# ACT Algebra Absolute Value

## SAT Question of the Day

The SAT question of the day is an Identifying Sentence Errors Question that has already been addressed on this blog: click here to see an explanation.

## ACT Math Question of the Day

What are the values of a and b, if any, where a|b – 2| < 0 ?

There are three things you must understand to solve this problem: number properties, absolute value, and inequalities.

Start by considering the equation as a whole. You know that the side that contains the variables must be less than zero. What kind of numbers are less than zero? Negative numbers! Now you know that a|b – 2| must be a negative number.

Break down a|b – 2| into its essential parts. It is really just the variable a multiplied by |b – 2|. What kinds of numbers do you have to multiply together in order to get a negative number? You must have a positive number times a negative number. You know that anything inside the absolute value bars will be positive. That is your positive number. Now you know that variable a must be negative! In other words a < 0!

Now that you know the restrictions on variable a, look at b. You know that you need a negative number times a positive number and it must be less than 0. Think about the properties of 0. Zero is neither negative nor positive. You must make sure that the second part of your equation (|b – 2|) does not equal 0. When does |b – 2| = 0? When b = 2. Therefore, for your equation to work, b ≠ 2.

A.a < 0 and b ≠ 2
B.a < 0 and b = 2
C.a ≠ 0 and b > 2
D.a > 0 and b < 2
E. There are no such values of a and b.

For the ACT Question of the Day, visit http://www.act.org/qotd/.

To get help preparing for the SAT, PSAT, or ACT Exam, visit www.myknowsys.com!

# ACT English

## SAT Question of the Day

The SAT question of the day is a Sentence Completions Question that has already been addressed on this blog:

## ACT English Question of the Day

English questions on the ACT test many of the same concepts as writing questions on the SAT, but they provide more context.  Take a look at this question:

 Modern broadcasting began to develop after the First World War. Before 1920, radio was simply a useful way to send electrical signals ashore from a ship at sea, or, from one "ham" operator to another. The new technology associated with movies and airplanes was already developing rapidly by the time soldiers started returning from European trenches in 1918. The vast potential of the airwaves, therefore, had scarcely been touched.

Choose the best alternative for the underlined part.

This question tests your ability to use logical transitions.  The word “therefore” makes sense if you only read one sentence, but if you read the paragraph, you will see that it is out of place.  The word “therefore” signifies causation.  You could insert the word “consequently” in its place.  The lack of knowledge about airwaves was not a consequence of developing technology for movies and airplanes.  Instead, the paragraph makes a contrast between actual development and potential development.  You need a contrast word such as “but,” “yet,” or “however.”

F. NO CHANGE
G. however,
H. also,
J. in fact,

(F) You already know that “therefore” is not correct.  Eliminate this choice.  (G) Perfect match!  Keep this choice.  (H) The word “also” continues an idea or means “likewise.”  It does not express contrast.  Eliminate this choice.  (J)  Although the author is making a factual statement, this choice does not connect the sentence to the previous sentence to create a cohesive paragraph.  Eliminate this choice.

For the ACT Question of the Day, visit To get help preparing for the SAT, PSAT, or ACT Exam, visit www.myknowsys.com!

## SAT Question of the Day

The SAT question of the day is an Improving Sentences Question that has already been addressed on this blog:

## ACT Reading Question of the Day

The ACT often gives you a lot more than you need to know.  Before reading the following passage, look down at the question that follows it.

 SOCIAL SCIENCE: This passage is adapted from Leonard W. Levy's Origins of the Fifth Amendment: The Right Against Self Incrimination. (©1968 by Clio Enterprises Inc.).

According to the passage, an oath was declared "burst" during compurgation if the:

Your job it to find the word “burst.”  Quickly look through the passage.  Do you see it in line 35?  You can answer the question just by reading the sentence that contains the word “burst.”  What is responsible for “bursting” the oath?  A mistake!  Look down at your answer choices.

F. swearer made an error in the exact form of the required ritual.
G. swearer could not round up the required number of oath-helpers.
H. swearer preferred trial by ordeal, or by battle.
J. judges decided that the oath was false or unnecessary.

(F) What is another word for mistake?  Error!  This answer choice matches your prediction.  (G)  This answer may distract you if you read the entire paragraph including “burst.”  If you read the sentence carefully, you will see that even if a swearer has a lot of oath-helpers, he has to use the exact form of the required ritual without any mistake.  The mistake is what “burst” the oath.  (H)  The trial by ordeal and the trial by battle are not introduced until after the word “burst” appears.  In both of these trials, no oath is necessary because the outcome of the trial is what determines a person’s innocence or guilt, not words.  (J) Notice that lines 78-82 tells you that judges do not decide a verdict, they just decide who should be put to proof.  Judges did not determine what was true or false, they just made sure that each side followed the legal rules.

For the ACT Question of the Day, visit To get help preparing for the SAT, PSAT, or ACT Exam, visit

# ACT Math

## SAT Question of the Day

The SAT question of the day is a Sentence Completion Question that has already been addressed on this blog:  click here to see an explanation.

## ACT Math Question of the Day

Many ACT math questions are exactly like SAT questions.  Use the same process as you would to answer an SAT question.  Read the question carefully, and identify the bottom line.  Assess your options and use the most efficient method to attack the problem.  When you have an answer, loop back to verify that it matches the bottom line.

There are students in a class. If, among those students, p% play at least 1 musical instrument, which of the following general expressions represents the number of students who play NO musical instrument?

Bottom Line:  #kids no musical instrument = ?

Assess your Options:  You could write an equation using the variables that you are given, but many students make mistakes using this method.  Instead, use the strategy of plugging in numbers to make sure that you arrive at the correct answer.

Attack the problem:  When you have a percent problem, use the number 100 for any total that you do not know.  This makes the problem easier because a percent is just a number out of one hundred.  If you start with the number of 100, your answer will automatically be out of 100!

Look up at the problem.  There are students in the class, so let = 100.  You still have another variable, p.  Pick a number for p as well.  It must be less than 100, but not too difficult for this problem, so let’s pick = 30.

Answer the question using the numbers you have chosen.  If you have 100 students and 30 play at least one musical instrument, how many do not play any musical instrument?  70!  100 – 30 = 70.

Now you need to look down at your answer choices and see which choice equals 70 when you plug in = 100 and = 30.

A.  np

B.  .01np

C.

D.

E.  100(1 –p)n

Loop Back: You are just looking for a matching number.

A.  np  = 100(30) = 3,000, not 70

B.  .01np = .01(100)(30) = 30, not 70

C

: Plug in = 100 and cancel the 100 on the top and bottom of the fraction.  You are left with 100 – 30 = 70.  On the actual test, there would be no reason to check any of the other answers, but you can practice working the remaining answer choices now.

D.

=

= –290,000, not 70

E.  100(1 –p)= 100(1 - 30)(100) = –290,000, not 70

For the ACT Question of the Day, visit

http://www.act.org/qotd/

.

To get help preparing for the SAT, PSAT, or ACT Exam, visit www.myknowsys.com!

# ACT English

## SAT Question of the Day

The SAT question of the day is an Algebra Question that has already been addressed on this blog: click here to see an explanation.

## ACT English Question of the Day

The ACT tests many of the same English grammar questions as the SAT, but grammar questions come from a passage rather than a single sentence.

 The newspaperman got in touch with a flight school in France that was willing to teach this determined young woman to fly. [4] [1] While they're, she had as one of her instructors Anthony Fokker, the famous aircraft designer. [2] Bessie Coleman took a quick course in French, should she settle her affairs, and sailed for Europe.  Choose the best alternative for the underlined part of the passage. The ACT and SAT both love to test the difference between “there,” “their,” and “they’re.”  In context, you can see that the “they’re” refers to a place, a flight school in France.  However, “they’re” is actually a contraction meaning “they are.”  Change it to “there,” the correct word to indicate a place.  The rest of the underlined portion is clear; there are no more errors.  Look down at your answer choices. F. NO CHANGE G. they’re H. there, J. there, she had as The correct answer is (J).  Notice that (H) fixes the incorrect “they’re” but eliminates the rest of the underlined portion, creating a sentence fragment.  Always make sure that you can substitute the answer choice for the entire underlined portion. For the ACT Question of the Day, visit http://www.act.org/qotd/. To get help preparing for the SAT, PSAT, or ACT Exam, visit www.myknowsys.com!

# ACT Science

## SAT Question of the Day

The SAT question of the day is an Identifying Sentence Errors Question that has already been addressed on this blog:

## ACT Science Question of the Day

Science Questions on the ACT are not about memorizing facts, they are about finding information and being able to read charts.  They do not require you to know anything that is not given to you!

Passage II
The Sun's path from sunrise to sunset varies with the time of year. A student performed the following experiments on three clear, sunny days at three- or four-month intervals throughout the course of a year to study the path of the Sun through the sky.

Experiment 1
At a chosen Northern Hemisphere location, the student placed a stick vertically into the ground so that 1 meter of its length was left above ground. The student knew that the length of the shadow was related to the height of the Sun above the horizon and that the shadow would point away from the direction of the Sun. The length in meters (m) and direction of the shadow cast by the stick were measured one hour after sunrise (Shadow A), at mid-morning (B), at noon (C), at mid-afternoon (D), and one hour before sunset (E) on each of the three days. The direction of each shadow was determined by placing a magnetic compass at the base of the stick and aligning the north arrow with the north mark on the compass. The direction of each shadow was then determined by a comparison with the compass face markings. The results are recorded in Table 1.

 Table 1 Shadow Day 1 Day 2 Day 3 Length (m) Shadow  direction Length  (m) Shadow  direction Length  (m) Shadow  direction A 5.0 SW 8.6 NW 6.8 W B 1.2 W 2.9 NNW 1.7 NW C 0.3 N 2.3 N 0.9 N D 1.2 E 3.0 NNE 1.8 NE E 5.0 SE 8.6 NE 6.9 E

 Experiment 2     The following year, the student repeated Experiment 1 at a chosen location in the Southern Hemisphere. The results are in Table 2.

 Table 2 Shadow Day 1 Day 2 Day 3 Length (m) Shadow  direction Length  (m) Shadow  direction Length  (m) Shadow  direction A 9.0 SW 5.0 NW 6.9 W B 3.2 SSW 1.1 W 1.8 SW C 2.5 S 0.3 S 1.0 S D 3.2 SSE 1.1 E 1.8 SE E 9.1 SE 5.0 NE 6.9 E

When the Sun is at an altitude 45° above the horizon, a vertical object will cast a shadow with a length equal to the object’s height. Which of the following days included a measurement taken when the Sun was at an altitude of 45°?

The first paragraph under Experiment 1 tells you that the stick (the vertical object) has 1 meter above the ground.  You must find a shadow length that is equal to the height in order to know that the Sun was at an altitude of 45° at that moment.  Check the charts.  There is only one shadow that is 1 meter long.  It is in the second chart (Experiment 2) under Day 3, Shadow C.  Circle it and look down at your answer choices.

A. Day 1 in Experiment 1
B. Day 1 in Experiment 2
C. Day 2 in Experiment 1
D. Day 3 in Experiment 2

For the ACT Question of the Day, visit To get help preparing for the SAT, PSAT, or ACT Exam, visit www.myknowsys.com!

## SAT Question of the Day

The SAT question of the day is a Sentence Completion Question that has already been addressed on this blog:

## ACT Question of the Day

ACT prose fiction:

This passage is adapted from Elizabeth Bishop’s short story "The Housekeeper" (©1984 by Alice Methfessel).

Note: on the ACT test, this passage is about 100 lines long.  Can you answer this question using only the lines that are cited in the question?  Yes!

 65 this over and over to me, loudly, and her turbans and kerchiefs grew more and more distrait. One evening, Mary came to call on me and we sat on an old table in the back yard to watch the sunset. "Papa came today," she said, "and we've got to go 70 back day after tomorrow." "Is Mrs. Sennett going to stay here?" "She said at supper she was. She said this time she really was, because she'd said that last year and came back, but now she means it." 75 I said, "Oh dear," scarcely knowing which side I was on. "It was awful at supper. I cried and cried." "Did Theresa cry?" "Oh, we all cried. Papa cried, too. We always do." 80 "But don't you think Mrs. Sennett needs a rest?" "Yes, but I think she'll come, though. Papa told her he'd cry every single night at supper if she didn't, and then we all did." The next day I heard that Mrs. Sennett was going 85 back with them just to "help settle." She came over the following morning to say goodbye, supported by all five children. She was wearing her traveling hat of black satin and black straw, with sequins. High and somber, above her ravaged face, it had quite a Spanish- 90 grandee air. "This isn't really goodbye," she said. "I'll be back as soon as I get these bad, noisy children off my hands." But the children hung on to her skirt and tugged at 95 her sleeves, shaking their heads frantically, silently saying, "No! No! No!" to her with their puckered-up mouths.
What is the main insight suggested by the conversation in lines 69–83?

For this question, you must determine the main insight.  That is something that you can predict.  If you read the lines, you know that Mrs. Sennett seems to need a rest, but she cannot leave because an entire family starts to cry.  The family seems to use tears to control Mrs. Sennett’s actions.  Look down at your answer choices.

(F) The Curley family cries to manipulate Mrs. Sennett into doing what they want.
(G) The narrator regrets that she is not going to Boston and is a little jealous of Mrs. Sennett.
(H) Mrs. Sennett is happy to leave the Curley family because they are always whining and crying.
(J) Mrs. Sennett intends to return to the Cape soon because she has discovered that they have been manipulating and taking advantage of her.

(F) This matches your prediction exactly.  (G)  Does anyone even mention Boston in these lines?  No.  There is also no mention of jealousy.  (H)  Someone who is happy to leave would not have a problem saying no to the children.  Mrs. Sennett keeps coming back, so even if she says the children are bad (outside the lines that you are to evaluate), she really cares about them.  (J)  Whether or not Mrs. Sennett is aware of the family’s manipulation of her, the main point of this passage is that the manipulation is occurring.

For the ACT Question of the Day, visit http://www.act.org/qotd/.

To get help preparing for the SAT, PSAT, or ACT Exam, visit
www.myknowsys.com
!

# Inequalities

## Algebra: Inequalities

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

Always read the question carefully, identifying the bottom line.  Assess your options for reaching the bottom line and use the most efficient method to attack the problem.  When you have an answer, loop back to verify that your answer matches the bottom line.

On the line above, if AB < BC < CD < DE, which of the following must be true?

Bottom Line: wotf must be true = ? (which of the following)

Assess your Options:  For a “wotf” question, you will have to look at the answer choices.  Most students will start with “A,” so Knowsys recommends that you start with “E.”  You may also find that this is a good problem to use the strategy of plugging in numbers.

(A) AC < CD
(B) AC < CE
(E) BD < DE

(E) BD < DE  Look up at the figure.  On the figure, does BD look smaller than DE?  No!  It looks slightly larger.  You know that the figure is not drawn to scale, but the figure does give you one possible depiction of the rule.  Use the figure!  If it is possible for BD to be bigger than DE, then this answer is incorrect because you are looking for something that must be true.  Eliminate this choice.

(D) AD < DE  Look up at the figure.  The figure shows you that it is possible for AD to be larger than DE.  Eliminate this choice.

(C) AD < CE  These lengths are very similar on the line.  Break each length down into the parts that compose it so that you can make a precise comparison.  For example, AD contains AB + BC + CD.  CE contains CD + CE.  You now have: AB + BC + CD < CD + DE.  When you have the same thing on both sides of an equation, it cancels.  Eliminate the CD.  You now have AB + BC < DE.
You cannot come to a conclusion about these lengths.  If you want to prove this, try plugging in numbers.  Suppose AB starts at 10 and each portion along this line gets larger by 1.  AB = 10, BC = 11, CD = 12, DE = 13.  Is 10 + 11 < 13?  No.  Eliminate this choice.
(B) AC < CE  This one looks like it could be true, based on the figure.  See if you can prove it.  Break it down into its parts just as you broke down the last answer choice.  AC contains AB + BC.  CE contains CD + DE.  At first it seems as if you cannot compare these either because all of the numbers are different.  Try plugging in the same values as you used before: AB = 10, BC = 11, CD = 12, DE = 13.  Is 10 + 11 < 12 + 13?  Yes!  Will this work for all numbers?  Yes!  You are adding a small number plus a medium number and comparing it to a big number plus an even bigger number.  The former will always be smaller than the latter.  Once you know this, you do not even need to check (A).

(A) AC < CD You can tell from the figure that this does not have to be true.

Loop back:  You solved for what must be true, so you should select the answer you found.

On sat.collegeboard.org, 68% of the responses were correct.

To get help preparing for the SAT exam, visit www.myknowsys.com!

## ACT Question of the Day:

If you have gone 4.8 miles in 24 minutes, what was your average speed, in miles per hour?

Your bottom line here is in miles per hour.  That would be miles over hours.  Your distance (miles) is in the correct unit, but your time (minutes) is not.  You know that there are 60 minutes in an hour.   Find the fraction of an hour that was spent traveling. Take your minutes and put them over the total minutes in an hour:

$\frac{24\: min}{60\: min}=\frac{2}{5}\: of\: an\: hour =.4\: hr$

Now you know that you went 4.8 miles in .4 hours.  How many miles per hour was that?  Divide 4.8 by .4 and you will see that the answer is 12.

Note: You can do this in your head if you realize that this is the same thing as dividing 48 by 4.  This whole problem can be done in seconds if you know your times table all the way up to 12.

(A)  5.0
(B) 10.0
(C) 12.0
(D) 19.2
(E) 50.0

For the ACT Question of the Day, visit http://www.act.org/qotd/.

To get help preparing for the ACT exam, visit
www.myknowsys.com!

# Style

## Writing: 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 entire sentence to yourself, listening for errors.  Then focus in on the underlined portion, and evaluate it using the Big 8 Grammar Rules.

The first public botanical garden in the United States, the Elgin Botanic Garden in New York City was established to provide plant materials for studying by medical students.

The underlined portion of the sentence should sound awkward and wordy to you.  Look at the phrase “by medical students.”  You normally use the word “by” with a finished product.  For example, a book is “by an author,” but these medical students are just studying.  This sentence concerns the reason for something's existence so you know that how you use the word "for" will be important   Why are the plants provided?  The primary reason that they are there is that they are for medical students.  Others can also study these plants, but they are intended for medical students.  The correct answer will probably have the preposition “for” followed by “medical students.”

(A) for studying by medical students
(B) for medical students to study
(C) to medical students for their study
(D) for the study of medical students
(E) that medical students will study

(A)  This answer choice matches the awkward original.  Eliminate it.
(B)  This answer choice matches your prediction, and it is clear and concise.  Keep it.
(C)  This answer choice is not glaringly incorrect, but it is not as concise as it could be.  You can construct the sentence so that the pronoun “their” is unnecessary.  Eliminate this choice.
(D)  This answer choice subtly changes the meaning of the sentence.  Now it seems as if the medical students are being studied!  Eliminate this choice.
(E)   This answer choice seems okay, but remember that the original sentence is about the purpose of the plants.  The plants should be there for a specific group of people or a specific reason.  This answer choice makes the medical students of secondary importance and does not adequately indicate the purpose of the plant materials.  The park seems as if it was established simply to provide plants.  Eliminate this choice.

On sat.collegeboard.org, 72% of the responses were correct.

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

## ACT Question of the Day:

The ACT English questions are structured a little differently than the Grammar questions on the SAT, but they test the same rules.  Check out this question:

The RCA executives who created the
powerful NBC network were right to see that
sizable profits would come from this new medium.

Choose the best alternative for the underlined part.

(A) NO CHANGE
(B) which
(C) having
(D) as

To answer this question correctly, all you have to know is that executives are people.  When you refer to people you use the word “who.”

For the ACT Question of the Day, visit http://www.act.org/qotd/.

For more help with ACT questions, visit www.myknowsys.com!

# ACT Science

## SAT Question of the Day

The SAT question of the day is a Sentence Completion Question that has already been addressed on this blog: click here to see an explanation.

## ACT Question of the Day

The ACT contains a science section that is not on the SAT.  However, you do not have to memorize science information to do well on this test!  All you have to do is be able to logically analyze and evaluate the information that you are given.  Even if you are only preparing for the SAT right now, take a look at this science question and consider whether your strengths are suited to the ACT.

Note:  ACT science passages throw a lot of information at you.  It is best to ignore the details in the charts until you know what information the question asks you to find.
Passage II
The Sun's path from sunrise to sunset varies with the time of year. A student performed the following experiments on three clear, sunny days at three- or four-month intervals throughout the course of a year to study the path of the Sun through the sky.

Experiment 1
At a chosen Northern Hemisphere location, the student placed a stick vertically into the ground so that 1 meter of its length was left above ground. The student knew that the length of the shadow was related to the height of the Sun above the horizon and that the shadow would point away from the direction of the Sun. The length in meters (m) and direction of the shadow cast by the stick were measured one hour after sunrise (Shadow A), at mid-morning (B), at noon (C), at mid-afternoon (D), and one hour before sunset (E) on each of the three days. The direction of each shadow was determined by placing a magnetic compass at the base of the stick and aligning the north arrow with the north mark on the compass. The direction of each shadow was then determined by a comparison with the compass face markings. The results are recorded in Table 1.

 Table 1 Shadow Day 1 Day 2 Day 3 Length (m) Shadow  direction Length  (m) Shadow  direction Length  (m) Shadow  direction A 5.0 SW 8.6 NW 6.8 W B 1.2 W 2.9 NNW 1.7 NW C 0.3 N 2.3 N 0.9 N D 1.2 E 3.0 NNE 1.8 NE E 5.0 SE 8.6 NE 6.9 E

 Experiment 2     The following year, the student repeated Experiment 1 at a chosen location in the Southern Hemisphere. The results are in Table 2.

 Table 2 Shadow Day 1 Day 2 Day 3 Length (m) Shadow  direction Length  (m) Shadow  direction Length  (m) Shadow  direction A 9.0 SW 5.0 NW 6.9 W B 3.2 SSW 1.1 W 1.8 SW C 2.5 S 0.3 S 1.0 S D 3.2 SSE 1.1 E 1.8 SE E 9.1 SE 5.0 NE 6.9 E

If the experiments were repeated after pounding the stick farther into the ground so that only 0.5 m was exposed, how would this affect the shadow lengths?

You are given a lot of information that you do not need to know to answer this question.  The passage tells you that the original stick had one meter exposed above the ground.  If you pound it in until .5 meters are exposed, you have taken half of the stick away.  Smaller things logically must make smaller shadows (think of a bug and a building at the same time of day), so look down at your answer choices.

A. They would be twice as long as those in the original experiments.
B. They would be one-and-one-half times as long as those in the original experiments.
C. They would be one-half as long as those in the original experiments.
D. They would be one-fourth as long as those in the original experiments.

(A)  The shadows would only get larger if more of the stick were exposed.  Eliminate this choice.
(B)  The shadows would only get larger if more of the stick were exposed.  Eliminate this choice.
(C)  This answer makes sense because if half of the original stick is showing, it must have half the shadow of the original stick as well.
(D)  Even if you carefully analyze all of the numbers in the chart, there are no important numbers that have a relationship of one-fourth.  Eliminate this choice.