOTION

Let us begin our explanation of how Newton changed our understanding of the Universe by enumerating his Three Laws of Motion:-

First Law : An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

This law is often called    "the law of inertia".Example
You can remove a paper from beneath a standing clothes pin and the pin will fall into the container beneath it. Discover for Yourself:   Place an index card over the mouth of a heavy drinking glass or jar. Stand a clothespin on top of the card so that it is centered over the glass. Quickly and forcefully thump the card straight forward with your finger. You want only to hit the card and you want the card to move in a horizontal direction.Results: The clothespin falls straight into the glass about half of the time; the other half of the time it flips over landing upside down in the glass.

Reason :
Your finger applies force to the card, moving it forward. The card quickly moves out from under the clothespin and the pin falls straight down due to the pull of gravity. If you do not hit the card straight forward and/or it is not hit with enough force, the cards pulls the bottom of the pin forward and gravity pulls the top of the [pin down, causing the pin to flip before it lands.

Newton's Second Law

Second lawIf the net force on an object is not zero, the object will accelerate. The direction of the acceleration is the same as the direction of the net force. The magnitude of the acceleration is directly proportional to the net force applied, and inversely proportional to the mass of the object.
Force = mass x acceleration
F = maProblem :
A box with a mass of 40 kg sits at rest on a frictionless tile floor. With your foot, you apply a 20 N force in a horizontal direction. What is the acceleration of the box?
Ans.

The object is at rest, so there is no net force except for the force your foot is applying. Friction is eliminated. Also, there's only one direction of force to worry about. So this problem is very straightforward.

F = m * a

F / m = a

20 N / 40 kg = a = 0.5 m / s2

Newtons Third Law

Third Law

Each and every action has an equal and opposite reaction.

In the top picture, a physics student is pulling upon a rope which is attached to a wall. In the bottom picture, the physics student is pulling upon a rope which is held by the Strongman. In each case, the force scale reads 500 Newtons. The physics student is pulling  the same force in each case.

Newtons three law

Newtons three law changed the entire world. They are seen in our day to day life. In this article we are going to learn newtons three laws with some examples so that you understand it very easily.

Newtons First Law of newtons three law

This law states that if a body is at rest it will remain the same unless acted up on by some force and an object in motion continues to be in motion unless acted up on by some external force. This law is often called as Law Of Inertia.

This means that objects keep on doing what they do. Every object resists change of its state. If there is no force acting up on the body it will maintain its state of motion.

From the figure above we can see trolley is moving towards right. It continues to move, but it stopped when it hit a pole. So here pole is the object which put some opposite force on the trolley to change its motion.

This is all about first law in newtons three laws.

Newton's Second Law of newtons three law

This law states that when force is acted up on some body acceleration is produced. The greater the mass of the body the more the force is needed to accelerate the body. If F is the force applied, m is the mass applied and a is the acceleration produced then applied force = mass * produced acceleration.

This can be written in equation form as

                                                                F = ma            

Here force and acceleration are vectors and direction of force vector is same as direction of acceleration vector.

Example below explains you use of second law.

From the above figure we can three kids applying a force of N newtons. They want to accelerate a car weighing 1000 KGS at 1.0 m/s2 . Now by applying the formula F=ma

                                          N = 1000 * 1.0

                                             = 1000 newtons

So the force the three kids needed to apply is 1000 newtons.

This is all about second law in newtons three law.  Let us go to third law in newtons three law.       

Newtons Third Law of newtons three law

This law states that " For every action there is equal and opposite reaction". This tells that if you apply some force there will be equal and opposite force .

From the above figure we can see that rocket ejects gases with heavy force in down ward direction. This is the action. For this action rocket moves upward and this the reaction.

This is all about newtons three laws. Very easy naaaaaaa Koooooolllllllllll.....!!!!!!

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How To Effectively Help Children Overcome Their Learning Disability

How To Effectively Help Children Overcome Their Learning Disability
By Floyd B Rivers

Dyslexia is a well-known learning disability that occurs when the brain recognizes, processes, and interprets symbols or information in another way. It is a lifelong challenge that many children go through as it prevents them from acquiring the proper skills of reading, writing, spelling, and to some degree, speaking. And oftentimes, such learning disability is mistaken for poor intelligence and also laziness.

Understanding dyslexia will help parents recognize the essential symptoms of the learning disability and this can be a great factor in effectively treating it should specialists confirm such a condition in their child. Once the symptoms are recognized, the family as well as the teachers of the child with dyslexia should come together and think about the best intervention programs that will promote dyslexia treatment.

Dyslexia symptoms in children may include difficulty in pronouncing words, recognizing letters as well as matching letters to sounds, problems with learning and accurately using new vocabulary words, troubles in rhyming, and many more. Since there is no known cure for dyslexia yet, the only solution is to seek literacy programs that are designed to address the many symptoms of the learning disability and help the child overcome certain difficulties associated with it.

Educational tools are generally used as treatment as opposed to medication. Basically, an initial assessment should be conducted to evaluate the child's weaknesses and strengths. Parents should approach a specialist or perhaps an innovative education establishment that are centered on treating dyslexia. Then expert teachers together with assessors will work hand in hand to formulate an individualized education program that will address the child's difficulties in reading, writing, spelling, and speaking. Such intensive literacy program must enumerate in detail the child's particular disabilities along with the specific teaching methods.

Well-structured programs created by professionals with countless experiences with children with dyslexia usually apply a multi-sensory approach that may focus on vocabulary, fluency, comprehension, reading and writing, synthetic and analytical phonics, and phonemic awareness.

When it comes to treating dyslexia, it does not solely depend on the teachers at school, the tutors, and other educators who specialize in the learning disability. An effective treatment of a child's dyslexia should also include the responsibilities of the parents. Having a structured environment at home can definitely motivate a child to work on his or her skills in reading and writing. Parents and other family members can instrumentally reinforce the child's comprehension by helping him or her to maintain focus and also by emphasizing certain lessons. For more info, click here.

Children with dyslexia can effectively gain the core skills they need to overcome their disability. But it will be more effective when they have a dedicated support system at home from their families. Visit this site for more.

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Solve Math Questions Online and Enhance Your Skill

Solve Math Questions Online and Enhance Your Skill
By Sandy D'Souza

Rigorous practice is the main key to achieve success in math. Research suggests that most students do not spend enough time to practice math on a regular basis. The reasons can be varied, from disinterest to inefficiency. The fact is that when students do not understand the topic properly, they lose their interest and end up disappointed due to poor grades in exams. To solve a mathematical problem accurately, students need to be completely involved. The process of solving a mathematical problem demands several sequential steps. First, students need to find the method involved in the problem. Second, they need to apply the right formula to get the correct solution. Third, they can find the alternate method to solve the same problem.

Practice math questions and answers

To make each learning session more effective, students should practice various problems on the same topic. This gives students more clarity on each topic. Additionally, they can easily find out their learning problems and take required steps to overcome these. However, students have a tendency to stick to a topic which is easy to solve. Experts suggest that they should change this habit and try to solve all kinds of problems to get familiar with the entire curriculum. To become an ace in math, students need to practice math regularly.

Several websites offer math help. When a student feels that he/she does not understand the math concepts thoroughly in a classroom environment and cannot cover the syllabus on time, they can opt for online math assistance. This learning process gives them better understanding of each topic. Most importantly, with this service, students can choose grades, topics and level of difficulties accordance to their preference. They can choose the worksheet which they want to work on. Online math help is fast and easy to use for students. They can find instant solutions related to any topic including algebra, calculus, etc. Students can also use some math quizzes and games available on those websites to make math interesting.

Take online help to solve tricky math problems

Students need to have patience to solve any tricky math problem accurately. However, most students do not practice math regularly and try to memorize some easy methods to solve all problems in exams. This is definitely a wrong technique to prepare for the math exam. Any student can learn math by following step-by-step and detailed explanations. Students can have this facility with online math help. They can choose their preferred tutor along with suitable timings.

Online math help is few steps away from students. Students can access online help anytime and from any place. It enables a good number of students to score well in exams. This innovative learning process also enhances students' confidence. In short, by using this online service, students get adequate learning help in a convenient and comfortable way.

To improve your mathematical skills students can take extra care in some parts like more practice and they can also take help of math tutors or with online math help and also the most important thing is working on the assignments given in regular class sessions. This makes you score good marks and enhances your skills.

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The Student Quiz

The Student Quiz
By Richard D Boyce

Early in my teaching career, I was always looking for something different to stimulate student learning. I found the simple quiz was a great diversion for the students from the normal chalk and talk lesson of that era. Therefore, I created a series of different quizzes that I used in a variety of subjects that I taught in lower high school classes. This is one of those quizzes. It is called the Student's Quiz and I have included the two versions I have used.

Essentially, the individual student or groups of students develop the questions and become the quizmaster.

Here is the procedure for the two versions.

Version One

1. Select a topic. This may be one you have just taught or it could be one which needs revision.

2. As homework, the students are instructed to devise five questions each (with answers). These are to be written out neatly.

3. During the next lesson, the teacher asks a student for his/her questions, checks them and the answers and if they are satisfactory, the teacher asks the student to give the class his/her test.

4. Ensure that the student delivers the questions in a way that the class can hear and understand. Check volume and speed of delivery and that there is enough time between each question to allow the students to write their answers.

5. The student gives and explains the answer.

6. The teacher adds any teaching comments and/or supports and/or corrects the answer given by the student.

7. The process is repeated as often as the teacher wants in the time available.

8. The teacher must check the questions of the next student to ensure that no question is repeated and that all questions are suitable.

9. To ensure that every student get a chance to ask a question during the one lesson, I sometimes allowed each student to select only one of their questions to give to the class.

Version Two

1. Divide your class into groups of four or five.
2. Each group is given a different topic, e.g. Topics for the forthcoming exam.
3. Each member of the group devises five questions of varying difficulty on the topic as a homework exercise. Answers must be included.
4. In class the next day, each group test the questions on each other and then develop a five question quiz on their topic - the questions from easy to hard with answers included. (All group members get a copy of their group's quiz.)
5. The teacher rearranges the whole class into the same number of groups but this time each new group consists of one person with questions from each of the previous groups.
6. Each member of the new group 'quizzes' their new group with their questions. This process may take more than one lesson but would allow the revision of several topics.
7. The teacher needs to roam the classroom, keeping the students on task and clearing up any problems.
8. The teacher is given a copy of each group's questions.

A special note:

Students invariably ask questions which are harder than those of the teacher so it is important to instruct the students to write five questions which vary from easy to hard.

Outcomes that can occur:

1. Better understanding is created by:
   1. individual question creation and
   2. group discussion of the best questions and the correct answers.
2. Students have ownership of the questions.


3. Several topics can be covered.


4. Students get experience in oral work and in explaining their Maths or Science and so on.


5. Students gain more confidence in their various subjects.


6. Students want to have the 'best' or 'trickiest' questions. This is a great motivation for many students.


7. The group acts as the 'correction mechanism' for errors in question technique, understanding of the students' learning and the answers.


8. Students enjoy their learning.


9. The teacher may gain a valuable reservoir of questions and answers.


10. The questions asked are often ones which students feel they need or want to know - almost a self-diagnosis.

This article explains one of a series of different types of quizzes that our author has used to great effect during his career in high school classrooms. In his early career, he taught several subjects to junior high school classes where he learnt the art of using the quiz as a revision tool and as an introduction to a new topic where he reviewed past knowledge. You will find two eBooks on his website http://www.realteachingsolutions.com explaining his use of his different types of quizzes. The titles are, "The Quiz in Middle School Mathematics" and "The Quiz as a Teaching Strategy".

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Sample of Basic Algebra Test

Author: Matthew David

Sample of Basic Algebra Test

Introduction to algebra:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. (Source: Wikipedia)

In this topic we are discuss about Sample of Basic Algebra Test  introduction and Sample of Basic Algebra Test examples

Sample of Basic Algebra Test Questions:

1) Solve the add sum of 4x4 – x2 + 2x + 1 and x + 3x3 – 3x2 – 1.
2) Solve this problems Subtract 5x3 – 2x2 – 2 from x3 + 4x2 – 3x – 5
3) Find the product of 2x3 – 3x2 – 5 and 3x2 + 4x – 2 .
4) Solve the following system:x + y + z  = 4; x - 2y - z = 1; 2x - y - 2z = -1
5) Find the coefficients of a4, a3, a2 and a term in the product of 7a3 – 6a2 – 9a + 8 and 5a2 – 3a + 5 without doing actual multiplication.
6) Solve the equation by completing the square (2x - 3)2.
7) Solve the equation by completing the square x2 + 6x – 7 = 0.
8) What should be added with x2 + 12x to get a perfect square? What is that square?
9) Express (5 – 3i) 3 in the form a + ib.
10) Express (v3 + v2) (2 v3 -i) in the form of a + ib
11) Multiply (3AB + 2A)(A2 + 2AB2).
12) Multiply (X + Y)3
13) Find the statement is equal or not equal: 7(-4x - 3) - (x - 4) = -8(2x + 6) + 11
14) To find the equation of the line through the points (-8, -6) and (-5, 8), we first use the slope m.
15) Solve: 8x - 2y = 3
16) Solve the equation 2x4 -x4 -8x2 + 4x2 + 8x = 0x3 - 35, if one of its roots is 2 + v3 i
17) Solve the quadratic equation x2  + 7 = -x2
18) Solve the equation x4 - 4x2 + 8x = 0x3 - 35, if one of its roots is 2 + v3 i

Sample of Basic Algebra Test Answers:

1) 4x4 + 3x3 – 4x2 +3x + 0
2) –4x3 + 6x2 – x – 3.
3) 6x5 – 3x4 – 16x3 – 9x2 – 20x + 10.
4) The answer is (2, -1, 3).
5) So the coefficient of a term in X × Y is– 69; So the coefficient of a2 in X × Y is 37; So the coefficient of a3 in X × Y is 8; So the coefficient of a4 in the product of X × Y is –51.
6) 4x² - 12x + 9
7) The solution set = {1, –7}
8) 36.
9) – 10 – 198i.
10) (-6 + v2) +v3 (1+ 2 v2) i
11) 3A3B + 6A2B3 + 2A3 + 4A2B2
12) X3 + 3X2Y + 3XY2 + Y3
13) Not Equal.
14) Slope m =3/14
15) The x intercept is at the point (3/8 , 0).
16) Thus the roots are 2 ± iv 3 and - 2 ± i
17) (- 1 +v 3 i)/2 and (- 1 -v 3i)/2 are conjugate to each other.
18) Thus the roots are 2 ± iv 3 and - 2 ± i

Example problems for search answer to the algebra

Search algebra example problem 1:

Simplify the given [removed]13x + 23) + 50x = 10 - 43x

Solution:

Given expression is (13x + 23) + 50x = 10 - 43x

Expand the above expression, we get

13x + 23 + 50x = 10 - 43x

63x + 23 = 10 - 43x

Subtract (10 - 43x) on both the side of the equation, we get

106x + 13 = 0

Subtract 13 on both the sides, we get

106x = - 13

Divide the above equation by 106, we get

x = `(- 13 / 106)`

Answer:

The final answer is x = `(- 13 / 106)`

Search algebra example problem 2:

Find the x intercept of the given polynomial equation f (x) = 2x2 - 72

Solution:

The given polynomial equation is f (x) = 2x2 - 72

Plug f (x) = 0, for finding x intercept

0 = 2x2 - 72

Rearrange the above equation, we get

2x2 - 72 = 0

Add 72 on both the sides of the equation, we get

2x2 = 72

Divide the above equation by 2 on both the sides, we get

x2 = 36

Take square root on both the sides, we get

x = ± 6

x intercepts are ± 6

Answer:

The final answer is x = ± 6

Search algebra example problem 3:

Find the slope the line which passes through the (2, 8) and (0, 16).

Solution:

Given points are (2, 8) and (0, 16)

Here, x1 = 2, y1 = 8, x2 = 0 and y2 = 16

Slope formula:

Slope (m) = `((y_2 - y_1) / (x_2 - x_1))`

Substitute the given values in the above fomula, we get

Slope (m) = `((16 - 8) / (0 - 2))`

=` ((8 / - 2))`

= - 4

Slope of the line is m = - 4

Answer:

The final answer is m = - 4

Practice problems for search answer to the algebra

Search algebra practice problem 1:

Find the slope of the given straight line equation y = 5.3x - 17

Answer:

The final answer is slope (m) = 5.3

Search algebra practice problem 2:

Find the factors of the given quadratic equation x2 - 17x + 60 = 0

Answer:

The factors are (x - 12) and(x - 5)

Search algebra practice problem 3:

Simplify the expression 5x + 28 = 108

Answer:

The final answer is 16

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Pre algebra review tests

Author: Matthew David

Pre algebra review tests

Introduction to pre algebra review tests:-

In this article we are learning about the pre algebra review tests the concept. Algebra is cluster of mathematics and it process on the pre algebra review tests. Pre algebra review tests cover the four basic operations such as addition, subtraction, multiplication and division. The most important expression of pre algebra review tests is variable, constant coefficient, exponent, word and expression. Pre algebra review tests beside numeral we use symbol and alphabet in place of unknown number to make a statement. Hence, pre algebra review tests related problem shown below.

Pre-algebra is division of mathematics is that replacement letters for numbers. An algebraic equation is stand for the scale, what is finished on the one side of a scale with a number is also completed to the other side of the scale. This type of mathematics is called algebra. In this article we shall discuss about how to do pre-algebra problems with some examples.

Sample problem for how to do pre algebra:

Problem 1:

Find the value of given fraction numbers `2/3 ` + `1/3`

Solution:

In the proper fraction a denominator values are same. So we are directly added or subtract the numerator values.

Step 1: In here the denominator values are same.

Step 2: Add the numerator values and place over the same denominator values.

`2/3 ` + `1/3`= `(2 + 1)/3`

= `3 / 3`

Step 3: Now we are simplify the fraction values

= 1

Problem 2:

Solve the given values using simple arithmetic operations 9 + (7 * 2)

Solution:

We are going to find the value of given numerical values.

In the first step we are going to multiply the values 7 and 2, we get

7 x 2 = 14

In the next step add the value 14 and 9, we get

9 + 14 = 23

The sum value of the given numerical value is 23.

Pre-algebra Problem 3:

Evaluate the given problem and find the sum value 6 - `(8 / 2^2)`

Solution:

We are going to find the value of given numbers.

In the first step we are going to find the value of 8 and 22, we get              

`8 / 2^2 ` =` 8 / 4`

= 2

In the next step we are subtract the two terms 6 and 2 we get

6 – 2 = 4

The sum value of the given terms is 4.

Problem 4:

Solve the given equation X – 5 = 8.

Solution:

We are going to find the x value of the given equation. In the first step move -5 into the right side of the equation, we get

X = 8 + 5

X = 13

We get x value as 13.

Pre algebra review tests questions:-

1. Write b. b. b. b. b. a. a. a in exponential form.

2. Evaluate `x^4.y^2` when x = 2 and y = 5

3. What is the square of 13?

4. Find the quotient of 3270 and 32.

5. a. Find 0/16 b. Find 16/16 c. Find 16/0 d. Find 16/1

6. Simplify: 8+`6^2` +8÷2

7. Simplify: 20 + 4(5)

8. Simplify: 43+6·12-6÷2

9. Find the opposite of –6.

10. Find the opposite of 12.

11. Write the expression –4-(-3) in words.

12. Simplify: -(9)

13. Add.-31+75+ (-69)

14. What is 22 added to –19?

15. Evaluate the expression – a + b-c, when a = -6, b =4, and c = -3.

16. Use the Inverse Property of Addition to complete the statement_____+12=0

17. What is –21 decreased by –13?

18. Simplify. 13+ (-9)-18-(-5)-3+14

19. Evaluate yx--, when x = -12 and y = -23.

20. Is –11 a solution to 5-(-x) =16?

21. Find the temperature after a rise of 22° F from -31°F.

22. Solve -7+x=-5

23. Solve -4n=56.

24. The difference between a number and seven is twenty-eight. Find the number.

pre algebra review tests answer keys:-

1. `a^3b^5`

2. 400

3. 169

4. 102 R 6

5. a. 0 b. 1 c. undefined d. 16

6. 48

7. 40

8. 13 9. 54

9. 6

10. -12

11. negative four minus negative three

12. 3

13. –25

14. 3

15. 13

16. –12

17. –8

18. 2

19 35

20. NO

21. -9° F

22. x = 2

23. n = -14

24. x = 35.

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Students Gain Important Life Skills From Resource Classes

Students Gain Important Life Skills From Resource Classes
By Linda A Johnson

Most people have wonderful memories of sports activities and art projects while in school, but just how important are these activities? One of the main reasons for education is to prepare the students for jobs in the future, their social life and their family, but those familiar classrooms come from a different world. They were designed to prepare a student to be a worker on an assembly line, where they had to know how to function as the member of a team that rarely deviated. The ability of a student to stand in line at school is an important skill to learn because it teaches them to wait on the other team members, however today's work environment requires skills that are different.

In today's working world, it is very likely that a worker may change careers many times and may require many different skills and know the best way to apply them. By giving a student a variety of options, they can determine where their interests lay and the learn that change is sometimes fun. This also enables them to cope with changes that are inevitable. The act of switching from an activity involving paper and pencil, where the focus is mental concentration, to activities such as stomp or yoga, which require an awareness of balance and a focus on the different muscle groups is useful in that it helps the student learn the way to change strategy so they can be successful.

These extra activities can give the student an outlet in which their imagination can grow. A lot of teachers agree that these activities will give the student a chance to stop and reflect on what they just learned. For example, students who just learned about the solar system might incorporate what they learned into an art project. Another example is for students who learned about treaty negotiation might be able to apply that to resolving a dispute in sports. It is proven that students will retain what they learn better if they can process it in multiple ways. In addition, when students are involved in an activity they enjoy, the likelihood of them forming a better relationship with their teacher is greater and they will receive effective guidance.

The concept of developing multiple intelligence with different learning skills, is supported by the incorporation of enhanced activities. A good example is when one student has no problem learning by hearing, but another student learns better by touching things and manipulating with their hands. One student might find joy in art, while the other student may enjoy sports. A student who has the freedom to explore and choose will find success by enhancing their confidence to try something new. When students are allowed to try new things, it increases the chance of them finding something that will bring them success and happiness.

Education of the character can be part of activities that are enriched so that when success is experienced, the person can identify that "my success is directly linked to my choices and not exclusively to an environment that I cannot control." The more a person knows that they can control the events that affect them, the less depression they will suffer and the more success they will have. When students learn to balance different activities, they learn that success is a step by step process and they also develop patience. Even though resources classes do help with the emotional and relational thinking, there is still a need for cognitive and verbal thought and this is emphasized within the core curriculum.

What is the purpose of learning? It makes sense to develop multiple skills in different areas because there is no way of knowing what the future holds and students need to learn how to adapt in order to be successful. Resources classes provide a guided freedom of self discovery that will give the student the experience they need to build confidence. If a student has confidence, they have a solid foundation and can receive a mentor so they can learn the important relational skills. Schools that give a variety of choices in different areas to students who will then find different ways to be happy and successful, provide a foundation for a successful and happy life. These choices can mainly be found in private schools, which are a great option.

Private School Jacksonville, Hendricks Day School focuses on teaching your child how to think. Contact us for a tour of our school in Jacksonville: 904-720-0398.

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