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Proofreading for Parallel Structure on the SAT and ACT

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Overview:  What Is Parallel Structure?

Parallel structure in writing is a refinement technique in which verbs, subjects, and clauses are made similar.  It is tested on the ACT and SAT in grammar questions, as it is a feature that adds impact to writing.  Often, phrases that mean the same may not be parallel.

Checklist:  Are Verbs in the Same Tense?

Parallel verbs in each clause should be in the same tense.  For example, parallel verbs are “He came, he saw, and he conquered” not “he came, he saw, and he will conquer. ” Similarly, if helping verbs are used in one clause, the same helping verbs should be used in the other clauses.  “She may gather enough support, she may raise enough funds, and she may win the election,” rather than “she may gather enough support, she raised enough funds, and she will win the election.”

Checklist:   Is the Subject the Same in All Clauses?

In order for clauses to be parallel, the subjects should remain the same.  “The corporation will sponsor the fun run, the CEO will speak at the breakfast, and they will wear T-shirts advertising the event” is unclear and not parallel.  In order to make the structure parallel, one way to recast the clauses is, “The corporation will sponsor the fun run, its CEO will speak at the opening breakfast, and its employees will wear T-shirts advertising the event.”

Checklist:  Are the Same Types of Clauses Used?

More subtly, parallel clauses need to have the same structure.  A sentence like “The building manager will choose the maintenance projects that they think will make their properties more attractive” has two clauses that are less parallel than the recast sentence “The building manager will choose the maintenance projects that will make their properties more attractive.”  Sometimes it is a matter of eliminating unnecessary words in order to clarify the structure.

Checklist:  Is the Punctuation Parallel Between Parallel Clauses?

If clauses are parallel, they should be separated with the same type of punctuation.  For the most part, they will be independent from one another.  For example, in the sentence “He came, he saw, and he conquered” all the clauses are separated by commas.

Stoichiometry: Dealing with Excess and Limiting Reactants

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Overview:

In many chemical reactions there is an excess reactant a limiting reactant. The amount of product produced is determined by the stoichiometric calculations using the amount of limiting reactant present in the reaction. This means that not all of the excess reactant is used up during the reaction since there is no more of the other reactant present to react with.

Simpler Terms:

It is easier to think of limiting and excess reactants in terms of baking. If a recipe calls for 1 cup of peanut butter, and 3 cups of sugar to make 12 cookies and you start with 3 cups of peanut butter and 12 cups of sugar based on the amount of peanut butter you have you could make 36 cookies but based on the amount of sugar you have you could make 48 cookies. In this case peanut butter is our limiting reactant and we can only make 36 cookies but will have 3 cups of sugar left over when we are finished which means it is our excess reactant.

The idea behind limiting and excess reagents is identical to what we did above with the baking except we are dealing with elements instead of ingredients.

Example Question:

Four moles of propane reacts with ten moles of oxygen. How much carbon dioxide will be produced from this reaction?

Step One:

The first step in determining the excess and limiting reactants is to have your equation fully balanced so you can see the stoichiometric ratios between the different compounds.

C3H8 + 5 O2 → 3 CO2 + 4 H2O

Step Two:

The next step is to determine the conversion factor to multiply the moles of each element by to find the amount of product it will produce. To find the conversion factor simply divide the element by its coefficient and then multiply by the coefficient of the element you wish to know the amount of moles of.

O2 → CO2 conversion factor = 3/5

C3H8 → CO2 conversion factor = 3/1

Step Three:

Repeat step two for all the reactants in the equation with the amount of moles you have for that reactant and whichever one yields the least amount of product is the limiting reactant. All the other reactants are excess reactants. Use the limiting reactant for the amount of product formed.

Ten moles of O2 will produce, 10 * 3/5 = 6 moles of CO2 produced

Four moles of C3H8 will produce, 4 * 3/1 = 12 moles of CO2 produced

To answer the question at the beginning, when four moles of propane reacts with ten moles of oxygen only 6 moles of carbon dioxide will be produced and there will be an excess of propane at the end.

How to Calculate Work Done by a Force

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Work is the energy applied to an object as it moves some distance. The amount of work done is directly proportional to the magnitude of force applied, as well as the displacement of the object. In some cases, there may be an angle between the direction of displacement and force vector.

The force must be perpendicular to the direction of displacement in order to produce work. This can be considered through application of trigonometry, where the angle is found between the displacement distance and force vector. When the force opposes the direction of displacement, the work produced is negative.

Work Done by a Force 2

Work is a scalar quantity as it does not have a defined direction. The unit for work is the Newton meter (Nm), since force is measured in Newtons (N) and displacement is measured in meters (m). Most commonly, work is written in units of joules (J), an SI unit. All types of energy, such as heat and potential energy, are measured in terms of joules.

Work Done by a Force 3

We can determine the work done by specific forces in varying scenarios. As a hockey puck slides across a surface, multiple forces are present and play separate roles. No work is done by the normal force or gravitational force since the vectors are perpendicular to the direction of displacement. On the other hand, the friction force is parallel to the surface, and does work on the hockey puck. However, the friction force produces negative work. This will always be the case as friction constantly opposes movement.

Work Done by a Force 4

In the diagram above, an 8 kg crate is dragged 10 m across a wide room. The pulling force was applied with 20 N at a 30°angle. The coefficient of kinetic friction between the crate and carpeted floor is 0.1. What is the work done by each of the forces applied on the crate?

Work Done by a Force 7

 

A free body diagram can be produced to show all forces acting on the crate. The applied force can be broken down to the x-component and y-component through trigonometry. Because they are parallel to the direction of movement, the x-component of the applied force and the friction force both produce work. The remaining forces are perpendicular and do not produce work.

Work done by FX : WFX = F ∙ d ∙ cosθWFX = 20 ∙ 10 ∙ cos30°WFX = 173.21 J
Work done by Ff : WFf = Ff ∙ d ∙ cosω

WFf = μk ∙ FN ∙ d ∙ cosω

WFf = μk ∙ (FG – FY) ∙ d ∙ cosω

WFf = μk ∙ (mg – Fsinθ) ∙ d ∙ cosω

WFf = 0.1 ∙ ((8 ∙ 9.81) – 20sin30°) ∙ 10 ∙ cos180°

WFf = – 68.48 J

The basic formula for work can be applied to both forces, although some forces may have to be broken down to simpler terms. The downward and upward forces are in equilibrium, and as a result, the normal force can be determined. The difference between the gravitational force and y-component of the applied force is equivalent to the normal force. The total work of the system can be determined through the sum of work values.

Wtotal = WFX + WFf

Wtotal = 173.21 J – 68.48 J

Wtotal = 104.73 J

How to Prepare a Solution of Proper Concentration

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Overview:

When in a chemistry lab or just writing a test, many students struggle with how to create a solution of known concentration. Students find it difficult because they try to calculate the solution in terms of moles, which is a unit that cannot be measured in the lab. There are some easy to follow steps on how to prepare a proper solution with a known concentration.

Step 1: Determining the number of moles of compound

The first step is to determine what concentration of solution you need to make along with the volume you are looking to end up with. In this example we are going to make 1234 mL of a 1.54 molar solution of NaCl (Sodium chloride).

First, we will determine the number of mols of NaCl that are contained in 1234mL of a 1.54 molar solution. To do this, we will use the following formula:

Equation1

Where:

n = number of moles of solution in mol

C = concentration of solution in mol/L

V = volume of solution in L

NOTE: Always ensure that your units are consistent.

Note that the unit of volume is mL while the unit for C is mol/L. This means that we need to convert mL to L before solving the equation. 1234 mL is the same at 1.234 L. Now that all of our units are consistent, we can substitute our known values for concentration and volume:

Step 2: Determining the mass of the compound

We now know that we need to add 1.90 mol of NaCl to our solution; however, mol is not a unit we can measure out with common lab instruments. We must first convert it to a unit that is easily measured in the lab. This requires a new equation:

 Equation2

Where:

n = number of mole in mol

m = grams of compound in g

M = molar mass of compound in g/ mol ( This is taken directly from the periodic table)

To determine M, we need to take a closer look at our compound:

NaCl         = 1 Na + 1 Cl

 = (1 * 22.99 g/mol) + (1 * 35.45 g/mol)

 = 58.44 g/ mol

We have determined our molar mass (M) and calculated n in Step 1. We are now ready to use substitution to find m. Since all of our units are consistent, no further adjustments need to be made.

m         = n * M

Equation3

We now know that we must measure out 111.0 grams of NaCl on a scale for it to be added to solution.

NOTE: The key when creating any solution is to slowly add the compound to water while stirring. This will start off with a very low concentration of the compound and slowly increase to the desired concentration.  If water is added to the compound instead, this will start off with a very high concentration of the solution, potentially resulting in a hazardous compound.

Fill a beaker about ¾ full with deionized water, then add the 111.0 g of NaCl. After the NaCl is added, fill the container the rest of the way to the 1.234L mark. You now have 1.234 L of a 1.54 molar solution of NaCl.

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Newton’s Three Laws of Motion

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Overview:

Sir Isaac Newton is well-known for his work on creating the three laws of motion based on the theories of previous scientists as well as his own speculations. These 3 simple, intuitive laws lay the foundation for the basics of classical, Newtonian mechanics. The following are Newton’s three laws in more detail:

1. Newton’s First Law of Motion: The Law of Inertia

The first law of motion states that objects will remain in their current state of motion unless acted upon by an external, unbalanced force. This means that objects that are at rest, will remain at rest unless acted upon by an external, unbalanced force while objects that are moving, will continue in a constant state of movement unless acted upon by an external, unbalanced force.

In order to understand the law of inertia, we can imagine that a hockey puck is on ice (which in this case is frictionless). At first, the hockey puck is not moving, and we can assume that if it is not moving, it will stay that way. However, an unbalanced, external force such as a hockey player hitting the puck with their stick could cause the hockey puck to come out of rest and start to move.

In another scenario, we can imagine that a hockey puck is moving at a constant speed on frictionless ice. It will continue to move in constant motion unless something gets in its way and stops the motion, such as a hockey player stopping the puck.

2. Newton’s Second Law of Motion

The second law is based on the following equation:

F = m * a

In this equation, “F” represents a force measured in joules, “m” represents mass in kg and “a” represents acceleration in m/s2.

This law states that the acceleration of the object is dependent upon the magnitude of the force, and the size of the mass. The acceleration of any object is directly proportional to the force applied to the object. That is, a stronger force applied to the object will result in a larger acceleration. The acceleration of any object is also inversely proportional to the mass of the object. That is, the larger the mass of the object, the lower the acceleration will be.

3. Newton’s Third Law of Motion

Newton’s third law of motion states that “every action has an equal and opposite reaction.”

This law states that if object A applies a force to object B, object B will, in turn, apply a force of equal magnitude on object A. is applied from one body to another, no matter how large the force is, there will always be an equal force applied right back in the opposite direction but with the same amount of force. For example, when an individual punches a wall, they will feel the force of that punch hit them right back with the same magnitude, causing pain.

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Who’s Afraid of the Normal Curve?

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Overview:  What Is the Normal Curve?
The normal curve is a frequency distribution with special statistical properties.  The best-known application of the normal curve is the distribution of intelligence as measured by tests such as the Stanford-Binet, but there are other examples  that are close to the normal curve in human and animal behavior.  Biologists, other scientists, and mathematicians try to make it scary by calling it a “Gaussian distribution”. To social scientists and educators, it’s nothing but the normal curve.

What Does the Normal Curve Look Like?
The normal curve is a symmetrical distribution of scores with the mean (the average of all scores), the median (the point at which exactly half of all scores are below and the other half of scores are above), and the mode (the most frequent score) are equal.  The further scores get away from the mean, the closer they get to the baseline, but they never touch, even if the score is infinitely far away from the mean.  That is a property of the normal curve called “asymptotic.”  It is also a continuous curve.

Normal Is a Statistical Artifact
The normal curve itself is a theoretical distribution that first came from mathematicians interested in probability and observational errors, and Gauss was one of those mathematicians who developed it.  Scores in real life, such as measurements on IQ tests, ability scores, and the like, follow the normal curve closely, but do not fall exactly on the normal curve.   The mode is the most frequently occurring score in the distribution by definition, and a statistical artifact is a fancy way of saying that the scores follow a certain pattern.

What’s So Special about It?
The relative frequencies of scores that are in an approximate normal distribution fall under specific percentages, and no matter what is being measured, if those values follow a normal distribution, those percentages will hold true.  Statisticians call the measurement of the distance away from the mean the standard deviation, and about 68% of scores will fall  within one standard deviation on either side of the mean.  Just a little over 95 % will fall within two standard deviations on either side of the mean, and just over 99% will fall within three standard deviation on either side of the mean.  Because the tails never touch the X-axis, that’s as close as it gets.

Using the Normal Curve in Research
The mathematical properties of the normal curve make statistics easier to apply in research when the values that are obtained from observations fall close to the normal curve.  There are extensive statistical tables that describe the exact location of values on the normal curve.  In addition, because the normal curve was originally developed around probabilities, it is possible to determine how likely something will happen, such as winning the lottery.

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Diffusion, Osmosis and Osmotic Pressure

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Diffusion is the net movement of molecules because of a difference in the chemical potential or concentration between two regions. Molecules move faster when the difference/gradient is larger. Molecules tend to move to the region where their chemical potential or concentration is lower.

 

Osmosis is the diffusion/movement of water through a cell membrane. Since water molecules are small, they have a very high permeability through cell membranes. When there is a high concentration of solute, there’s a low concentration of solvent (ie. water). This means the chemical potential of water is low. On the other hand, a low concentration of solute means a high concentration of solvent. This leads to a high chemical potential of water.

 

When concentrations of solute and solvent are equal on both inside and outside the cell membrane, there is no movement of water molecules. The net movement of water is zero. The extracellular solution and cytoplasm is said to be isotonic. If the concentration of solute is higher in the extracellular solution compared to the cytoplasm, the net movement of water is out of the cell. The extracellular solution is said to be hypertonic. If the concentration of solute is lower in the extracellular solution compared to the cytoplasm, the net movement of water is into the cell. The extracellular solution is said to be hypotonic.

 

Since cell membranes have a limited surface area, they cannot stretch easily or as much compared to a balloon. As a result, the addition of water can only increase the volume of the cell by a little. The addition of more water increases the pressure inside the cell as well. Eventually, the pressure will increase enough to prevent more water from entering the cell. When this happens, the chemical potentials are equal and the pressure is called osmotic pressure. When the osmotic pressure is greater than the maximum pressure the membrane can withstand, the membrane can burst and have its contents disperse out. When this happens, the cell is said to have lysed.

 

This article was written for you by Samantha, one of the tutors with SchoolTutoring Academy.

DNA Repair Mechanisms

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We have very good DNA machinery that replicates DNA to make many different copies. However, this machinery in our cells is not perfect. With so much DNA replication going on, there are bound to be some mistakes and errors made during this process. These errors lead to mutations and if not corrected, it may be detrimental to the cell. Even though these mistakes are rare (1/100,000,000 bases), it is still important that cells and DNA have a system to repair these errors; these are called DNA repair mechanisms. There are hundreds of enzymes made by our cells to repair damaged DNA.

Direct Repair

– Sometimes, the cell is able to reverse any damages in our DNA.
Example: DNA polymerase has a proofreading function that recognizes mismatched nucleotides and corrects it immediately during DNA replication. This undoes any damage to the DNA molecule.

Excision Repair

– The damaged section of DNA is recognized and replaced by a newly synthesized correct copy.
1) Repair enzymes recognizes an incorrect base or distortion in the DNA double helix and cuts out the damaged section.
2) A new section is synthesized by DNA polymerase, using the undamaged DNA strand as the template.
3) The new section is sealed into place by ligase.

Recombination Repair

– This happens when both strands of the DNA is damaged.
– The homologous portion of a sister chromatid is used as a template to construct new DNA.
– Although this method is likely to contain errors, there is more damage if no repair is made at all.

Sometimes when the damage to the DNA is severe, it may trigger suicide genes instead of DNA repair mechanisms. These genes cause the cell to die, preventing it from passing on the mutation to future daughter cells.

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This article was written for you by Samantha, one of the tutors with SchoolTutoring Academy.

Monomials, Binomials and Polynomials

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When dealing with differing kinds of Polynomials, there are several varieties. Today we will explore a few different variations, and break down the simple formula for naming them.

A monomial is the product of non-negative powers of variables. A monomial has no variables in its denominator and will only have one term.

For example: 13, 3x, -57, x², 4y², or -2xy

 

A binomial is the sum of two monomials and thus will have two unlike terms.

For example: 3x + 1, x² – 4x, 2x + y, or y – y²

 

A trinomial is the sum of three monomials, meaning it will be the sum of three unlike terms.

For example: x² + 2x + 1, 3x² + 4x – 10, 2x + 3y + 2

 

A polynomial is the sum of one or more terms.

For example: x² + 2x, 3x³ + x² + 5x + 6, 4x – 6y + 8

 

A good clue when trying to remember the meaning of these terms is the prefix on each word. In the word monomial, the prefix “mono” means one. In the word binomial, the prefix “bi” implies two. In the word trinomial, the prefix “tri” means three and in the word polynomial, the prefix “poly” means many.

Polynomials are in simplest form when they contain no similar terms. Similar terms are terms in the polynomial which are raised to the same power. For example, in the polynomial, 4x² + 4x – 3 + 3x², the terms 4x² and 3x² are similar terms. The simplified form of 4x² + 4x – 3 + 3x² is 7x² + 4x – 3. Another example of simplifying a polynomial would be: x² +2x +1 + 3x² – 4x is simplified to 4x² – 2x + 1.

Polynomials are generally written in descending order. For example the polynomial 4x² – 2x + 1 is written in descending order. In order for a polynomial to be in descending order the exponents of the variables decrease from left to right.

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This article was written for you by Mia, one of the tutors with SchoolTutoring Academy.

Form and Structure: The Basics

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Structures are everywhere around us, be it the building keeping us dry from the rain, or the chair keeping us from falling to the ground. Even the cup you drink from is a type of structure! There are three different fundamental types of structures: shell, frame, and solid.

Shell

Shell structures are supported by their outer material. These structures are usually hollow inside and require no internal framework to stay upright. An everyday example of this type of structure that we see is the cup we drink water out of.

Frame

The frame structure on the other hand needs an internal frame or internal network of beams and pillars to be able to stay upright. It relies on the internal framework to be able to withstand external forces such as wind and rain. One famous example of this is the Eiffel Tower in France. It has a complicated iron lattice framework that has great wind resistance!

Solid

Lastly, there is the solid structure. Its name is telling of what kind of structure it is: a structure completely filled and packed on the inside, which provides a strong foundation to withstand anything. A famous example of this is actually one of the seven wonders of the ancient world, the Great Pyramid of Giza.

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This article was written for you by Frances, one of the tutors with SchoolTutoring Academy.

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