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Quadrilaterals

Geometry: Quadrilaterals 

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

Math questions should always be read carefully.  You will also avoid making errors by identifying the bottom line and assessing your options for solving the question.  Choose the most efficient method to attack the problem.  When you have finished, loop back to be sure that even if there were multiple steps, you reached the bottom line.

The length of a rectangle is increased by 20%, and the width of the rectangle is increased by 30%. By what percentage will the area of the rectangle be increased?

Bottom Line: % change = ?

Assess your Options:  You could work this problem without picking any numbers; however, picking easy numbers will allow you to think about the problem in a more concrete way and avoid errors.

Attack the Problem:  One of the easiest numbers to work with is one.  Think of your original rectangle as having a length of one and a width of one.  The formula for area of a rectangle is length times width.  If L × W = A, for your first rectangle you have 1 × 1 = 1.   The area of the original rectangle is one.

Then think about the changes that occur to that rectangle.  The length increases by 20%.  In order to find 20% of 1, all you have to do is move the decimal over twice to .2.  The new length is 1.2.  Use the same method to find the new width, and an increase of 30% becomes 1.3.  The area of the rectangle after the change is 1.2 × 1.3 = 1.56

The formula for percent change would require you to find the difference between these two areas and divide that by the original number.  You use the same formula whether you are looking for an increase or a decrease.  Notice that your original number is one, so dividing by one will not change your answer.  All you need to do is find the difference between the areas: 1.56 – 1 = .56.  What is .56 as a percent?  Your answer is 56%.

Loop Back:  You found the percent change, which was your bottom line.  Look down at your answer choices.

(A) 25%
(B) 36%
(C) 50%
(D) 56%
(E) 60%

The correct answer is (D).


On sat.collegeboard.org, 34% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

Pronouns

Link of the Day

Sometimes fact can sound like fiction, and produce an extremely interesting current event for your SAT essay.  Scientists have found a way to make a tiny cylinder invisible, creating a lot of excitement about the possible applications of such a feat.   Think about this accomplishment in terms of planning, creativity, imitation, and technology.  How could you relate this article about a current event to past SAT essay prompts?

11/13 Identifying Sentence Errors:  Pronouns

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. 

Read the entire sentence to yourself, listening for errors.  Then check each underlined portion of the sentence against the Big 8 Grammar Rules.  If you find an error, mark it and quickly check the remaining underlined words.

Whether the Sumerians were the first people to develop writing is uncertain, but theirs is the oldest known writing system. No error

(A)   Always check to make sure that a verb matches the subject.  The subject, Sumerians, is plural, so “were” is required instead of “was.”  Then check to make sure that the verb is in the correct tense.  This sentence is about the past, so “were” is required instead of “are.”

(B)  It is idiomatically correct to include the preposition “to” before the word “develop.”

(C)  The word “uncertain” denotes that this statement is not definite, clearly conveying the meaning of the sentence.

(D)  When you see a pronoun, you must check to make sure that it refers to a single antecedent and that it agrees with that antecedent.  You already established that the sentence is about certain people, so the pronoun must be plural, and it must show possession.  Think about the “s” on the end of “theirs” as a shorter way to say “their writing system.”  You don’t want to write out “their writing system” because it will make the last portion of the sentence redundant.

(E)  None of the underlined portions of the sentence has an error, so this is the only remaining answer choice.

The correct answer is (E).


On sat.collegeboard.org, 45% of the responses were correct.

For more help with SAT writing, visit www.myknowsys.com!

Ratios

Link of the Day

The election results are in!  The amount of information after an election day can be overwhelming, but limit yourself to one story from the election, and you will have an excellent current event for your SAT essay.  Many people focus on the presidential election, but there are hundreds of other important issues that were brought before the nation.  One group of United States citizens who currently cannot vote for the president of the United States voted about the possibility of becoming the 51st state.  Read this article about what is happening in Puerto Rico, and think about how this prospective state differs from or is similar to other territories that have become states.  Think of the broad themes raised by this story that could relate this article to SAT essay questions.

11/8 Algebra:  Ratios

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

Don’t just read the question; read it carefully.  Make sure you know which labels apply to which numbers.  Identify the bottom line.  Assess your options for solving the problem so that you can choose the most efficient method to attack the problem.  Once you have solved the problem, loop back to make sure that you have solved for the bottom line.

In a class of 80 seniors, there are 3 boys for every 5 girls. In the junior class, there are 3 boys for every 2 girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?

Bottom Line:  Number of juniors = ?

Assess your options:  You could work backwards by starting with the answer choices, but it might take you a long time to work through all of the possible answers.  Instead, start turning those ratios into actual numbers of students.

Attack the problem:  You know the most about the seniors, so start with them.  You are given a ratio of 3 boys to 5 girls, and you know that the total number of boys and girls must equal 80.  You know that 3 + 5 = 8, so all you have to do is multiply the 3 and the 5 each by 10 and you will have a total of 80 seniors.  There are 30 senior boys and 50 senior girls.



Now that you know the number of senior boys and senior girls, how does that help you find the number of juniors?  Remember that the two classes combined have an equal number of boys and girls.  That means that the senior boys plus the junior boys must be equal to the senior girls plus the junior girls. 



Plug in the numbers that you found for the senior boys and girls.  



What information do you know about the juniors?  You know that there are 3 boys for every 2 girls.  You do not know the total number of juniors, so use an x to represent this number.  What fraction of the total are the boys?  They are actually three fifths of the total number of juniors because you must add the boys and girls to find the total number of juniors.  That means that the girls are two fifths of the total number of juniors.  Plug this into your formula, remembering that anytime you have “of the total” that means that you must multiply by the unknown total. 



Now solve for x.  Rearrange the equation so that you have like terms on the same sides of the equation, and combine those like terms.  Start by subtracting the two fifths of x from each side.



Get those whole numbers together by subtracting 30 from each side.



To get rid of the fraction, you will need to multiply both sides by 5.  Your answer is x = 100.

Loop Back:  What does x represent?  It represents the total number of juniors, which matches your bottom line.  You are ready to look down at your answer choices.

(A) 72
(B) 80
(C) 84
(D) 100
(E) 120

The correct answer is (D).


On sat.collegeboard.org, 44% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!