Sneaky Trick with Systems of LInear Equations on the SAT

From the no calculator section of the May 2018 SAT

  11                                                                            
       
                               5x + 2y = 22
                                4x + y = 17

In the system of equations above, what is the value 
of x + y ?

A) 5
B) 4
C) 3
D) 2

To solve by elimination, I would (1) multiply the second equation by -2, (2) add the equations, (3) solve for y, (4) substitute back in to find x, and (5) add x and y.

(1)   
      5x + 2y = 22
  -2[4x + y = 17]

      5x + 2y = 22
     -8x + -2y = -34

(2)
      [5x +  2y =  22]
    +[-8x + -2y = -34]
      -3x +  0  = -12

(3)
     x = 4


(4)
      5(4) + 2y = 22
      2y=2
        y=1

(5)       x + y = 5

This is not terribly difficult, but there is a much quicker way to solve the problem. Simply subtract the second equation from the first.            
                      [5x + 2y = 22]
                     -[4x + y = 17]
                         x +  y =  5

It is rather interesting how often the SAT pulls this little trick, e.g., October 2018.

  191                                                                           

2x + 3y = 1200
3x + 2y = 1300

Based on the system of equations above, what is the value of 5x + 5y?

Once again, it is possible to solve for x and y, but adding the equations yields

   [2x + 3y = 1200]
+[3x + 2y = 1300] 

   5x + 5y = 2500.

This trick doesn't always work. Sometimes the question asks for the value of either x or y by itself, making it necessary to solve for the individual variable. Nevertheless, any time a question asks for the sum or difference of the variables or multiples of the variables (x + y, x - y, 2x + 3y) it's worth looking to see what happens when the equations are simply added or subtracted.

Obscure Dash Usage on the PSAT

There are two rules that a student needs to know about the long dash (or em dash):\.

(1) One long dash is equivalent to a colon;
(2) Two long dashes are equivalent to commas around a nonessential (or nonrestrictive).

I have never seen a long dash in an ACT English question that didn't fall under one of these rules two rules. The College Board, however, likes to mess with student's (and tutor's) heads by finding obscure dash usages.

For example, question 15, from the 10-15-16 PSAT:

Stress levels, immune system strength, male fertility, and weight and cholesterol— 15 which all appear to benefit from the regular consumption of nuts.

A)  NO CHANGE 
B)  that all appear
C)  all appearing
D)  all appear

Answer choice D would work perfectly if not for that dash: "Stress levels, immune system strength, male fertility, and weight and cholesterol all appear to benefit from the regular consumption of nuts." Unfortunately, the dash is not underlined so there is no way to get rid of it. 

Applying Rule #1, the dash is equivalent to a colon, but the colon is supposed to be preceded by an independent clause. One of the most common uses of a colon INDEPENDENT CLAUSE-COLON-LIST, but here it's LIST-COLON-INDEPENDENT CLAUSE.

Is that even legit?

Apparently it is, according to several grammar websites I found, although none of them explained how this fit in with the rule that a colon must be preceded by an independent clause.

Another obscure dash rule came up in question #3 from from the 11-2-17 PSAT:

A turning point in the musical  3 genre; however, came with Richard Rogers and Oscar Hammerstein II's 4 Oklahoma!

A) NO CHANGE

B) genre, however;

C) genre—however—

D) genre, however,

My first instinct here is to eliminate both C and D because two dashes are equivalent to two commas around the nonessential "however." However, a semicolon may only be used between two independent clauses, and "a turning point in the musical genre" sure ain't an independent clause—with or without the "however." So I'm left choosing between two forms of equivalent punctuation.

The key to the answer lies in the following question:

The writer is considering revising the underlined portion to the following.

Oklahoma!—the first musical to feature a sophisticated story served by music and dance elements.

Should the writer make this revision?

It turns out that the author should make that revision, which leaves the following sentence: "A turning point in the musical genre, however, came with Richard Rogers and Oscar Hammerstein II's Oklahoma!—the first musical to feature a sophisticated story served by music and dance elements." 

Now there is a reason to prefer D over C. While the two dashes in C are equivalent to the two commas in D, using three dashes in one sentence is frowned upon because it may create ambiguity. So the fact that the answer to #4 adds another dash to the sentence determines the correct answer to #3.

 

How the ACT Has Changed

Students frequently ask how much the ACT has changed in recent years and whether the older ACTs that they find online provide good practice for the current exam.

The short answers are "not that much" and "yes they do." The ACT has made some minor tweaks over the last few years, but the types of questions and passages that appear on the older exams appear on the current exams.

The big change on the Reading Test is that every ACT since 2015 has included a dual passage, i.e., a passage made up of two shorter passages offering different perspectives on a particular topic. Dual passages made occasional appearances prior to then, but there aren't many of them on older tests.

At about the same time, the Science Test reduced the number of passages from seven to six. The types of questions and passages did not change.

The mix of questions on the Math Test has gotten harder in the last few years. On the April 2019 ACT, a student could miss thirteen questions on the Math Test and still get a 30. In 2009, the same number of correct answers would only have netted a 27. However, the difficulty of the individual questions hasn't changed much. The hardest questions today aren't much different from the hardest questions ten years ago. It's the ratio of hard questions to easy questions that has changed.

Another thing the ACT has done over the last few years is to include more Statistics & Probability questions on each test. Since 2016, each exam has contained six such questions. Again, however, these questions aren't any more difficult than the ones that the ACT asked before 2016--there are simply more per test.

The section that has changed the least is the English Test. In 2008, the English Test stopped offering "OMIT the underlined portion" as an answer choice. Now, it says "DELETE the underlined portion" instead.

I would certainly recommend doing the most recent tests first, but the older tests are still excellent practice.

Terrible SAT Explanations

One of the ideas behind Kahn Academy was leveling the playing field. By making quality test prep materials available to everyone, students who have the money to pay for tutors and prep classes would no longer have an advantage. Unfortunately the explanations on Kahn Academy are sometimes so bad that they put the students who rely on it at a disadvantage.

Consider this question that was recently shared on reddit:

 

11.  A) NO CHANGE,
       B) field she
       C) field; she
       D) field: she

Personally, I think that either C or D should be acceptable. There are two independent clauses, and the second one elaborates on the first, so either a colon or a semicolon should be fine.

Kahn Academy insisted that only the semicolon is acceptable, but the reason it gives is flat out wrong.

"Walker was not only a trailblazer in the medical field" is not a relative clause. It is an independent clause that can stand alone as a sentence. It feels somewhat incomplete because it so clearly anticipates a discussion of the person's other accomplishments, but it is still an independent clause.

What it isn't is a relative clause, at least according to the Writing Center at the University of North Carolina (and every other source I could find):

A relative clause is one kind of dependent clause. It has a subject and verb, but can’t stand alone as a sentence. It is sometimes called an “adjective clause” because it functions like an adjective—it gives more information about a noun. A relative clause always begins with a “relative pronoun,” which substitutes for a noun, a noun phrase, or a pronoun when sentences are combined.

For example "who lives next door" is a relative clause in the sentence "I spoke to the woman who lives next door." It provides information about the woman. On the other hand, "Walker was not only a trailblazer in the medical field" contains no relative pronoun and it does not give information about any noun other than the one that appears in the clause.

I often think that there are much better ways to get to the right answer on a question than the one  given in the College Board's explanation. It is less frequent that I think that the College Board's explanation is objectively incorrect, but it happens enough that I don't think that test prep tutors  have to worry about being put out of business by Kahn Academy any time soon.

Why the SAT Annoys Me

When I was in school, I was the kind of student who argued with teachers about test questions. Actually, I argued with teachers about a lot of things, but that is neither here nor there. I have rarely found an ACT question that I would want to argue about, but the SAT is another matter. I can't say that I have ever found an SAT question on which I thought that there was an objectively better answer than the one that the College Board deemed correct, but there are several where I have thought that another answer was just as good as the College Board's choice. Question 28 from the October 2017 Writing and Language section is one example.

Dried collodion is unusable, so once the photo is snapped with a massive, tripod-mounted camera, the photographer has nominal minutes to develop it, using more chemicals.

The writer wants to emphasize how quickly wet plate photographers have to work. Which choice most effectively accomplishes this goal?

A)  NO CHANGE
B)  a few
C)  a matter of
D)  mere

The correct answer is D, but I am hard pressed to see a meaningful difference between "mere minutes" and "a matter of minutes." According to Merriam-Webster, "a matter of" is "used to refer to a small amount," while "mere" means "being nothing more than." If one of them does indicate a shorter period of time, I guess it would be "mere," but I am far from convinced that it does.

However v. Nevertheless

However and nevertheless are often synonymous, but not always. “However” can always be used in place of “nevertheless,” but “nevertheless” cannot always replace “however.”




Both words draw a contrast, but “however” merely points out the contrast; “nevertheless,” conveys the added idea that the contrast is surprising. “Nevertheless” means “despite that.”


1a) The full-sized van carries more passengers than the mini-van. 
1b) However, the mini-van gets better gas mileage. 

2a) The full-sized van carries more passengers than the mini-van. 
2b) Nevertheless, the full-sized van gets better mileage.

Both pairs of sentences draw contrasts between the full-sized van and the minivan, but the first contrast is expected. There is nothing surprising about the smaller vehicle getting better mileage than a bigger one. Only "however" is proper here. “Nevertheless” would not make sense.

In the the second pair of sentences, the contrast is surprising. Despite the fact that the full-sized van is bigger than the minivan--i.e., it holds more people--it also gets better mileage.  Either “however” or “nevertheless” would be proper here.


I don’t recall the ACT ever requiring the student to choose between “however” and “nevertheless,” but the SAT did so on Practice Test 2.

It has long been known that the sea otters living along the West Coast of North America help keep kelp forests in their habitat healthy and vital. They do this by feeding on sea urchins and other herbivorous invertebrates that graze voraciously on kelp. With sea otters to keep the population of sea urchins in check, kelp forests can flourish. In fact, even two years or less of sea otter presence can reduce the sea urchin threat in a coastal area Without sea otters present, nevertheless, kelp forests run the danger of becoming barren stretches of coastal wasteland known as urchin barrens.

25                                                                                                                                                

A) NO CHANGE
B) however,
C) hence,
D) likewise,

Here there is nothing surprising about what happens when there are no sea otters, so "nevertheless" is inappropriate.

Of course, the College Board's explanation is not particularly helpful:

Choice B is the best answer because the conjunctive adverb "however” accurately communicates the contrast between an environment shaped by the presence of sea otters, described in the preceding sentence, and an environment shaped by the absence of sea otters, described in this sentence.
Choices A, C, and D are incorrect because each presents a conjunctive adverb that does not accurately depict the relationship between the preceding sentence and the sentence with the underlined word.

In other words, "nevertheless" is wrong because it's not right.

Answering Science Questions without Science

Sometimes you can answer Science questions based purely on the units in the answers.  In the following question, knowing what S is or what Table 2 says is unnecessary.

34. Lightning strikes can occur when air between the ground and the base of a storm cloud is exposed to an electric field stronger than S for air. Suppose a certain storm cloud's based is 300m above the ground the ground. Based on Table 2, approximately what minimum voltage would be present between the storm cloud's base and the ground immediately before a bolt of lightning from this storm cloud strikes the ground? 

F.  300,000 mm x 3.13 kV/mm 
G. 300.000 m x 3.13 kV/mm
H.    300 mm    
     3.13 kV/mm
J.       300 m     
    3.13 kV/mm

December 2015 (72E)

The question asks for "minimum voltage." Therefore, the unit of the answer will be have to be some sort of voltage, and the only unit of voltage is kV.. Get rid of H and J because kV is in the denominator, so the unit in those will be 1/kV. Get rid of G because it has different length units in the  numerator (meters - m) and the denominator (millimeters -mm), and they won't cancel out. The only answer in which the length units will cancel, leaving a voltage unit, is F.