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# ACT

#### ACT Science: Data Representation

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The ACT science exam does not require students to have in-depth understanding of biology, chemistry and/ or physics. It simply tests students on how to read and analyze  scientific passages.

One of the passage types for ACT Science is data representation. Students will be asked to analyze tables, bar graphs, scatter plots, pie chart, histograms and various curves. These passages are easier to work with because they require a lesser amount of reading. As such, students are encouraged to work on questions associated with these types of passages first.  They can be simple to work with if attention is paid to detail.

Here are a few quick tips to conquer data representation questions:

• Read the questions before you read the passage: this will allow you to hone in on important details while reading the passage.
• Check title, axis-labels and legends for charts and graphs: oftentimes more than one graph will be presented to analyze different information. At such times, axis-labels will determine which graph to use.
• Pay attention to the units: the chart axes may be labelled in millimeters while the question is asking for meters.
• Interpolate or extrapolate graphs to find missing information: use a general trend to find unknown information.

TestPrep Academy is the premier SAT/ ACT services company for high school studies. We offer instructional programs and curriculum for students preparing for the PSAT, ACT and SAT.

#### Deciphering Meaning from Reading Passages on the SAT and ACT

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### Overview

Questions about longer reading passages on the SAT, ACT, and other standardized tests tap students’ abilities to find and use meaning from what they read.  These skills are important to college success, as students are expected to read and understand textbooks in unfamiliar subjects.  Students are expected to extract the main ideas from what they read, distinguish between fact and opinion, recognize the author’s point of view, and summarize the passage, along with other skills.

Most often, the main ideas in a reading passage will be in the first few sentences of a reading passage.  Multiple-choice questions will give alternative statements of what the main idea might be.  Read all the alternatives carefully before deciding on the best answer.  One alternative might be too brief to contain enough information, while another might ask for a conclusion or opinion, a third might give more information than is necessary,  and the correct alternative will give enough information to decide on the main idea.

### Distinguishing between Fact and Opinion

Even fairly short passages will contain a number of supporting facts and some opinions, as any event is open to interpretation.  Opinions will ask the reader to draw conclusions from the supporting facts rather than merely stating those facts.  Opinions ask the reader to draw inferences as may not be supported within the text,

### Recognizing the Point of View

Many of these questions ask readers to recognize the tone of the passage.  Does the author believe the research is valuable or does the author believe the research is a waste of time?  Is the author pessimistic or optimistic about the outcome of the research presented?  If it is a historical article, is the author on the side of the winners or the losers?

### Summarizing the Passage

Normal reading passages on standardized tests are relatively brief, so the summaries are no more than a sentence or two long.  They  restate key points , and cover the entire passage rather than just one section of the passage.  The best alternatives focus on the big picture rather than one section.

TestPrep Academy is the premier SAT/ ACT services company for high school studies. We offer instructional programs and curriculum for students preparing for the PSAT, ACT and SAT.

#### Recognizing Nonstandard English: Diction Errors

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### Overview

Diction errors are types of errors when the incorrect word is used in a nonstandard way.  Some word usage is colloquial: out of place in a formal essay.  Other errors in word usage occur when similar words are used in the incorrect context.

### What about Lots or A Lot?

The use of lots or a lot is colloquial, as well as non-specific.  Standard usage would refer to many, or very much.  A sentence such as “I like to write a lot” could either mean that I like to write very much, or I like to write a great quantity.    Similarly, “A bunch of people were at the concert” should be restated as, “A group of people were at the concert” or “Many people were at the concert.”  When referring to people, bunch is nonstandard.  Bunches can refer to flowers, grapes, or bananas and be correct.

The word guy is also colloquial.  Preferred usage would be “the man”, just as preferred usage for gal would be woman.  Plenty as in the sentence, “It is plenty hot this summer” is colloquial.  “It is very hot this summer,” is standard.  In the same way, “It is awful hot this summer” is colloquial, and could be recast as “It is very hot this summer.”

The word aggravate means to make worse, and aggravated is not a synonym for annoyed (or any of the other synonyms for annoyed that are not standard usage). ” Her headache was aggravated by lack of sleep,” would be standard usage.  “She was aggravated by the construction in the office building,” would not be.

### What about Anxious and Eager?

“The students were anxious for change” is nonstandard, and should be replaced with “The students were eager for change.”  The students did not fear change.  Similarly, can refers to ability, while may refers to permission or likelihood.

TestPrep Academy is the premier SAT/ ACT services company for high school studies. We offer instructional programs and curriculum for students preparing for the PSAT, ACT and SAT.

#### Math Review of Binomial Distributions

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### Overview

A binomial experiment  has a fixed number of independent trials, and each trial has only two possible outcomes.  Each of the trials has the same probability of success.  The probability distribution is called a binomial distribution.

### What Types of Problems Are Binomial?

All the characteristics of a binomial experiment are present, then the distribution will be binomial.  A quiz has 8 questions, and each question has 4 alternatives.  If a student guesses randomly on every question, what is the probability of getting 5 or more correct?  It is a binomial experiment because it has a fixed number of trials (8), and the student is guessing randomly, so each question is independent of every other.  Each question can either be answered correctly or incorrectly.  In addition, each question has the same probability of success.

### What Types of Problems Are Not Binomial?

In a problem that is not a binomial problem, all the characteristics are not present.  For example, suppose a standard deck of cards is used, and the number of aces in 5 trials are recorded, but the cards are not replaced after each trial.  It is not a binomial distribution, because every trial depends on one another.  During the first trial, the population of cards is 52, the second, 51, the third, 50, and the fourth 49, so the trials are not independent.  Similarly, if there are three possible outcomes, rather than two, the problem will not be binomial.

### What Does a Binomial Distribution Look Like?

A binomial distribution is symmetrical, with the smallest values on either side of the mean, when it is graphed with the probability held constant, the number of trials on the x axis and the function on the y axis.  The more trials are done, the more the distribution spreads out, and the more the distribution flattens.

### How Is the Binomial Distribution Used?

Many types of real-world situations have a fixed number of  independent trials with only two outcomes.  For example, treatments often have outcomes of success or failure, basketball players either hit or miss free throws, and potential voters either cast their votes or not in a particular election.  Binomial distributions can be used to determine the probabilities of those events and others like them.

TestPrep Academy is the premier SAT/ ACT services company for high school studies. We offer instructional programs and curriculum for students preparing for the PSAT, ACT and SAT.

#### Appropriate Sentence Construction for the SAT and ACT

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### Overview:

Some grammar questions on standardized tests such as the SAT and ACT ask students to apply the rules they have learned about sentence construction.  Sentence prompts may include dangling clauses, free-standing phrases, and run-on sentences.  The task is to choose the rewritten sentence that makes the most sense without changing the author’s intended meaning.

### What Is A Phrase?

A phrase is a group of words that does not contain a subject and verb.  The words in the phrase act together in a unit,  such as prepositional phases, adjective phrases, or adverb phrases.  For example, the prepositional phrase “to the lighthouse” has a preposition, an object, and the article modifying the object.  Within the nonsense sentence, “Deep green ideas sleep furiously”, there is an adverbial phrase, “deep green ideas.” The sentence could be made more convoluted by adding an adverbial phrase such as “in the dark” to read “Deep green ideas sleep furiously in the dark.”

### What Is a Clause?

A clause is a group of words with its own subject and verb.  Some clauses can stand alone as short sentences or independent clauses.  Dependent clauses cannot stand alone and act as adjectives, adverbs, and nouns within sentences.  An independent clause can be changed easily into a dependent clause by adding relative pronouns such as that, which, who, whom, or whose, or relative adverbs such as after, before, since, where, when, or why.

### What Are Some Ways to Combine Phrases without Changing the Meaning?

Phrases can be used to expand sentences and make them more vivid without changing the meaning of a sentence. They do not contain subjects and verbs, so they cannot stand alone as sentences.  For example, the adverb phrase “in the evening” can be combined with the short sentence “The moon rises” to form the sentence “The moon rises in the evening.”

### What Are Some Ways to Combine Clauses without Changing the Meaning?

It is important to carefully read test alternatives that contain ways that clauses can be combined to make sure the meaning does not change.  For example, suppose the passage stated  “Virginia Woolf was an important member of the Bloomsbury Group.  The Bloomsbury Group challenged many ideas that were current in England.”  Those sentences could be combined by making the second sentence a subordinate clause, changing the passage to read, “Virginia Woolf was an important member of the Bloomsbury Group, which challenged many ideas that were current in England.”

TestPrep Academy is the premier SAT/ ACT services company for high school studies. We offer instructional programs and curriculum for students preparing for the PSAT, ACT and SAT.

#### Properties of Probability

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### Overview:

Probability is the measure of the likelihood of an event.  The basic mathematics of probability theory started with games of chance, but it can be applied to many situations, from weather forecasting to politics.  Probabilities range from 0 (no likelihood) to 1 (certainty), and are expressed as rational numbers.

### What Is the Sample Space?

The sample space is the set of all possible outcomes of an event.  For a coin toss, the coin will either result in heads or tails.  For the roll of one die, the sample space is all the values on the faces of the die, or a set of {1, 2, 3, 4, 5, 6}.  For the roll of a pair of dice, the sums will be in a set from 2 (both dice give you a 1), the smallest sum possible, to 12 (both dice give you 6), the largest sum possible.

### What Is A Fair Experiment?

In a fair experiment, all possible outcomes are equally likely.  The probability of any outcome is related to the total number of outcomes by a ratio of the number of outcomes in that event to the number of all possible outcomes of the event (the sample space).  Therefore, the probability that a coin will be heads is 1/2.  The probability that if one die is rolled, the number on top will be a 3 is 1/6.

### What If Events Are Not Equally Likely?

Sometimes, possible outcomes can be combined in such a way so that not all outcomes are equally likely.  Suppose two fair coins are tossed: there are 4 possibilities in the sample space {HH, HT, TH, TT}.  The probability of each event when order is important equals 1/4 for each possibility. However, if the question is merely “How many heads come up when two coins are tossed?”, there are only 3 possibilities in the sample space, 0 heads, 1 head, or 2 heads.  The event 0 heads is defined as {TT}, and the event 2 heads is defined as {HH}.  However, there are two possibilities for 1 head, either {HT} or {TH}, so the outcomes are not equally likely.

### What Are Mutually Exclusive Events?

If events are mutually exclusive, it means that neither sample space A or sample space B contain common elements.  Therefore, the probabilities can be added to form the probability of one event or the other occurring.  The sample space for tossing two fair dice and getting a sum of 7 consists of {(6,1), (1, 6), (2, 5), (5,2), (3,4), and (4,3)}.  The sample space for tossing two fair dice and getting a sum of 11 consists of {(6,5), (5,6)}.  The sample space for getting either a sum of 7 or a sum of 11 is the union of both sets.

TestPrep Academy is the premier SAT/ ACT services company for high school studies. We offer instructional programs and curriculum for students preparing for the PSAT, ACT and SAT.

#### Math Review of Random Numbers

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### Overview:  What Are Random Numbers?

In a set of random numbers, the numbers do not follow any pattern.  Each number has an equal probability of occurring, and each number event is independent of any others .  Most of the time, numbers that are close to random are generated by computer programs or calculator programs designed to do just that.

### What Are Some Examples of Random Events?

Many events are close to random. For example, individual molecules within a gas tend to move randomly, so that it cannot be predicted where an individual molecule will be.  Similarly,  the theory of radioactivity predicts that a percentage of atoms in a substance will decay into isotopes given an amount of time, but it does not predict precisely which particular atom will decay.

### How Are Random Numbers Found?

Numbers that are close to random can be found by consulting random number tables, as the result of computer programs to generate random numbers, and by using a calculator to generate random numbers.  In addition, games that depend on giving all the players a fair chance are often determined by using dice or a spinner divided into equal parts.  That way each number has an equal probability of being chosen.

### How Is Randomness Used In Statistics?

In scientific experiments, statistics are used as a tool to judge the results of an experimental treatment.  Subjects have an equal chance to be assigned to a treatment condition through random assignment.  Often a random number generator is used in order to assign subjects to treatment groups.  Not only does each subject have an equal chance of being assigned to any of the treatment groups, but the choice of any one subject is independent of all the others.  This minimizes errors that could occur if the assignment is not random, but confounded.

### What Are Monte Carlo Methods?

Monte Carlo methods are mathematical simulations that use random numbers to generate solutions.  They are called Monte Carlo methods because the earliest studies used equipment to generate random numbers similar to the methods in gambling casinos, such as decks of cards and roulette wheels.  Some simulations include the common practice of airlines overbooking seats on flights, because there are probabilities generated for how many passengers will arrive to take seats.  The computer simulation can be run for the number of seats on the airplane as the number of trials, using random numbers to suggest a possible outcome.

Test Prep Academy is the premier SAT/ACT services company for high school students. We offer instructional programs and curriculum for students preparing for the PSAT,  ACT, and SAT.

#### Review of Nonstandard English: Idiom Errors

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### Overview:  What Do the SAT and ACT Test in English Grammar?

The SAT and ACT test for formal, academic, standard English, which is not necessarily the same way that students speak or write.  Many errors are especially insidious because the correct form and the incorrect form are very close.  However, some idiom errors involve words that actually mean the opposite from each other.

### What Is the Proper Form of the Verb?

The verb form doesn’t is used with third-person singular subjects, such as in the sentence “He doesn’t want to take the test this month.”  The verb form don’t is used with all other subjects, but never when the subject is in the third person singular.  Similarly, the verbs done and seen are used with helping verbs, such as had, has, or have, never alone.  When gone is used as a verb, it is also used with a helping verb.  However, the verb went is the past tense of to go, and is not used with a helping verb.

### What about Lie and Lay?

Correct usage of the verbs lie and lay depend on what is doing the action.  The verb lie, with parts lying, lay, and lain, means “to recline.”  It is not followed by a direct object, but often by an adverb or adverb phrase, telling just where someone or something is reclining.  The verb lay, with parts laying, laid, and laid, means “to put (something) down.”  It is followed by a direct object, such as “Lay the plates on the table.”  The verbs set and sit follow similar patterns, as sit is never followed by a direct object, but set is.

Homonyms can be especially troublesome, as they are words that sound the same, but are spelled differently.  For example, their is a possessive pronoun, such as “their books,” there is an adverb referring to place, and they’re is a contraction of they are.  The word too means the same as also, two is a number, and to is a preposition.

### What Word Pairs Mean the Opposite of Each Other?

The words take and bring are not synonyms.  Bring means to carry from a distant place to a nearer one, while take means from a near place to a distant place.  Similarly, learn and teach are not synonyms.  To learn is to get knowledge, while to teach is to give knowledge.

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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.