Lines and Angles

Geometry: Lines and Angles

Read the following SAT test question and then select the correct answer.

For every math problem, you should use the Knowsys method: read the question carefully, identify the bottom line, assess your options, attack the problem, and loop back to verify that the answer you found addresses the bottom line. 

In the figure above, x = 60 and y = 40. If the dashed lines bisect the angles with measures of x° and y°, what is the value of z?

Geometry questions often include figures with multiple variables.  When you are assessing your options, realize that you can estimate values with figures that are drawn to scale, but that figures that are not drawn to scale may be misleading and estimation may result in a wrong answer.  When you are prepared to attack your problem, it is especially important to write your scratch work so that you can see how each number you find relates to the figure.  The easiest way to do that is to add the values you find to the figure.

Modifiers and Verbs

8/3 Identifying Sentence Errors

The following sentence contains either a single error or no error at all. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence contains no error, select choice E.

Searching a sentence for a grammatical error may seem like a daunting task because there are so many rules in the English language.  However, if you remember the Knowsys method, you need not be intimidated.  Read the sentence carefully and evaluate each underlined portion using the Big 8 Grammar Rules.  For each blank, ask yourself whether there are any problems.

The results of the study Aindicate that the new drug is Bboth safer and more effective than Cwas previously Dassumed.   ENo error

Sentence Completions

Link of the Day

Another tale of dedication and accomplishment comes out of the Olympics! Gabby Douglas, a 16-year-old girl from the USA, "made history" in London by winning the women's all-around title--the first African-American to ever do so. She had the highest score on both balance beam and vault, and she was the only American to compete on all four women's events. Dedication to her sport pulled her away from her parents at 14, when she moved from Virginia Beach to Des Moines to work with a world-famous gymnastics coach. Read more here.

8/2 Sentence Completion

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

The Knowsys Strategy for Sentence Completions is to cover the answer choices before you read the sentences.  If you read the entire sentence carefully, then you will be able to predict an answer for the blank and match your prediction to the correct answer choice.  When you use this method, you will not be distracted by wrong, but promising, answers because you can eliminate all the answers that do not match your prediction.  Be sure to look at all the answer choices, even if one matches immediately.

Exotics and indigenous weeds include some of the most ------- species: their visual impact often eclipses that of nearby plants.

After reading this sentence, you know that you must predict a word to describe “species.”  This word must give us more information than that they are “exotics and indigenous weeds.”  Think about the colon right after “species.”  Colons introduce explanations of the terms that precede them, so we should look after the colon for additional information.  After the colon you find that the species are known for “their visual impact.” You need a word to describe “visual impact,” so you might predict “eye-catching,” or “noticeable,” or even “attractive” (in the sense that they attract more attention than other plants).  Take your prediction and match it to the answer choices.

(A) lethal

(B) diffuse

(C) varied

(D) striking

(E) resilient 

Equations

Read the following SAT test question and then select the correct answer.

Read the question carefully, identify the bottom line (what the question is asking), and assess your options for solving it. You want to be as efficient as possible when solving math questions, so for most problems you should not look at the multiple choice answers before attacking the problem with the method you have chosen. Always loop back at the end of the problem to make sure that your answer addresses the bottom line.

If , what is the value of (t + 3)(t + 6)?

You must find the value of (t - 3)(t + 6). In order to do this, you must first find the value of t. Paraphrase the question in your mind: “If this is true, then solve this.” This question is already set up in two steps for you.  Solve the first equation and you will have the key to solving the second part of the problem because there is only one variable involved: t.

Think about the first equation logically. Something squared is equal to zero, so what can be multiplied by itself and equal zero? The only possible answer is zero! The squared portion of the problem must be equal to zero.

 and , therefore t - 2 = 0.

When you add the 2 to both sides of your new equation, you will see that t = 2. Now that you know the value of t, you have all the information that you need to solve the second part of the problem with simple arithmetic.

Subject-Verb Agreement

Link of the Day

Teachers and schools have gone back and forth on the value of rote memorization. Some claim that forcing students to endlessly repeat facts and processes only kills their creativity. Others argue that practice is essential to make certain information and tasks automatic--freeing up mental energy for higher-level applications. One value of memorization and repetition is that it can be highly effective as a way to learn facts on your own, without a teacher or classroom. If you've ever used vocabulary flashcards or a multiplication app, you've experienced rote learning! Learn more about the value of memorization here, and sign up for the Knowsys online vocabulary flashcards here. 

7/31 Improving Sentences

 Part or all of the following sentence is underlined; beneath the sentence are five ways of phrasing the underlined material. Select the option that produces the best sentence. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A. 

Read the following sentence to yourself, listening for errors.  Evaluate the underlined portion using the Big 8 Grammar Rules and predict a correction for any errors that you find.  Remember that after an improving sentences question, choice (A) will always be the same as the original sentence.  Eliminate any answer choices that do not help you towards your goal of creating a clear and precise sentence.

Rote learning, the process of memorizing by repetition, is how many young children learn the alphabet or the multiplication tables.

The underlined portion of this sentence includes a verb.  The third Big 8 Grammar Rule concerns subject and verb agreement.  Think back to this section in your Knowsys book.  You learned that the exam writers use 5 subject/verb tricks to make identifying a subject/verb agreement error more difficult.  One of these tricks is to separate subjects from verbs.  In this sentence, the subject is separated from the verb by an appositive phrase. An appositive phrase is a defining phrase that is set off by commas.  Because this phrase merely defines the subject, you should be able to ignore that portion of the sentence and still have a complete sentence.  You have now simplified the sentence to read: “Rote learning is how many young children learn the alphabet or the multiplication tables.”

You can now easily see that the subject matches the verb.  You can also see that for this to be a complete sentence, the very first word in the underlined portion must be a verb.  You want your subject and verb to be as close as possible, so you can eliminate any answer choices that do not begin with a verb.  

Sentence Completions

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

Sentence completion questions with more than one blank may look more intimidating than questions with only one blank, but they can be just as straightforward.  In most cases, you will focus on the blank that seems easy, eliminate any answers that do not match your prediction, and then move on to the other blank.

The actor’s ------- decline in popularity was as striking and unexpected as his ------- rise to prominence had been.

Examine the first blank.  You need a word to describe a decline in popularity that means “striking and unexpected.” Before you put too much time into in the first blank, take a look at the second blank.  Notice that it is connected to the first blank by the phrase “was as striking and unexpected as.” The same words that applied for the first blank also apply to the second blank, so the two words you are looking for must be synonyms.  If the words mean the same thing, then they are equally easy and you can make the same prediction for both, which means you will only have to look at the answer choices one time.  Rather than building a new prediction for each of these two blanks, predict your answer using the exact words from the sentence: “striking and unexpected.”  Eliminate any answer choices that do not include synonyms or do not mean “striking and unexpected.”

(A) sudden . . meteoric

(B) gradual . . equivocal

(C) precipitous . . obscure

(D) dazzling . . secret

(E) inevitable . . unpredictable 

Fractions

Link of the Day

Have you ever wanted to try something but thought you wouldn't be any good at it? Don't let that stop you! Some mind-blowing stories of unstoppable dedication have been coming out of the Olympics, especially the tale of Im Dong-Hyun, a South Korean man with 20% vision or less in each eye. This makes him legally 'blind,' but it has not stopped him from setting two world records in archery! Read more here and here. What kinds of essay prompts might you answer with the story of Im Dong-Hyun?

7/29 Fractions

Read the following SAT test question and then select the correct answer.

For every math problem, always be sure to follow the Knowsys Method. This will keep you from falling for traps and trick questions! First, read the question carefully.  You have to understand the information that you are given before you can begin working the problem.  The second step is to identify the bottom line, the question that you must answer.  In this case, you are asked to identify the total number of students who study art.  Next, assess your options to find the most efficient way to solve the problem, attack the problem, and loop back to make sure you answered the correct question.

Every student who studies art in a certain school receives exactly one of the grades A, B, C, or D. If of the students receive A’s, receive B’s, receive C’s, and 10 students receive D’s, how many students inthe school study art?

In this problem, you have fractions for the students who receive A’s, B’s, and C’s, but you have an actual number of students who receive D’s. To find the total number of students, you will need to find out what fraction of the whole is represented by the 10 students who receive D’s. Find out what fraction of the whole is represented by the students who receive A’s, B’s and C’s first. To add these fractions together, you need to find the least common denominator. You don't need to worry much about the 2 since it is a factor of 4. Instead, focus on the 5; the least common denominator will be the product of 4 and 5.

then becomes