STRATEGY 13: NARROWING THE SEARCH ........................................................................................... 61 STRATEGY 14: WHAT ABOUT THE OPPOSITE ...................................................................................... 62 STRATEGY 15: YOU’RE NOT EXPECTED TO BE EINSTEIN .................................................................... 63 STRATEGY 16: IDENTIFYING THE KEY COMPONENT ........................................................................... 64 STRATEGY 17: FULFILLING ALL THE REQUIREMENTS.......................................................................... 65 STRATEGY 18: WHEN IT DOESN’T MAKE SENSE – CHECK IT SYSTEMATICALLY ............................. 65 WRITING................................................................................................................................................. 66 STRATEGY 1: PLANNING STAGE ........................................................................................................... 66 STRATEGY 2: STICKING TO THE PLAN.................................................................................................. 66 STRATEGY 3: REVIEWING THE PLAN .................................................................................................... 68 STRATEGY 4: BRAINSTORMING SMART ................................................................................................ 68 STRATEGY 5: MAKING THE CUTS ......................................................................................................... 70 STRATEGY 6: ENDING AT THE START .................................................................................................. 71 STRATEGY 7: STAYING CONSISTENT ................................................................................................... 72 STRATEGY 8: MAINTAINING THE FLOW................................................................................................ 73 STRATEGY 9: BACKING UP YOUR POINTS ............................................................................................ 73 STRATEGY 10: USING PROPER GRAMMAR ........................................................................................... 74 STRATEGY 11: WATCHING YOUR VOCABULARY .................................................................................. 75 STRATEGY 12: AVOIDING TUNNEL VISION ......................................................................................... 76 STRATEGY 13: JUST DO IT ................................................................................................................... 77 STRATEGY 14: CONCLUSION IS REVIEW ............................................................................................. 78 STRATEGY 15: COMMUNICATING REASON, NOT PASSION................................................................ 78 STRATEGY 16: ANSWERING THE WHY?............................................................................................... 79
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Social Studies & English/Language Arts The Social Studies & English/Language Arts test measures a test taker’s ability to understand, analyze and evaluate written passages. The passages will contain material that will be from a variety of sources and on a number of different topics. Each of the passages and statements in the English/Language Arts test will be followed by a series of questions covering the content of the passage or statement, in which you will have to answer questions, which will demonstrate how well you understand the passages and are able to draw conclusions about the material.
detail will be forgotten by the time you get to the questions anyway. Therefore, you should fly over the passage. You should read it very quickly for a high-level overview (hence the flyover) understanding of what is contained in the passage. In part, this is a compromise between the theories that gains most of the benefits of each. You won’t waste time on the details and yet will have a general idea of what the passage is about and what to expect.
you’ve already “eliminated” from consideration and reconsider it as a possibility. If you think an answer choice contradicts your initial summary, you’re probably right, but are not infallible.
Strategy 3: Openings and Endings A main focus of this flyover will be the opening and ending sentences in each paragraph. These are likely to contain the main ideas of the paragraphs and should be mentally tagged for future reference. Try to remember a vague idea of what the different paragraphs are about, because this will save you time when answering questions later. For the most part, make sure you never try to just answer the questions from this first flyover. Always try to go back and confirm the answer, as your memory will play tricks on you and the writers of the test questions may deliberately have planted a trap for you – remember that they don’t exactly have your best interests at heart.
at your kitchen table. So, when faced with identifying the main idea of a difficult passage, make it easier on yourself by backing away from the passage and thinking about it in terms of using easy “kitchen logic”.
Strategy 5: Getting into the Author’s Mind A number of questions become much easier when you place yourself into the mind of the author of the passage. Ask yourself a few different questions: “Why did the author write this passage?” “What was the author trying to say?” What angle is the author taking?” “What is the single most important point the author is trying to make?” Put yourself in the shoes of the author and imagine that you wrote the passage and try to identify what you were trying to describe and how you were trying to describe it. If you take on the opinions and ideas expressed by the author as your own, then it becomes easier to answer questions that would be easy for the author to answer.
Strategy 6: Emotional Words Each question will be about a different angle of the passage. For questions asking about the author’s emotions, find words in the passage that are adjectives describing emotions.
So, if a question asks what sort of attitude an author had towards the passage or subject, then look throughout the passage for attitude words that might convey a positive or negative attitude. Are words such as brilliant, excited, delightful used, or are words such as depressive, gloomy, disappointing used? A lot of questions could be answered correctly simply by going through and circling all the adjectives in a passage. Without looking at anything else except for the adjectives in a passage, most questions about attitude or emotion could be answered correctly. Another way of handling these situations is to arrange all of the answer choices in a list going from most negative to most positive. Example: Question: The author’s attitude on this topic is best described as: A. indignation B. eagerness C. impartiality D. fear Now arrange these in order from negative to positive: ( - ) indignation, fear, impartiality, eagerness (+) This will help sort out the different choices and keep you from overlooking an answer choice and making an easy mistake.
The strategy of finding certain “give-away” words does not only apply to adjectives in questions about emotions or attitude. Many questions about specific details will have key words that hold the “key” to finding the right part of the passage to look in for the answer. Rather than answering based on your memory of the passage, you always want to have support for your answer choice rooted in a specific part of the passage. To gain that support, it follows that you have to identify which part of the passage to look in. While reading back over the entire passage may be the most foolproof method of finding that important part of the passage, it definitely is not the most time economical method of finding that part of the passage. A better route is to find key words in the question or answer choices that are likely to stand out in the passage and will enable you to quickly narrow your search down. These key words will be nouns or verbs in the question or answer choices. Once you’ve identified possible key words, then you should scan through the passage quickly looking for either those key words to be repeated in the passage, or their synonyms to appear in the passage. Once you find a particular part of the passage that either has the exact key word repeated or a synonym of the key word, you have probably identified the particular part of the passage that will contain the support or justification that you need to correctly answer the question and will allow you to be confident in your answer choice selection. One warning that should be made here is that often question writers may use the exact same word or wording in their answer choices that are used in the passage, but have done so in such a way as to mislead
you. So, simply because a particular word or phrase appears in an answer choice and also appears exactly the same in a passage does not make that answer choice correct. Be sure that you reread the answer choice and consider the context that it is in, to ensure that you are not misled by a cheap trick. In conclusion, always try to connect the question to the right words in the passage that will allow you to save time in finding the right part of the passage to look in for the answer and will give you the key to the correct answer choice.
Strategy 8: Making Proper Inferences Questions that ask you to make an inference from the passage will require you to use your own personal judgment. Anything directly stated by the author is not an inference. You will need to understand the main idea of the passage in order to make a proper inference about the author’s intent and mindset. The obvious will not be enough to answer an inference question. You must logically deduce what follows from what the author has stated in the passage. You are looking for what can be inferred by the passage, not what is directly stated in the passage.
Strategy 9: Applying Ideas for Generalizations Generalization questions are similar to inference questions in that you have to go beyond what is directly stated in the passage by the author. It helps to put yourself again in the author’s shoes. If you were the author and believed in what you had just written, how would you feel about another similar situation? What would either strengthen or weaken your argument. How would you apply the information you have just expressed to a completely different situation?
Strategy 10: Using Context Clues Context clues are a valuable aide in helping you understand difficult phrases or words in the passage. A number of questions will ask you about the meaning of words as they are used in a given passage. If you already know the definition of the word, or have some familiarity with it, a common mistake is to go with your first impulse and choose the answer that you immediately recognize. However, the reason the test writers may have chosen that particular vocabulary word is because it is used in an unusual context. Therefore, return to the passage and find where the word is used and make sure that you understand how it is being used in the passage. Once you’ve made your choice of a good definition go back again to the passage and reread that particular section, but mentally replace the answer choice you’ve chosen for the word being asked about.
Example: A passage states: “He was notorious for making decisions on the spur of the moment…” Question: Which of the following words, if substituted for the word “notorious” would introduce the LEAST change in the meaning of the sentence? A. evil B. disturbed C. famous D. despised If you knew that the most common definition for “notorious” meant being known in an unfavorable sense, then you might be tempted to choose choice A, “evil.” But once you review back over the passage, choice C, “famous” fits in better into the context of the sentence of passage. Read the sentence again and substitute your chosen answer choice for the word it replaces. This gives you: ““He was famous for making decisions on the spur of the moment…,” which makes sense and is correct.
simplest way to find the answer is to note how the opening sentence in a passage or paragraph relates to the rest of the passage. How does the author’s main idea get developed and broken down into supporting ideas and statements? As you go through the answer choices for these organization problems, quiz yourself on each answer choice. Example: Question: Which of the following best describes the organization of the author’s discussion of this topic? A. He provides an example – Ask yourself, is there an example in the question? Don’t work exclusively from your memory. Make sure you can go back and actually find the example in the passage. B. He makes a comparison – Ask yourself, is there a comparison in the question? Again, go back to the passage and actually find the comparison being made and verify that it exists. C. He makes an acknowledgement – Ask yourself, where is the acknowledgement made and to whom? D. He discusses a theory – Ask yourself, which theory is being discussed? After each of these initial questions, remember that it is not enough for them simply to be true, they have to answer the question. Simply because the author provided an example, doesn’t make choice A correct. The example provided may have been to support a comparison that he was making and the comparison may be the main method of organization, which in this case would make answer choice
B correct. So always read all the answer choices and only choose the one that is the best, not just the first one you read that is factually correct.
Strategy 12: First Word Analysis When asked for main ideas that best summarize the passage, an easy strategy is to look at the first words in each answer choice and without looking at the rest of the answer choice, see if you could make a decision based on those first words alone. Example: Question: Which of the following best explains the author’s primary purpose? A. dispute… B. describe… C. condemn… D. convince… If you know that the passage is fairly neutral about the subject, then even if you know nothing else, you can probably eliminate the stronger verbs used in answer choices A, C, and D, leaving you with “describe” or answer choice B as being correct.
across a passage that you are familiar with, consider yourself lucky, but don’t plan on that happening. The passages will also frequently be drawn from longer passages in books, articles, journals, etc. Therefore, the passage that you will face on the test may almost seem out of context and as though it begins in the middle of a thought process. You won’t have a nice title overhead explaining the general topic being covered but will immediately be thrown into the middle of a strange format that you don’t recognize. Also, while the topics chosen may have originally been interesting reading in their original state, after a particular section is pulled and used for the test passage, it will likely be dry and boring. Getting hit by strange reading topics that you don’t recognize, of which you may only have a small part of the original selection, and that are dry and boring can be a bit intimidating if you’re not adequately prepared. Just remember that the passages themselves will contain all the information necessary to answer the questions and you don’t need any prior knowledge of the topic in order to succeed and do well on the test.
on the flyover, you are looking for only a surface level knowledge and are not trying to comprehend the minutia of details that will be contained in the passages. You can practice with any form of reading material. Read an article at your normal pace and then after you’re finished, ask yourself some questions about what you just read and see how well you can comprehend. Experiment with reading articles faster and slower and always gauge how well you comprehended what you read at the end. Train your brain to remember the details and absorb the facts. With practice, you will find the pace that you should maintain on the test while going back through passages. It should be a comfortable rate. This is not a speed reading exercise. If you have a good pace, and don’t spend too much time on any question, you should have a sufficient amount of time to read the different sections of the passages at a comfortable rate. The two extremes you want to avoid are the dumbfounded mode, in which you are lip reading every word individually and mouthing each word as though in a stupor, and the overwhelmed mode, where you are panicked and are buzzing back and forth through the passage in a frenzy and not comprehending anything. You must find your own pace that is relaxed and focused, allowing you to have time for every question and give you optimal comprehension. Note that you are looking for optimal comprehension, not maximum comprehension. If you spent hours on each word and memorized the passage, you would have maximum comprehension. That isn’t the goal though, you want to optimize how much you comprehend with
Strategy 16: Factually Correct, but Actually Wrong A favorite ploy of question writers is to write answer choices that are factually correct on their own, but fail to answer the question, and so are actually wrong. When you are going through the answer choices and one jumps out for being factually correct, watch out. Before you mark it as your answer choice, first make sure that you go back to the question and confirm that the answer choice answers the question being asked.
Strategy 17: Different Viewpoints Some passages will express the author’s viewpoint on a topic, along with the viewpoint of other experts or other individuals. This can lead to trouble in answering questions though. If asked for the viewpoint of the author, you might go back to the passage, find where a certain viewpoint is expressed, answer the question based on what you read and move on. For most passages, that would be fine, but when other viewpoints besides the author’s are expressed, you have to discern who is expressing their opinion in the passage. Make sure that if multiple individuals are giving their viewpoint on a topic, that you sort them out for any questions and associate the right viewpoint with the right individual.
Strategy 18: Extraneous Information Some answer choices will seem to fit in and answer the question being asked. They might even be factually correct. Everything seems to check out, so what could possibly be wrong? Does the answer choice actually match the passage, or is it based on extraneous information not even contained in the passage. Just because an answer choice seems right, don’t assume that you overlooked information while reading the passage. Always try to go back and find the support for the answer choice in the passage. Your mind can easily play tricks on you and make you think that you read something or that you overlooked a phrase. Unless you are behind on time, always go back to the passage and make sure that the answer choice “checks out.”
Strategy 19: Apostrophes An apostrophe is used to form a possessive or a contraction. Check for the following common apostrophe errors. The bracketed parenthetical demonstrates the correct use. Possessive Nouns
Singular possessive nouns. Use 's to show that a singular noun is possessive [the defendant's motion]. You can apply this rule even when the singular noun already ends in "s" (Charles's
costume) though many writers add only the apostrophe [Charles' shoes]. 2.
Plural possessive nouns not ending in "s." Use 's to show that a plural noun not ending in "s" is possessive [the children's toy].
Plural possessive nouns ending in "s." Add only an apostrophe to make plural nouns possessive [the boys' game].
Nouns that are not possessive. Do not add an apostrophe to a noun that is not possessive [the teachers (not teacher's or teachers') have claimed; the Joneses (not Jones' or Jones's) did not attend].
Possessive Personal Pronouns vs. Contractions
Apostrophe errors with possessive personal pronouns are common because possessive personal pronouns indicate possession and we are used to using apostrophes to indicate possession. Also possessive personal pronouns are easily confused with contractions. Here are the basic rules: 5.
Possessive personal pronouns. Do not add an apostrophe to a possessive pronoun [the problem is hers (not her's); the corporation must disclose its (not it's) assets.]
Contractions. Do use an apostrophe in a contraction (it's time to go; you're the one).
* Watch especially for errors in using "it's" or "its." Remember that "it's" means "it is" and "its" indicates ownership. Confusing these two words is the most common apostrophe error.
Strategy 20: Comma Errors Commas are also major troublemakers. Watch for these situations: 1.
Use a comma to separate two independent clauses joined with a coordinating conjunction (and, or, but, nor, so, for). [The child agreed, but the parent objected].
Use a semicolon or a period, not a comma, to separate two independent clauses not joined by a coordinating conjunction [The child agreed; however, the parent objected.]. The following transitional words and phrases are conjunctive adverbs, not conjunctions:
on the other hand
moreover for example
otherwise for instance
Therefore, do not use a comma to separate two independent clauses on either side of one of these words.
The city must increase its tax base, however, the citizens
must be able to accept the additional tax burden. Correct:
The city must increase its tax base; however, the citizens
must be able to accept the additional tax burden. 3.
Conjunctive adverbs signal the relationship between the point(s) made in the material before their sentence and the material of that sentence. The words and phrases in the list above are examples. When you begin an independent clause with a conjunctive adverb or when you use it in the middle of a sentence, set it off with a comma.
Moreover, the defendant has not yet established a proper foundation for this testimony. The student, moreover, has not yet turned in an acceptable project to meet his assignment’s requirements. 4.
Use commas to set off the year if you also identify the day [The birth of Norma Kelly on June 2, 1974, brought the . . . .], but omit the commas otherwise [The birth of Norma Kelly in June 1974 brought . . . .].
Use commas to separate three or more simple items in a list. If the descriptions of the items are long or complex, use semicolons to separate them.
[Was the possibility a disaster for the officers, the conflicts, or the suppliers?] Referring to an antecedent that is only implied: The corporate officers had failed to disclose the serious conflict of interest raised by the possible bankruptcy of T&J's primary supplier. This was a disaster for the officers. [What was a disaster -- the failure to disclose, the conflict, or the possible bankruptcy?] Notice that the confusing reference in this last example is caused by using "this" alone. Using the pronoun "this" or "that" without a noun following immediately is usually inadvisable. Here, for instance, the confusion could be resolved easily by adding the clarifying noun after "this": The corporate officers had failed to disclose the serious conflict of interest raised by the possible bankruptcy of T&J's primary supplier. This failure was a disaster for the officers. The three primary strategies for solving reference problems are: (1) repeating the antecedent (as in the prior example); (2) re-arranging the material to place the referent close to the antecedent; or (3) rearranging the material to eliminate the need for the referent. For instance, here is another possible solution to the reference problem above:
some For example: All [singers] are permitted . . . . All of the money is counted . . . . None of them are satisfied . . . . None of the royalty was present . . . . 2.
"The court" is a singular term, taking a singular pronoun:
The court overruled the traditional rule originally announced in December. It [not "They"] held that . . . . 3.
This same kind of error can slip in when referring to any institution or business:
He said that he is very grateful to St. Catherine's Hospital. They treated him with respect. The problem sometimes occurs because the writer is avoiding the awkwardness of attributing a human action to an "it." For instance, in the St. Catherine's example, the writer is probably avoiding "It treated him with respect." That problem can usually be solved by changing the antecedent to the humans who actually performed the action: He said that he is very grateful to the staff at St. Catherine's Hospital. They treated him with respect.
Watch for both verb agreement and pronoun agreement when a singular subject is modified by a phrase or clause containing a plural noun:
The confidence of several families was [not were] attained. Each of the groups agrees [not agree] to resolve the problem peacefully. Every student who had already taken both courses is [not are] excused from this requirement. 5.
Use a possessive pronoun before a gerund phrase. A gerund is an "ing" verb that serves as a noun. The gerund can stand alone or can begin a gerund phrase, but either way, the word or phrase functions as a noun:
Running is good for you. Coming to work late can result in disciplinary action. Since a gerund or gerund phrase functions as a noun, it takes a possessive pronoun: We'll go to their house for the party instead of their [not them] coming to ours.
Where possible, similar ideas should be expressed in a similar (parallel) structure and grammatical form. Parallelism makes for easier reading and clearer meanings. It also improves sentence rhythm and cuts down on verbiage. Parallel structure: Parallelism makes for easier reading and clearer meanings. "easier reading" and "clearer meanings" are parallel. Non-parallel structure: Problems occur when the business conceals relevant documents or by deluging the auditors with irrelevant documents. In the non-parallel example, the writer identifies two situations in which problems occur; however, the two situations are phrased in non-parallel structure. A parallel structure would be: Problems occur when the business conceals relevant documents or when they deluge the auditors with irrelevant documents. Now that the structure is parallel, extra words can go: Problems occur when the business conceals relevant documents or deluge the auditors with irrelevant documents. Parallel structure is especially important in a list.
When the new commander arrived at the post, he immediately posted a new list of orders: no leaves were to be granted, and no leniency was to be given.
Strategy 24: Miscellaneous Problems 1.
Use the subjective case for a pronoun that functions as the subject of an understood verb. The subjective case is the form the pronoun takes when used as the subject of the sentence ("I," "we," "they"). For example, consider these two sentences:
The corporation's president worked harder than me. The corporation's president worked harder than I. Which is correct? The second version is correct, because "I" is the subject of an understood verb "worked." In other words, the sentence is actually a shortened version of "The corporation's president worked harder than I worked." This is an easy mistake to make because the correct case may sound wrong. If so, the best solution is to add the understood verb or to rephrase the sentence completely to avoid the awkwardness. 2.
Use the subjective case for a pronoun that functions as the complement of a subject. A pronoun is a subjective complement when it actually equals the subject of the sentence. For example, consider these two sentences:
The person least anxious after the test was her. The person least anxious after the test was she. Which is correct? The second version is correct, because the pronoun in the predicate, "she," actually equals the subject, "the person least anxious after the test." In other words, the sentence is like an algebra equation: The person least anxious after the test = she. In a sentence like this one, the noun or pronoun in the predicate functions like the subject of the sentence. The sentence should read the same as if you turned it around: She was the person least anxious after the test. Once again, this is an easy mistake to make because the correct case may sound wrong. In spoken English we often hear "It's him," or "It's me."
Again, the best solution may be to reverse the sentence or to
re-phrase the sentence completely to avoid the awkwardness. 3.
Use "try to" and "sure to" rather than "try and" or "sure and."
Ms. Thompson wanted to try and finish the project by
Ms. Thompson wanted to try to finish the project by
This rule makes sense if you think about it. The proper function of the word "and" is to connect two different things. Thus, the "and" in the first sentence should mean that Ms. Thompson wanted to do two different things, but she didn't; she only wanted to do one thing – finish the project. The same is true for the third sentence. The "and" seems to tell the reader that the sentence is an instruction to do two different things, but it isn't. The reader is only to do one thing – pick up the baby. 4.
"Hopefully" is an adverb that explains how someone does something, as in "She asked hopefully." Often "hopefully" is misused in this or a similar fashion: "Hopefully the storm will pass." This use actually asserts that the storm’s passing will be full of hope. The writer actually means "I hope that the storm will pass."
Watch out for one more common error with adverbs: the difference between "I feel bad" and "I feel badly." In the first sentence, the writer is commenting on how she feels, either physically (perhaps she has the flu) or emotionally (perhaps she is sad). The first sentence is the proper use of "bad" as an adjective.
However, the second sentence uses "bad" in its form as an adverb. The writer is commenting on her ability to feel; perhaps her fingers are numb. Sometimes writers use the adverbial form "badly" when they mean "bad," perhaps believing that "badly" sounds more elevated.
Mathematics The Mathematics test measures a test taker’s ability to solve problems representing some of the key concepts in mathematics. Some problems will only test one concept, while others will involve multiple concepts integrated together in a single problem. The problems will have few technical terms, aside from basics, such as area, perimeter, integer, and ratio, which are expected to be common mathematical knowledge. All figures shown will be drawn accurately and lie in a single plane, unless noted otherwise.
Number Types Integers, Odd and Even Numbers, Prime Numbers, Digits
Integers…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …
Consecutive Integers: Integers that follow in sequence; for example, 22, 23, 24, 25. Consecutive Integers can be more generally represented by n, n + 1, n + 2, n + 3, …
n = 1,500, so 1,500 is the number Percent Increase/Decrease
Problem 4: If the price of a computer was decreased from $1,000 to $750, by what percent was the price decreased? Solution: The price decrease is $250. The percent decrease is the value of n in the equation 250/1000 = n/100. The value of n is 25, so the price was decreased by 25%. Notes: n% increase means increase/original = n/100; n% decrease means decrease/original = n/100.
Average An average is a statistic that is used to summarize data. The most common type of average is the arithmetic mean. The average (arithmetic mean) of a list of n numbers is equal to the sum of the numbers divided by n. For example, the mean of 2, 3, 5, 7, and 13 is equal to 2 + 3 + 5 + 7 + 13 / 5 = 6 When the average of a list of n numbers is given, the sum of the numbers can be found. For example if the average of six numbers is 12, the sum of these six numbers is 12 x 6, or 72.
The median of a list of numbers is the number in the middle when the numbers are ordered from greatest to least or from least to greatest. For example, the median of 3, 8, 2, 6, and 9 is 6 because when the numbers are ordered, 2, 3, 6, 8, 9, the number in the middle is 6. When there is an even number of values, the median is the same as the mean of the two middle numbers. For example, the median of 6, 8, 9, 13, 14, and 16 is 9 + 13 / 2 = 11 The mode of a list of numbers is the number that occurs most often in the list.
For example, 7 is the mode of 2, 7, 5, 8, 7, and 12.
numbers 10, 12, 14, 16, and 18 have no mode and the numbers 2, 4, 2, 8, 2, 4, 7, 4, 9, and 11 have two modes, 2 and 4. Note: The mean, median, and mode can each be considered an average.
On the test, the use of the word average refers the
arithmetic mean and is indicated by “average (arithmetic mean).” The exception is when a question involves average speed (see problem 2 below).
Questions involving the median and mode will have those
terms stated as part of the question’s text.
Weighted Average Problem 1: In a group of 10 students, 7 are 13 years old and 3 are 17 years old. What is the average (arithmetic mean) age of these 10 students?
Solution: The solution is not the average of 13 and 17, which is 15. In this case the average is 7(13) + 3(17) / 10 = 91 + 51 / 10 = 14.2 years The expression “weighted average” comes from the fact that 13 gets a weight factor of 7, whereas 17 gets a weight factor of 3. Average Speed
Problem 2: Jane traveled for 2 hours at a rate of 70 kilometers per hour and for 5 hours at a rate of 60 kilometers per hour. What was her average speed for the 7-hour time period? Solution: In this situation, the average speed is: Total Distance/Total Time The total distance is 2(70) + 5(60) = 440 km. The total time is 7 hours. Thus the average speed was 440/7 = 62 6/7 kilometers per hour. Note: In this example the average speed is not the average of the two separate speeds, which would be 65.
Properties of Signed Numbers positive x negative = negative
probability that a specific outcome will occur, values of p fall in the range 0 < p < 1. Probability may be expressed as either a decimal or a fraction.
Geometric Figures Figures that accompany problems are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a particular problem that the figure is not drawn to scale. In general, even when figure is not drawn to scale, the relative positions of points and angles may be assumed to be in the order shown. Also, line segments that extend through points and appear to lie on the same line may be assumed to be on the same line. The text “Note: Figure not drawn to scale.” is included on the test when degree measures may not be accurately shown and specific lengths may not be drawn proportionally. The following examples illustrate the way different figures can be interpreted. Example 1
Since UY and VX are line segments, angels UWV and XWY are vertical angles. Therefore, you can conclude that c° = d°. Even though the figure is drawn to scale, you should NOT make any other assumptions without additional information. For example, you should NOT assume
4. The sum of the two acute angles in a right triangle is 90 degrees.
x = 15 (Because 2x + 4x = 90.) 5. The sum of the interior angles of a polygon can be found by drawing all diagonals of the polygon from one vertex and multiplying the number of triangles formed by 180 degrees.
Since the polygon is divided into 3 triangles, the sum of the angles is 3 x 180° or 540°. Side Relationships
1. Pythagorean Theorem: In any right triangle, a2 + b2 = c2, where c is the length of the longest side and a and b are the lengths of the two shorter sides.
a2= 32 + 42 a2 = 9 = 16 a2 = 25 a = square root of 25 = 5 2. In any equilateral triangle, all sides are equal and all angles are equal.
a=b=5 (Because the measure of the unmarked angle is 60°, the measure of all angles of the triangle are equal, and therefore, the lengths of all sides of the triangle are equal.) 3. In an isosceles triangle, the angles opposite equal sides are equal. Also the sides opposite equal angles are equal.
If A = B, then a° = b°. Also, if a° = b°, then A = B. 4. In any triangle, the longest side is opposite the largest angle ( and the shortest side is opposite the smallest angle.)
Volume of a cylinder = Πr2h (where r is the radius of the base and h is the height of the cylinder)
Volume = Π X 42 X 7 = Π X 16 X 7 = 112Π
In questions that involve the x and y axes, x values to the right of the y axis are positive and x values to the left of the y axis are negative. Also, y values above the x axis are positive and y values below the x axis are negative. In an (x,y) ordered pair, the x value is written first, and the y value is written second. For example, in the ordered pair (1,-2), the x coordinate is 1 and the y coordinate is -2. Slope of a line = rise/run or vertical distance/horizontal distance.
This line runs through points (1,-2) and (4,4). The slope = (4 – (2))/(4 – 1) or 6/3 = 2. Any line that slopes upward from left to right has a positive slope. Any line that slopes downward from right to left has a negative slope.
Science Strategy 1: Understanding Charts and Tables Much of the difficulty that most test takers have with this section of the test is the charts, tables and graphs that are referenced in its questions. Properly understanding how to read each of these is critical to succeeding on the test.
30 25 20 15 10 5 0 1980
Question 1: Ask yourself what is being shown in the data presented? In this chart a decade’s worth of data is displayed, showing varying amounts of some quantity each year. Question 2: Ask yourself if any trends can be detected? As you review the chart, you can see that it appears that there is a 4 year cycle in occurrence. Every 4 years, the data increases, then decreases again, with cycle highs and lows each separated by 4 year intervals.
Question 3: Ask yourself if there is anything remarkable about any of the data points? It appears that there was an extremely low point in 1988. Odds are one of the questions will ask about this data point and any other unusual features of the chart. Average Mixture mass A
You can ask yourself the same questions concerning a table. What’s being shown? What are the trends? What is unusual? If you know what to expect and are familiar with using them, charts and graphs are actually quite simple and easy to use. They contain information contained horizontally along the x-axis, and other information contained vertically along the y-axis. When you find the point along the x-axis and y-axis that you are looking for and then identify their intersection, you will find the information that you need to solve the question.
Strategy 2: When Vagueness is Clear When a graph doesn’t have exact measurements that are easily identifiable, odds are you will not need to differentiate between two close data points.
Example: Bird watchers are interested in seeing rare birds. According to the figure above, during which observation period, would one be LEAST likely to see a rare bird. A. period 2 B. period 4 C. period 7 D. period 8 In this graph, the y-axis only lists three data points (0, 100, and 200). This makes it difficult to determine whether close observations actually differ. For example, period 2 and period 8 appear to have approximately the same number of birds and it is difficult to determine if either has more or less. Therefore, you will typically NOT be asked to make such a differentiation. So, as you go through the answer choices, you don’t have to worry about choosing between choice A and D, since choice C clearly had the fewest number of birds, making it the least likely opportunity for an observer to see a rare bird.
Strategy 3: Avoiding Definites Answer choices that make definite statements with no “wiggle room” are often wrong. Try to choose answer choices that make less definite
and more general statements that would likely be correct in a wider range of situations and aren’t exclusive. Example: A. Some of the highest values occurred during periods of low activity. B. The highest values occurred at an activity level of 5 throughout the observed period. C. The lowest values occurred at an activity level of 2 throughout the observed period. D. The activity level remained at the same throughout the observed period. Without knowing anything about the question, answer choice A uses the term “some,” which has wiggle room, meaning there could have been a few data points that had high values that didn’t occur during periods of low activity. All of the other answer choices have a more definite sense about them, implying a more precise answer choice without wiggle room that is often wrong.
Strategy 4: Using Common Sense The questions on the test are not intended to be trick questions. Therefore, most of the answer choices will have a sense of normalcy about them that may be fairly obvious and could be answered simply by using common sense. While many of the topics will be ones that you are completely unfamiliar with, there will likely be a couple of topics that you have
some prior indirect knowledge about that will help you solve the problems. Example: Which of the following conclusions about the length of day is consistent with the information provided? A. the longer the day, the more photosynthesis takes place B. the length of day has no affect on photosynthesis C. the length of day was the most important variable tested D. further trials need to be conducted to determine the true effect of the length of day You probably have a vague understanding of day length and photosynthesis and can probably put together this commonsense equation: Length of day = more sunlight = more photosynthesis Choice A passes the test with this equation and is correct.
Example: If scientist 1 is correct, the larger the ant colony, the: A. less frequently foraging will occur B. more frequently foraging will occur C. larger the size of the foraging area D. smaller the size of the foraging area Your first instinct is that the size of the ant colony would affect the size of the foraging area allowing you to choose choice C.
Strategy 6: No Fear The science test can be a bit intimidating to a lot of people as it can deal with topics that have never been encountered before and are highly technical. Don’t get bogged down by the data presented. Don’t try to understand every facet of the experiment. You won’t have to write an essay about the topics afterwards, so don’t memorize the facts. These topics are technical and are likely to be in an area that you have no background. Don’t get overwhelmed.
Strategy 7: Looking for the Changes Anything odd is likely to be asked about. Any differences that occur between experiments or scientists are guaranteed to have questions to make sure you understand those differences. Make sure that as you review the information, you are on the lookout for changes. If one of the experiments deals with the duration of lifetimes for various materials – make sure you take note of the ones that were extremely short or extremely long. Circle them in your answer booklet, and be ready to go back and identify them in later questions.
Strategy 8: Quick Checks Many of the questions will require you to examine each answer choice, return to the graph or chart and see where it falls and then compare it to the other answer choices. Remembering that questions will typically focus on the differences, the extremes, the outliers in a series of data, this can help you quickly hone in on the correct answer. Example: Which period would be MOST likely to have….? 100 80 60 40 20 0 1
Rather than looking at each answer choice and then comparing them to see which was best, odds are the correct answer choice will not just be the period in the graph that is highest among the provided answer choices, it will likely be the period that has the highest of any period. A. period 2 B. period 4 C. period 6 D. period 7 Without looking at the answer choices, the period that is MOST likely to contain anything is probably going to be period 6, because it is the highest peak on the graph. Now look and see if period 6 is among the answer choices. It is, making answer choice C correct. For questions that ask about the MOST or LEAST, the highest peak or lowest valley on the graph will probably be the correct answer choice, meaning you can look first at the graph, and then at the answer choices, saving you time. The question above could have the following answer choices: A. period 2 B. period 4 C. period 5 D. period 7 This would make answer choice B correct, as period 4 is greater than the others listed. Since period 6 isn’t a viable choice, you would be forced to choose period 4. However, rarely will you be faced with a
question like this in which the period or point on a graph that is the absolute MOST or LEAST is not listed as a possible answer choice.
Strategy 9: Looking for Matches Questions that have long answers will often give away the right answer choice. Test writers will try to trick up the test taker, but a smart test taker can often use those tricks in their favor to point to the correct answer choice. Example: Which of the following combinations of characteristics would create the optimal living conditions? A. 50 ft of depth at 30° B. 100 ft of depth at 20° C. 100 ft of depth at 40° D. 150 ft of depth at 20° Without knowing anything about the living conditions or experiments, you can see that 20° is listed twice, making it the most popular, and 100 ft is listed twice, making it the most popular. Therefore, look for an answer choice that combines the most popular of each characteristic, which makes answer choice B correct.
Strategy 10: Information is Provided for a Reason When a question offers new information to consider, remember that it is given for a reason. Look for the correct answer choice to include the new information in what form or another.
Example: Burrowing animals create spots of bare earth in the meadow. On the basis of the experimental results, one would predict that over several years the wildflowers would: A. not grow or reproduce in the meadow B. not grow in the meadow but their seeds would be found in the meadow C. grow in the meadow and reproduce in the cleared areas created by animals D. grow in the meadow and reproduce only in the areas containing woody plants Only choice C contains a phrase that actually links to the question “cleared areas created by animals.”
Strategy 11: Watching for Similar Rewording In order to increase the difficulty of otherwise simple questions, test writers will often reword the correct answer using similar wording that is somewhat different but still means the same thing. Don’t get distracted in trying to find the perfect match, as a similarly worded answer choice may likely be the correct answer choice. Example: Which of the following factors was controlled by the scientist? A. plant mass B. soil moisture C. presence of rabbits D. presence of neighboring plants
Choice D “presence of neighboring plants” means the same as clearing the ground of vegetation, which is what was described in the experiment and was the exact wording of the answer choice you were expecting.
Strategy 12: Don’t Get Thrown Off by New Information Sometimes test writers will include completely new information in answer choices that are wrong. Test takers will get thrown off by the new information and if it seems like it might be related, they could choose that answer choice incorrectly. Make sure that you don’t get distracted by answer choices containing new information that doesn’t answer the question. Example: Which conclusion is best supported? A. unable to reproduce due to the absence of bee pollination Was bee pollination even discussed? NO – then don’t consider this answer choice, it is wrong.
Strategy 13: Narrowing the Search Whenever two answer choices are direct opposites, the correct answer choice is usually one of the two. It is hard for test writers to resist making one of the wrong answer choices with the same wording, but changing one word to make it the direct opposite in meaning. This can usually cue a test taker in that one of the two choices is correct.
Example: A. There would be more holes visible in images taken on days when thunderstorms are present B. There would be fewer holes visible in images taken on days when thunderstorms are present. These answer choices are direct opposites, meaning one of them is likely correct. You can typically rule out the other two answer choices.
B. The receiving station CAN collect data during a thunderstorm C. Atmospheric holes appear in DIFFERENT locations in all images D. A number of very LIGHT pixels are seen in the images By mentally reversing each of the answer choices, sometimes it will make it easier to determine which ones are correct and incorrect.
Strategy 17: Fulfilling all the Requirements Example: How many of the trial sets in the three experiments would the scientist call successful? Your first impulse might be to look at the trial set in experiment 1 and see how many of the trials met the criteria for success. But remember that the question asked about all three experiments, so you have to count the ones that are successful in experiments 2 and 3 as well as experiment 1. Just before you make your final answer choice selection, glance back over the question and confirm that you have satisfied all the question requirements.
both. When your only choice is an answer choice that isn’t what you expected, but might be “good enough,” go back through and see if you made a simple mistake in understanding the question.
particularly true when you have an answer choice of numbers that you found on a table or graph. Number answers should be exact, not just “good enough.”
Writing The Writing section of the GHSGT is a test that measures your ability to write an effective essay. You need to know that in evaluating your essay, readers are looking for your essay to be well organized and properly developed. All of the main ideas should be clearly outlined and explained. It should be error free and contain a variety of examples and reasoning to explain your ideas.
Strategy 1: Planning Stage You should spend a few minutes planning and jotting down a few quick notes. Consider the position you are taking, determine a few good reasons for making your choice, some evidence or explanation that support the choice, some effective details you might include, and what order you should use to effectively present your points.
choice or take a position, and explain your reasoning in some detail. You should also consider the criterion specified so that your essay is convincing to the addressed audience. Make sure that the language you choose communicates your ideas clearly and appropriately.
Strategy 3: Reviewing the Plan You should spend a few minutes reviewing your writing, adding or removing as necessary and making any changes needed to enhance clarity. You should make clear the answer and angle you will choose for your essay, offering a few good reasons for your choice and explaining your reasoning in some detail. As you explain the reasons for your choice, you should develop explanations for each, including such things as evidence, examples, or observations.
Strategy 4: Brainstorming Smart Brainstorming is a process of directing your mind toward idea generation. Every book on essays will advise you to brainstorm. It’s a method proven to be successful for several reasons. This is the point at which different writers will begin to disagree about how to brainstorm. The method of brainstorming that is recommended here is two-tier. First you have to brainstorm about what you are going to write about. You want to determine what is going to be the focus of your essay. Example: Sample topic: “If you could change one thing about yourself, what would it be? Discuss why.” Example Brainstorming Level 1: What should I write about?
Intelligence, looks, personality, wealth, family, friends, time, fame, etc. Your first impulse, and honest reaction, might be to respond with something such as making yourself more beautiful, more intelligent, or more popular. But remember that you want to be able to write at length about this topic. If you choose an answer that while truthful, may sound shallow to an essay reader, such as to become more beautiful and better looking, then you probably won’t win any points with the reader. Don’t automatically go with your first impulse. The scorer is not giving points for essays that are the most honest, but for essays that are the best written. A well-written essay needs substantial support to explain the reasoning behind your choice. A choice such as more intelligence could sound shallow, but with a little creativity, you can turn this into an excellent essay. Instead of stating that you want to be more intelligent in order to get better grades, use deeper reasoning. Explain what you would do with that added intelligence. Give examples of how your side research into molecular biology and genetics would be greatly improved with added intelligence and enable you to have a greater chance at your goal of contributing to finding a cure for cancer or diabetes. If you choose “more popularity” as your topic, you could discuss how you would use your popularity in order to persuade more people to support your humanitarian causes and to be a positive role model for others.
After you’ve decided which topic you are going to write about, then you should begin the second wave of brainstorming, which will be about what you want to discuss about your chosen topic, which examples you want to use and which observations you hope to present. Example Brainstorming Level 2: You’ve chosen to write about having more free time. Now you brainstorm about what you should say to support that choice. spend more time with friends and family, work at a local homeless shelter, write a novel, open a new business, adopt some children, enjoy your hobbies, etc. You have to have a proper balance at each level. If you spent too much time at brainstorming level 1, then you won’t have time to decide on what you want to use as examples in level 2. But if you spend too little time at brainstorming level 1, then you may not come up with a really good topic to use for your essay. A good strategy is to practice using this two level brainstorming process until you get comfortable with using it and quickly generating lots of ideas.
Strategy 5: Making the Cuts Once you’ve finished the brainstorming level 2 process, you should look over the supporting ideas you hope to use and the examples you’ve written down from the brainstorming process. Look back over the ideas and see which ones look the best. Which ones could you
write the most about and would give you the most sound reasoning and logic to back up your initial decision of what to write about? Make mental notes about which supporting ideas from brainstorming level 2 you hope to use, because those will be the ones that will comprise your successive body paragraphs. Your goal is to hit the high notes. Pick the best ideas you’ve developed and write about those. You only need 3-5 good ideas to write about and may have a loss of focus if you try to write about more than a few important supporting topics.
yet, you can just adopt the new ideas as you write and incorporate them into your body paragraphs. When you’re finished writing your body paragraphs, which should each include at least one primary supporting idea, then you can go back and write your introductory paragraph and make sure that it matches up with each of your body paragraphs and covers the overall topic you are discussing. Additionally, don’t make the mistake of writing too much in your introductory paragraph. The introduction is not where you explain your reasoning. Save your logic for the body paragraphs, and only use the introductory paragraph in order to briefly outline what you are going to discuss. Brevity is better than wordiness in an introduction.
Writing your introduction at the end, after you’ve written your body paragraphs, and then following it with your conclusion will be a huge help in maintaining the consistency, but always look back over your essay when you’re finished and make sure that the essay keeps the same focus all the way through.
Strategy 8: Maintaining the Flow Part of maintaining consistency in your essay is the proper use of transition words while you’re writing. Use transition words to maintain the essay’s flow. Transition words such as first, second, third, finally, also, additionally, in conclusion, in summary, and furthermore all give the reader an understanding of how the paragraphs flow together. Example: Paragraph 1: Introduction Paragraph 2: First of all, … Paragraph 3: Secondly, … Paragraph 4: Finally, … Paragraph 5: In summary, …
Strategy 9: Backing up Your Points If you make a point or statement in your essay, make sure that you back it up with clear examples from your personal experience or observation. Don’t let your points remain unsupported, but ensure that they are provided with some back up substance.
Example: You make the statement, “Renovating older downtowns can be expensive, but is definitely a worthwhile endeavor.” While many readers may agree with this statement, it shouldn’t be made without backup support: Consider the following as backup for that example statement: My own hometown created a ten year plan to renovate their downtown area. A higher sales tax was passed in order to pay for the renovation, which ultimately cost $1 million dollars. But once it was finished, the sales tax was removed and the antique shops, which now fill much of the downtown, attract tourists and collectors from hundreds of miles away. The downtown is now completely self-supporting and is a constant source of both pride and new tax revenue to the town’s residents.
Strategy 10: Using Proper Grammar Remember that this essay is your chance to write and make yourself look good and well educated. It is not a test of your knowledge of grammar rules. You don’t have to demonstrate knowledge of every nuance of grammar. Therefore, if you find yourself wondering whether a given phrase should have commas around it or not, rewrite the phrase such that you’re confident it doesn’t need commas or does need commas. There is no need to have any punctuation in your essay that you are only 50% confident of being correct and conforming to the rules of grammar.
Example: You write, “Each of us must choose which path to take in life, whether to strive for improvement, or to settle in to their surroundings.” You aren’t sure whether you need a comma or a colon after the phrase “to take in life” in the preceding sentence. Simply rewrite the sentence until you are confident in how it is phrased. Change it to something such as: “There are two paths: strive for improvement, or settle into surroundings.” At this point you know you are using the colon properly, and so you can feel free to move on in your essay without fear of having made a grammar mistake.
of its meaning and are sure that you are using it at the right place. Most of the time, you will be safer by sticking with words you are familiar with and accustomed to using.
Strategy 12: Avoiding Tunnel Vision Remember that the goal of your essay is to properly cover a topic and write an essay that is somewhat exhaustive in showing every angle and perspective. A lot of writers get tunnel vision. One particular angle occurs to them as the most important and they hammer away at that angle of the topic throughout the entire essay. Discussing the same angle of a topic at length is considered essay depth. Discussing different angles of the same topic is considered essay breadth. Your goal is to have greater breadth than depth. This isn’t a 20-page thesis written on a specific, obscure topic.
will be fairly generic and broad-based and should have lots of different angles to consider and write about. You want to touch on as many different angles as you can, while still providing supporting backup for each statement you make. Don’t get stuck in a rut with tunnel vision. Be sure you are spending proper amounts of time on each angle you intend to discuss and not spend the entire essay writing about the same angle. Example: The topic is whether or not athletics represents too much a part of today’s academic institutions, and you intend to take the side that athletics is not too much of a part.
Your main angle is that an education is far more than simply academics and that athletics programs foster a richer, more diverse education. However, don’t get stuck talking about that one angle. Consider writing about how athletic programs create ties to the community that academics does not. Discuss how athletic programs also encourage donations that benefit academics, as well as athletics. Always try to consider multiple angles and avoid getting tunnel vision.
individuals, and exposes their true nature. When obstacles arise, character provides the strength to overcome them. Notice how this second example is clear, concise, and does not ramble on about the decision or ideas that are occurring to the writer.
Strategy 14: Conclusion is Review A conclusion is just that: a conclusion. It wraps everything that you’ve written thus far up into a neat summary paragraph. This is not the time to begin introducing new arguments and new reasoning. You want to make sure that you are quickly and concisely reviewing what you’ve written and have a solid ending in which you come across as having proved your point, and made your case effectively. So, when you’re ready to begin your conclusion, make sure that you’ve flushed out all the new angles you want to cover. Then go back over what you’re written and tie it all together at the end, hitting briefly on all the angles that you’ve discussed. Additionally, a conclusion is not an apology. You should never apologize for not knowing more or writing more. End your essay with purpose and definitively summarize what you have stated.
arguments and logic, backed up by sound examples and observations. If the topic you choose is one that you are passionate about, make sure that you present more than just heated emotion, but also cool logic. Example: The topic is about school uniforms, and you are passionately opposed. Rather than writing, “School uniforms is a stupid idea, and will never work,” try writing, “School uniforms have been an admitted failure by their original sponsors in all three implementation efforts during the last decade.” The first statement may be full of passion, but clearly lacks reason, while the second statement contains solid facts as examples.
Strategy 16: Answering the Why? While it’s important that you communicate reason, misguided reason is ineffective. Always make sure that the examples you are providing and the reasoning you are using is being directed at answering the topic question. Flawless logic that doesn’t answer the question and doesn’t contribute to the point you’re trying to make is completely useless. As you think of main ideas and supporting ideas to use, take a few seconds and confirm that they will adequately answer the topic and veer off down a tangent that is not directly related.
Example: The topic is about what was the most important thing you have ever learned in school and asks you to discuss why. Your answer is a quest for knowledge. Your supporting ideas include having been forced to work on large projects and do exhaustive research into topics that you normally wouldn’t read about, which expanded your mind. A tangent that you would not want to pursue might be to provide statistics on how many hours you worked on a research paper in elementary school. While factual, those facts do not help answer why a quest for knowledge is the most important thing you have ever learned in school. Make sure that the facts and reasons you are stating directly help you in your goal of answering the topic question.