SAT Quick Challenge  Week 11
Saturday, April 17, 2021
Providence Baptist Church is concerned about you, your family, your friends, and the community. We are following the recommendations to limit the number of people in our inperson gatherings. For this reason, all SAT Preparation classes at the church are cancelled until further notice.
Although the current COVID19 pandemic abruptly ended the Spring 2020 SAT classes, technology offers an opportunity for students to refresh, retain, and/or acquire SAT knowledge and skills essential for answering various kinds of questions often found on the SAT. Therefore, the Providence Baptist Church SAT Preparation Program has provided this “SAT Quick Challenge” website. Each Saturday, this site will be updated with a set of activities that will help students acquire and maintain mastery of important skills that help lead to high SAT scores. Be sure to review the SAT Math Formulas and the SAT Math Operations each week. You can find them in the dropdowns at the bottom of this page.
Please stay healthy and safe. Remember the three Ws: Wear, Wait, Wash.
SAT Math  Questions from Week 11 (April 17, 2021)
Statistical Sampling: Margin of Error
Some sampling questions on the SAT require the use of a “margin of error.” Consider the following situation: The Guilford County School Board has directed the superintendent of schools to prepare an obesity report on children in the Guilford County public schools. Among other information in the data section of the report, the average weight of 8th graders will be indicated. It will be expensive and time consuming to weigh every 8th grader, since there are over 6,000 8th graders in Guilford County public schools. Instead, the average weight of a random sample of Guilford County 8th graders will be determined.
Suppose this average is 94 pounds. Based on this result, what conclusion can be made about the average weight of the entire population of 8th graders? Since the sample was a random sample, it is plausible that the average weight of the population of 8th grades is 94 pounds. The estimate is reasonable, but it is unlikely to be exactly correct; the actual average for the population may be somewhat less than 94 pounds or somewhat more than 94 pounds. Statisticians use a “margin of error” to describe the precision of an estimate.
If this example were an SAT question, you might be given results indicating that, for a random sample of 100 8th graders, the estimated average weight was 94 pounds with a margin of error of 3 pounds. A logical interpretation of this result is that it is plausible that the average weight of all 8th graders in the population is greater than 91 pounds and less than 97 pounds.
There are two factors that affect the value of the margin of error: the variability (standard deviation) in the data and the sample size.
 Variability: the larger the standard deviation, the larger the margin of error; the smaller the standard deviation, the smaller the margin of error.
 Sample size: the larger the sample size, the smaller the margin of error.
Answer the following questions.
 A researcher surveyed a random sample of students from a large university about how often they see movies. Using the sample data, the researcher estimated that 23% of the students in the population saw a movie at least once each month, with a margin of error of 4%. Which of the following is the most appropriate conclusion about all students at the university, based on the given estimate and margin of error?
 It is unlikely that less than 23% of the students see a movie at least once per month
 At least 23%, but no more than 25%, of the students see a movie at least once per month
 The researcher is between 19% and 27% sure that most students see a movie at least once per month
 It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%.
 Jason conducted a survey of a randomly selected group of 1824year old American males to determine how many basketball games young men of that age watch in a month. He excluded tournament games, “March madness,” and other playoff games. After reviewing his results, he decided that his margin of error was too high and that he would conduct the survey again. Which of the following changes could Jason make to decrease his margin of error?
 Increase his sample size.
 Decrease his sample size.
 Increase the age range in his sample.
 Include 1824 year old American females in his sample.
 A group of researchers conducted a phone survey of 200 randomly selected people in Durham in an attempt to determine the average amount spent by people in the city every month on groceries. They calculate that the average is $197 with a margin of error of 6%. Rounded to whole dollars, which of the following represents the confidence interval the researchers should report?
 $102  $192
 $185  $209
 $187  $207
 $191  $203
SAT Math  Answers to Questions from Week 11 (April 17, 2021)
 D is correct.
A is incorrect; it could be less than 23%.
B is incorrect: it could be less than 23%, and it could be more than 25%.
C is incorrect: this is an incorrect interpretation of the margin of error  A is correct  Increase the sample size.
B and C would increase the margin of error.
D is incorrect since the research is about young men.  This is one of those SAT trap questions: if you do not read the question carefully, you will be trapped into choosing the wrong answer. The trap is the “6%” margin of error and the average of $197. The trap is adding 6 to 197 and getting 203, subtracting 6 from 197 and getting 191, and choosing D  $191  $203. This calculation is incorrect because we should add and subtract dollars, not a percentage point. We must express the margin of error in dollars.
6% of $197 = $197 x .06 = $11.82 This is the margin of error.
$197  $11.82 = $185.18 and $197 + $11.82 = $208.82
These round to $185 and $209
Thus, the correct answer is B: $185  $209
SAT Verbal  Questions from Week 11 (April 17, 2021)
SAT Quick Challenge K21
Formal or Casual Language
Formal speech is reserved for people who understand, and may have special training in, what is being discussed (science, technology, politics, etc.). Therefore, such communication can involve long, complex sentences that use elaborate, unusual words and phrases related specifically to the topic being discussed. Casual speech, however, is used for everyday language. It is noted for shorter, conversational sentences which may include friendly chatter, figures of speech, or even slang. Some SAT questions ask you (1) to determine whether a passage uses formal or casual language and then (2) to complete a sentence with a word or word group which matches the language used in the passage.
Practice classifying language as formal or casual by reading the sample passage below. Then select the choice beneath the passage which best replaces the underlined part of the last sentence in the paragraph. However, if you think that the underlined part is already correct, select choice A  NO CHANGE.
Tip: A formal passage must have a formal answer, and a casual passage must have a casual answer.
Sample Passage: Kinds of Locksets. Locksets routinely fall into two main categories: mortise and cylindrical. The former has a rectangular body that will glide into a similarly shaped pocket. The latter has a rotund body that slips into a bore hole and connects with the latch bolt. Mortise locksets are generally used for warehouses and industrial sites, while cylindrical locksets are routinely used for a wide range of residential spaces. Locksets are generally sold (1) in major chain stores such as Lowe's and Home Depot, and (2) in department stores such as Walmart and Sears, but you can often find larger selections and the best prices online. Hence, locksets are likely to be less expensive at Lowe's.
A. NO CHANGE B. cheaper at Sears C. higher at Walmart D. more costeffective online
Answer: Since you can often find larger selections and the best prices online, locksets sold online are likely to cost less than the others. Also, costeffective is a formal term that matches the language used in the passage. Hence, D is the correct answer. NOW, COMPLETE EXERCISE K21 BELOW.
Exercise K21  Formal or Casual Language Directions. On the blank line after each passage, write the answer choice which best replaces the underlined part 




SAT Verbal  Answers to Questions from Week 11 (April 17, 2021)
 C
 C
SAT Verbal  Questions from Week 10 (April 10, 2021)
SAT QUICK CHALLENGE J21
Using the Correct Word
Deciding which of two commonly confused words should be used may not be as difficult as one might think initially. The tips below explain how to use some words in that category correctly.
Commonly Confused Word Pair A: "less" vs. "fewer"
RULE: If the commonly confused word is followed by a singular noun and refers to something that cannot be counted, use the word "less." If the commonly confused word is followed by a plural noun and refers to something that can be counted, use the word fewer.
Sentence 1:
During meals, Mrs. Parker usually has food on her plate than her son has on his.
Explanation 1:
A singular noun (food) follows the word in question and names something that cannot be counted. (NOTE: You can count individual food items, but not the concept of "food.") Therefore, the missing word must be "less."
Correct Sentence:
Mrs. Parks usually has less food on her plate than her son has on his.
Sentence 2:
When I take my time, I make mistakes than I do when I rush.
Explanation 2:
A plural noun (mistakes) follows the commonly confused word and refers to something that can be counted. Therefore, the missing word is "fewer."
Correct Sentence:
When I take my time, I make fewer mistakes than I do when I rush.
Commonly Confused Word Pair B: "much" vs. "many"
RULE: If the commonly confused word is followed by a singular noun and refers to something that cannot be counted, use the word "much." If the commonly confused word is followed by a plural noun and refers to something that can be counted, use the word many.
Sentence 3:
During meals, Mrs. Parker's son usually has more food on his plate than she has on hers.
Explanation 3:
A singular noun (food) follows the commonly confused word and names something that cannot be counted. (NOTE: You can count individual food items, but not the concept of "food.") Therefore, the missing word is "much."
Correct Sentence:
Mrs. Hall's son usually has much more food on his plate than she has on hers.
Sentence 4:
When I rush, I make more mistakes than I do when I take my time.
Explanation 4:
A plural noun (mistakes) follows the commonly confused word and refers to something that can be counted. Therefore, the missing word is "many."
Correct Sentence:
When I rush, I make many more mistakes than I do when I take my time.
Directions. On the line that follows each statement below, place the letter of the answer choice that corrects any error in the statement. If there is no error, mark choice "A" as your answer. When you have finished the exercise, use the answer key in the "SAT Verbal  Answers to Questions from Week 10" dropdown below to check your work. 

1. The debate team students say that they have much more fun at the amusement park than at the zoo. A. NO CHANGE B. more better C. lots of more D. many more fun 

2. We scored much more points in the game this week than we scored last week. 

3. Our Girl Scouts sold less boxes of cookies at the school fair than they sold at the mall. 
SAT Verbal  Answers to Questions from Week 10 (April 10, 2021)
 A
 C
 B
SAT Math  Questions from Week 10 (April 10, 2021)
Statistical Sampling: Sample vs Population
The SAT will usually include two or three questions where you are asked to interpret the results of a sample based on a research study. For example, you might want to know what percent of the registered voters in Greensboro prefer a specific candidate. It would be expensive and time consuming to contact every registered voter in Greensboro to get their preference. Instead, pollsters would contact a sample of the voters and determine their preferences, and then use this figure as an approximation for the entire Greensboro population. However, to be able to draw conclusions about the population from the sample results, the sample must be randomly selected. To repeat, in order to generalize your findings to the entire population, the sample must be randomly selected from that population.
 The members of the Greensboro City Council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who owned dogs. The survey showed that the majority of those surveyed were in favor of the dog park. Which of the following is true about the city council’s survey?
 It shows that the majority of city residents are in favor of the dog park.
 The survey sample should have included more residents who are dog owners.
 The survey sample should have consisted entirely of residents who do not own dogs.
 The survey sample is biased because it is not representative of all city residents.
 A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?
 The majority of all fish in the pond weigh less than 2 pounds.
 The average weight of all fish in the pond is approximately 2 pounds.
 Approximately 30% of all fish in the pond weigh more than 2 pounds.
 Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.
 A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?
 At least 95% of people who go to see movies will dislike this movie.
 At least 95% of people who read books will dislike this movie.
 Most people who like this book will dislike this movie.
 Most people who dislike this book will like this movie.
SAT Math  Answers to Questions from Week 10 (April 10, 2021)

The sample was not randomly selected; it consisted only of residents who owned dogs. Thus the sample is biased and the results cannot be generalized to the entire population of Greensboro. The changes suggested in B and C would not make the sample a random sample. The correct choice is D.

What is the population here? It is not all of the fish in the pond. The population in this problem consists of all of the largemouth bass in the pond, and the sample consists of 150 of the largemouth bass. Thus, any conclusions drawn from the sample relate only to the population of largemouth bass, not to the population of all of the fish in the pond. The answer is D.

What is the population here? It is the group of people who indicated that they liked a certain book, and a random sample of 200 people was taken from that population. The population in this problem was not people who go to see movies, and it is not people who read books. Thus A and B are incorrect. There is no information about people who dislike the book; thus D is incorrect. Since the sample was randomly selected from the group of people who indicated that they liked the book, we can conclude that most people who like this book will dislike this movie. Thus answer choice C is correct.
SAT Verbal  Questions from Week 9 (March 27, 2021)
SAT QUICK CHALLENGE
Exercise I21
Gender Specific and Gender Neutral Pronouns
Pronouns for "Gender Specific" and "Gender Neutral" Nouns. A noun that identifies a male (for example, "boy") can be replaced with a corresponding gender specific pronoun such as "he" or "him." Likewise, a gender specific noun that identifies a female (for example, "girl") can be replaced with a corresponding gender specific pronoun such as "she" or "her." Be sure to replace a singular noun with a singular pronoun or pronoun phrase. Also, remember that if the noun that is being replaced has the word "each" or "every" in front of it, that noun is singular and must be replaced with a singular pronoun or pronoun phrase.
To replace a noun which does not indicate gender, you must use a gender neutral pronoun or pronoun phrase. Hence, you can replace the noun "leader" with a pronoun phrase such as "he or she" or "him or her." Plural pronouns do not indicate gender, so you must replace plural nouns, regardless to the gender they indicate, with gender neutral pronouns such as "they" or "them."
Using "One" and "You" Correctly. Whether a noun being replaced names a male or female, you can use the gender neutral pronoun "one" or "you" to replace that noun. However, do not mix or match those two pronouns (1) with each other or (2) with any other pronouns within either the same sentence or the same paragraph. Instead, maintain consistency by using the same pronoun you began with. Note the ERROR below, its explanation, and the two ways shown to correct it.
ERROR: Doctors say that to avoid catching COVID19, you should wear a mask, wash your hands at least 20 seconds, and wait at least six feet away from other people. One should also get one's COVID19 vaccination as soon as possible.
EXPLANATION: You must not use in the same sentence or paragraph both "you" and "one." Note the following two ways of correcting that error.
POSSIBLE CORRECTION 1: Doctors say that to avoid catching COVID19, one should wear a mask, wash one's hands at least 20 seconds, wait at least six feet away from other people, and get the COVID19 vaccination as soon as possible.
POSSIBLE CORRECTION 2: Doctors say that to avoid catching COVID19, you should wear a mask, wash your hands at least 20 seconds, wait at least six feet away from other people, and get the COVID19 vaccination as soon as possible.
Keeping in mind the information above, complete Exercise I21 below.
Exercise I21  Using Gender Specific and Gender Neutral Pronouns Correctly Directions. On the line that follows each statement below, place the letter of the answer choice that corrects any error in the statement. If there is no error, mark choice "A" as your answer. When you have finished the exercise, use the answer key in the "SAT Verbal  Answers to Questions from Week 9" dropdown below to check your work. 

1. Each coach can get Activity Kits for his or her team from the Special Activities Desk in the lobby. A. NO CHANGE B. their C. its D. his 

2. They can get a 15% discount on the entire cost of the event if you register before the "Early Bird" deadline of May 27.. 

3. A guest who would like to arrive early and get settled before the 10 am practice time will be glad that you can check in at 8 am. 
SAT Verbal  Answers to Questions from Week 9 (March 27, 2021)
 A
 D
 C
SAT Math  Questions from Week 9 (March 27, 2021)
Standard Deviation
The standard deviation is a measure of how far the data set values are from the mean.
The standard deviation is low if most of the values are near the mean and close together.
The standard deviation is high if most of the values are spread out over the range of values.
The SAT will not require you to calculate the standard deviation, but you must be familiar with the concept.
 The table below gives the distribution of high temperatures in degrees Fahrenheit (°F) for City A and City B over the same 21 days in March.
City A City B Temperature (°F) Frequency Temperature (°F) Frequency 80 3 80 6 79 14 79 3 78 2 78 2 77 1 77 4 76 1 76 6 Which of the following is true about the data shown for these 21 days?
 The standard deviation of temperatures in City A is larger.
 The standard deviation of temperatures in City B is larger.
 The standard deviation of temperatures in City A is the same as that of City B.
 The standard deviation of temperatures in City A is 0 and the standard deviation of temperatures in City B is negative.
 The table below shows two lists of numbers.
List A 1 2 3 4 5 6 List B 2 3 3 4 4 5 Which of the following is a true statement comparing List A and List B?
 The means are the same and the standard deviations are different.
 The means are the same and the standard deviations are the same.
 The means are different and the standard deviations are different.
 The means are different and the standard deviations are the same.
 Martin Zimmer, the star basketball player at Spingarn High School, is being evaluated by the University of Maryland for a basketball scholarship. The points he scored per game in the 19 games he played in his senior year ranged from a low of 12 points to a high of 26 points. The mean, median, and standard deviation were calculated for these points. If the lowest number of points scored and the highest number of points scored were removed from the data set, and the mean, median, and standard deviation were recalculated, which of the following is true with regard to the recalculated figures?
 The median is the same and the standard deviation is higher.
 The median is the same and the standard deviation is smaller,
 The median is different and the standard deviation is higher.
 The median is different and the standard deviation is smaller.
SAT Math  Answers to Questions from Week 9 (March 27, 2021)
 The data for City B are more spread out than the data for City A, indicating a higher standard deviation.
> B
Note: the standard deviation will never be negative. The standard deviation = 0 only if all of the numbers in the data set are exactly the same.  The mean is the same for List A and List B; it is 3.5. List B contains numbers that are closer to
the mean than are the numbers is List A. The numbers in List A are more spread out than the
numbers in List B. Thus the standard deviations are different.
> A
(Generally, the wider the range, the greater is the standard deviation.)  The median is the same; removing the smallest and largest values will not change the middle
number, which is the median. The standard deviation will be lower since numbers that are the
greatest distance from the mean are removed.
> B
SAT Verbal  Questions from Week 8 (March 20, 2021)
SAT QUICK CHALLENGE
Exercise H21
Unclear Pronoun Use
Missing, Ambiguous, or Unclear Antecedent. An antecedent is the noun (or noun phrase or noun clause) that a pronoun replaces. When that noun is not provided, a reader may not understand clearly the message the writer is trying to get across. Note ERROR 1 below.
ERROR 1. The new 4Star Video System can record and save what is happening in a baby's room much longer than any other system currently being sold. They can watch the video up to six months after it was recorded.
EXPLANATION. The message is unclear because the antecedent for the pronoun "they" was not given, and we do not know who can watch the video up to six months later. Is it police officials who are trying to find out about an incident that happened in that room? Is it family members who want to find out how the baby got our of her bed the night before? We do not know the answer.
POSSIBLE CORRECTION: "The new 4Star Video System can record and save for parents and other observers" what is happening in a baby's room much longer than any other system now being sold. They can watch the video up to six months after it was recorded." The added antecedent lets us know that the underlined pronoun "they" is talking about "parents and other observers."
Incorrect Use of "This" and "That." The pronouns "this" and "that," as well as their plural counterparts, "these" and "those," should be followed by a noun to indicate what those pronouns are referring to. Otherwise, the message will be ambiguous or unclear. Note ERROR 2 below.
ERROR 2. Health officials say that we should all fight COVID19 by wearing masks, washing our hands properly, staying at least six feet away from other people, and getting vaccinated as soon as we can. These can help us stay safe and healthy.
EXPLANATION. These what? The sentence should say what the pronoun "these" refers to.
POSSIBLE CORRECTION: "Health officials say that we should all fight COVID19 by wearing masks, washing our hands properly, and staying at least six feet away from other people. These precautions can help us stay safe and healthy." Placing the noun precautions right after the pronoun "these" tells us that the pronoun refers to the precautions.
Now complete Exercise H21 below.
Exercise H21  Unclear Pronoun Use Directions. On the line that follows each statement below, place the letter of the answer choice that corrects any error in that statement. If there is no error, mark choice "A" as your answer. When you have finished the exercise, use the answer key in the "SAT Verbal  Answers to Questions from Week 8" dropdown below to check your work. 

1. According to Mrs. Eva Harper, whether it's laying out school clothes, preparing breakfast, checking A. NO CHANGE B. theirs C. they're tasks D. it 

2. Mr. Ed Murray says that he must turn the temperature in the house down to 73 degrees at night, or the baby's 

3. Parents must now accompany their children who are under 18 whenever those children are at the mall. They are 
SAT Verbal  Answers to Questions from Week 8 (March 20, 2021)
SAT QUICK CHALLENGE H21 ANSWER KEY
Unclear Pronoun Use
 A
 B
 B
SAT Math  Questions from Week 8 (March 20, 2021 )
On the SAT, the use of the word average usually refers to the mean and is indicated by "average (arithmetic mean)."
 The key to solving any problem involving an average (mean) is to find the total of the items before you do anything else.
 There are two ways to find the total:
1) Add all of the items
2) Multiply the average by the total number of items. For many SAT problems we must use this second method.

On a given day there are 12 trains to City X with an average (arithmetic mean) of 1,400 commuters per train. If the number of trains was cut to 7 and the total number of commuters remained the same, there would be an average of how many more commuters per train?
A) 800 B) 1,000 C) 1,600 D) 2,400  Peter’s average (arithmetic mean) score on the first three of four tests is 85. If Peter wants to raise his average by 2 points, what score must he earn on the fourth test?
 The average (arithmetic mean) of 6 positive numbers is 5. If the average of the least and greatest of these numbers is 7, what is the average of the other four numbers?
A) 3 B) 4 C) 5 D) 6
SAT Math  Answers to Questions from Week 8 (March 20, 2021 )

The first thing to do is to get the total. The total number of commuters = 1,400 x 12 = 16,800 . Since the number of trains is cut to 7, we divide this total of 16,800 by 7: 16,800/7 = 2,400.
Many students make the mistake of choosing D here since we got 2,400. But the question asks: how many more commuters per train?
The answer is: 2,400
1,400

1,000 The answer is (B) 1,000 
Total number of points for the 3 tests = 85 x 3 = 255
Total number of points for 4 tests if the average is 87 = 87 x 4 = 348
The difference between the two totals is what he needs on test number 4 = 348 – 255 = 93. 
There are three totals in this problem: (1) the sum of the six numbers, (2) the sum of the largest and smallest numbers, and (3) the sum of the other four numbers
The total of the six numbers = 6 x 5 = 30
The total of the largest and smallest numbers = 7 x 2 = 14
The total of the other four numbers = 30 – 14 = 16
The average of the other four numbers = 16/4 = 4 
SAT Verbal  Questions from Week 7 (March 13, 2021)
SAT QUICK CHALLENGE
Exercise G21  The Pronoun and the Apostrophe
What is the difference between a/ noun and a pronoun? Well, there are many, but this lesson focuses on one  the use of the apostrophe. We add an apostrophe and the letter "s" to a noun to show ownership. For example, we write Carla's dog or Ron's pigeon, or even the children's school.
The Pronoun and the Apostrophe. We never add an apostrophe and the letter "s" to a pronoun to show ownership. Instead, we use special pronoun ownership words. For Carla, we would write "her" dog; for Ron, we would write "his" pigeon; and for the children, we would write "their" school.
Sometimes, we do use the apostrophe and the letter "s" for pronouns  but only to make contractions.
You will recall that a contraction is a ''short cut;" it combines two words to make one word. Examples of contractions include "I'm" (I am), "You're" (You are), etc. Remembering the difference between how apostrophes are used for nouns and how they are used for pronouns will help you earn points each time an SAT question requires you to show that you know the difference.
Study the possessive pronouns, subject pronouns, and pronoun contractions in the chart below. Then, complete Exercise G21 (beneath the chart), and use the Answer Key in the section below to check your work.
SUBJECT PRONOUNS  POSSESSIVE PRONOUNS  PRONOUN CONTRACTIONS (with the verb "to be") 

Singular  Plural  Singular  Plural  Singular  Plural  
I  We  My  Our  I'm (I am)  We're (We are)  
You  You  Your  Your  You're (You are)  You're (You are)  
He, She, It  They  His, Her, Its  Their  He's, She's, It's (He is, She is, It is) 
They're (They are) 
Now, complete Exercise G21 below.
Exercise G21  The Pronoun and the Apostrophe Directions. On the line that follows each statement below, place the letter of the answer choice that corrects any error in that statement. If there is no error, mark choice "A" as your answer. When you have finished the exercise, use the answer key in the section below to check your work. 

1. Your going to be late for school if you don't hurry up. A. NO CHANGE 

2. Its not wise to ignore the CDC guidelines for avoiding COVID19 infections. 

3. Our dance students will win the trophy because they're such excellent dancers. 
SAT Verbal  Answers to Questions from Week 7 (March 13, 2021)
SAT QUICK CHALLENGE G21 ANSWER KEY
The Pronoun and the Apostrophe
 D
 B
 A
SAT Math  Questions from Week 7 (March 13, 2021 )
There are three averages: mean, median, and mode.
 Mean; the total of the items divided by the number of items
 Median: the number that is exactly in the middle of a group of numbers when the numbers are arranged from smallest to largest,
 Mode: the number that appears most often
 The range is the difference between the largest number and the smallest number
 On the SAT the use of the word average usually refers to the mean and is indicated by “average (arithmetic mean).”
 The key to solving any problem involving an average (mean) is to find the total of the items before you do anything else.
 There are two ways to find the total:
1) Add all of the items
2) Multiply the average by the total number of items. For many SAT problems we must use this second method.
Now answer the following questions.

The average of four numbers is 5. If three of the four numbers are 3, 4, and 5, what is the fourth number?

In a class of 27 students, the average (arithmetic mean) score of boys on the final exam was 83. If the average score of the 15 girls in the class was 92, what was the average for the whole class?
A) 85 B) 86 C) 88 D) 90 
Mary’s average salary for her first 6 years of work was $30,000; her average salary for the next two years was $32,000. What was her average salary over the entire 8 years?
A) $30,900 B) $30,500 C) $31,200 D) $31,700
SAT Math  Answers to Questions from Week 7 (March 13, 2021 )

The first thing to do is to get the total.
The total = 5 x 4 = 20.
The four numbers must total 20.
3 + 4 + 5 = 12; to make 20, the fourth number must be 8. 
Girls: 92 x 15 = 1380 total for girls
Boys: 83 x 12 = 996 total for boys

2376 total for the entire class
Average for the entire class = 2376/27 = 88  30,000 x 6 = 180,000 total for the first 6 years
32,000 x 2 = 64,000 total for the next 2 years

244,000 total for the entire 8 years
Average salary over the entire 8 years = 244,000/8 = 30,500.
SAT Verbal  Questions from Week 6 (March 6, 2021)
SAT QUICK CHALLENGE
Exercise F21  Noun Pronoun Agreement Errors
A pronoun is a general word that takes the place of a noun  often, its antecedent. The antecedent is the specific noun that the pronoun is replacing, The pronoun and its antecedent will be somewhere near each other  frequently, in the same sentence. Often, the antecedent comes first.
The antecedent and the pronoun replacing it must match. Therefore, a female antecedent (Loretta or girl) requires a female replacement pronoun (she or her), and a male antecedent (Matt or boy) requires a male replacement pronoun (he or him). A singular antecedent requires a singular replacement pronoun (as in Matt or boy), and a plural antecedent (as in Loretta and Matt or the students) requires a plural replacement pronoun (as in they or them). Did you notice that the plural replacement pronouns they and them do not indicate gender? Now, note Errors 1 and 2 below.
ERROR 1: Human resources workers interview potential employees, asking him or her questions that can indicate whether those job candidates are likely to help the business achieve important company goals.
PROBLEM: The plural antecedent "potential employees" and the plural, synonymous followup noun phrase "job candidates" indicate that the missing pronoun (or pronoun phrase) must also be plural. However, the pronoun phrase "him or her" is singular.
CORRECTION: Human resources workers interview potential employees, asking them questions that can indicate whether those job candidates are likely to help the business achieve important company goals.
Now, the antecedent ("potential employees"), the needed pronoun ("them"), and the synonymous followup noun phrase ("job candidates") are all plural as they should be.
ERROR 2: Because of their keen sense of smell, a dog can be trained to locate bombs and other dangerous objects.
PROBLEM: Dog, the subject, is singular, but the pronoun antecedent, their, is plural. Since both the subject and its antecedent must match, both must be the same  both singular OR both plural.
CORRECTION: Because of its keen sense of smell, a dog can be trained to locate bombs and other dangerous objects.
Now, the the subject (dog) and the pronoun antecedent (its) are both singular.
Now, complete Exercise F21 below.
Exercise F21  Noun / Pronoun Agreement Errors Directions. Place on the line that follows each statement below the letter of the answer choice that corrects the error in the statement. If there is no error, mark choice "A" as your answer. Use the answer key in the section below to check your work. 

1. While cucumbers are generally thought of as a vegetable, it is actually a fruit. A. NO CHANGE 

2. When an unknown singer suddenly comes out with a big hit, they can get popular very fast. 

3. Thanks to his team's superior practices, they threw three Super Bowl touchdown passes. 
SAT Verbal  Answers to Questions from Week 6 (March 6, 2021)
SAT QUICK CHALLENGE F21 ANSWER KEY
Noun Pronoun Agreement Errors
 B
 D
 C
SAT Math  Questions from Week 6 (March 6, 2021 )
Solving Equations by Cross Multiplying  Continued
 We cross multiply when both sides of an equation are fractions.
 Multiply the denominator of the left side of the equation by the numerator of the right side of the equation, and multiply the numerator of the left side of the equation by the denominator of the right side of the equation.
 Set the two items equal to each other, and solve the resulting equation.
Now solve the following equations.

Assume that the following is true.
What is the value of x?
1 4 5 1
 (x) +  (x) =   
3 9 9 6 
Assume that the following three items are true.
 x ≠ 0
 x = y
 3a 9b
 = 
x y
What is the value of a in terms of b?
A) b / 3
B) b
C) 3b
D) 6b 
Assume that the following two items are true.
 x and y are positive integers
 1 7
x   = 
y 2
What is the value of x?
A) 3
B) 4
C) 6
D) 7
SAT Math  Answers to Questions from Week 6 (March 6, 2021 )

Assume that the following is true.
What is the value of x?
1 4 5 1
 (x) +  (x) =   
3 9 9 6
1 4 5 1
 (x) +  (x) =   
3 9 9 6The least common denominator for the left side of the equation is 9.
3 4 10 3
 (x) +  (x) =   
9 9 18 18
The least common denominator for the right side of the equation is 18.
7 7
 (x) = 
9 18
63x = 126
x = 0.5 
Assume that the following three items are true.
 x ≠ 0
 x = y
 3a 9b
 = 
x y
What is the value of a in terms of b?
Since x = y, substitute x for y, then solve for a.
3a 9b
 = 
x x
3ax = 9bx
3a = 9b
a = 3b
> C 
Assume that the following two items are true.
 x and y are positive integers
 1 7
x   = 
y 2
What is the value of x?
This problem might appear to be unsolvable since there are two unknowns and only one equation. But read the question carefully and proceed to solve for x.
1 7
x   = 
y 27 1
x =  + 
2 y1 1
x = (3)  + 
2 yx is a positive integer; from the answer choices we know that x = 3 or 4 or 6 or 7.
1
x = (3)  + some other value that will make the total = 3 or 4 or 6 or 7.
21
What can we add to (3)  so that we will have an integer?
21
The other value that we add is  and y = 2 since y is a positive integer.
2
Thus x = 4 > B
SAT Verbal  Questions from Week 5 (February 27, 2021)
SAT QUICK CHALLENGE
Exercise E21  Noun Pronoun Agreement Errors
Effective writers use synonymous words or phrases to rename or refer to words that have already been used in a sentence or passage. Even so, making comparisons, a singular noun must be replaced by a singular noun/noun phrase, and a plural noun must be replaced by a plural noun/noun phrase. Note Errors 1 and 2 below.
ERROR 1: The little boys in Mrs. Brown's class want to be a basketball player when they grow up.
PROBLEM: The plural noun "boys" has been replaced with the singular noun phrase "a basketball player."
CORRECTION: The little boys in Mrs. Brown's class want to be basketball players when they grow up. Now, the noun "boys" and the replacement noun phrase "basketball players" are both plural.
ERROR 2: Tina and Kenny will be a star in the school's spring play.
PROBLEM: The plural, compound subject names two people  Tina and Kenny. Yet, a singular noun phrase  "a star"  is used to replace that plural compound subject.
CORRECTION: Tina and Kenny will be stars in the school's spring play. Now, the plural compound subject, "Tina and Kenny," and the replacement noun, "stars," are both plural.
Now, complete Exercise E21 below.
Directions. Place on the line that follows each statement below the letter of the answer choice that corrects any error in the statement. If there is no error, mark choice "A" as your answer. Use the answer key at the bottom of the page to check your work.  
1. New attendance rules for football games say that fans no longer have to be limited to just the family and a A. NO CHANGE 

2. People say that the star of the new horror film is crooked thieves who cannot be trusted. 

3. The honor students received a special pass that lets them get into talent shows free. 
SAT Verbal  Answers to Questions from Week 5 (February 27, 2021)
SAT QUICK CHALLENGE E21 ANSWER KEY
Noun Pronoun Agreement Errors
 B
 D
 D
SAT Math  Questions from Week 5 (February 27, 2021 )
Solving Equations by Cross Multiplying
 We cross multiply when both sides of an equation are fractions.
 Multiply the denominator of the left side of the equation by the numerator of the right side of the equation, and multiply the numerator of the left side of the equation by the denominator of the right side of the equation.
 Set the two items equal to each other, and solve the resulting equation.
Here is an example:
6 3
 = 
x 10
3x = 60
x = 20
Now solve the following equations.

5 2x + 7
A) 0.25
 = 
2 3
B) 1.00
C) 2.5
D) 3 
Assume that the following is true.
Compute the value of the following:
3x + 2y 17
 = 
y 4
x

y

Assume that the following is true.
What is r?
p + q + r p + q
 = 
3 2
A) q + p
B) 2p + 2q
C) (1 / 2) * (p + q)
D) 1
SAT Math  Answers to Questions from Week 5 (February 27, 2021)

5 2x + 7
2(2x + 7) = 15
 = 
2 3
4x + 14 = 15
4x = 1
x = 1/4 = 0.25
> A 
3x + 2y 17
17y = 4(3x + 2y)
 = 
y 4
17y = 12x + 8y
9y = 12x
x 9 3
 =  = 
y 12 4 
p + q + r p + q
2(p + q + r) = 3(p + q)
 = 
3 2
2p + 2q + 2r = 3p + 3q
2r = p + q
p + q
> C
r =  = (1/2) (p + q)
2
SAT Math Formulas
Formulas Given in the Test Booklet
At the beginning of each math section these formulas are given in the test booklet. If you haven’t memorized them, you should be familiar with what they mean.
 Area of a circle: A = πr^{2 }
 Circumference of a circle: c = 2πr
 Area of a rectangle: A = lw
 Area of a triangle: A = ½ bh
 Pythagorean theorem: c^{2} = a^{2} + b^{2}
 30° – 60° right triangle:
 the length of the hypotenuse = twice the length of the side opposite the 30° angle.
 the length of the side opposite the 60° angle = the length of the side opposite the 30° angle times √3
 the length of the side opposite the 30° angle = ½ the length of the hypotenuse
 45° – 45° right triangle:
 the two legs are equal
 the length of the hypotenuse = the length of the either leg times √2
 The volume of a rectangular solid: V = lwh
 The volume of a cylinder: V = πr^{2}h
 The volume of a sphere: V = (4/3) πr^{3}
 The volume of a cone: V = (1/3)πr^{2}h
 The volume of a pyramid: V = (1/3)lwh
 The number of degrees in a circle = 360
 The number of degrees in a triangle = 180
 The number of radians in a circle = 2π
You are given these 12 formulas and three geometry laws on the test itself. It can be helpful and save you time and effort to memorize the given formulas, but it is ultimately unnecessary, as they are given on every SAT math section.
Formulas NOT Given in the Test Booklet
The following formulas are not printed on the test booklet; you will have to memorize them.
 The area of a square: A = s^{2}
 The perimeter of figure = the sum of all of the sides
 Area of a parallelogram: A = lw
 Area of a trapezoid: A = ½ h(b_{1} + b_{2})
 Given a radius and a degree measure of an arc from the center of a circle, find the area of the sector that is defined by the angle and the arc:
Area of a sector of a circle: A = (t/360) πr^{2} when t = the number of degrees in the central angle  Given a radius and a degree measure of an arc from the center, find the length of the arc:
Length of an arc: L = (t/360) (2πr) when t = the number of degrees in the central angle  When the angles of triangle A are equal to the angles of triangle B, the sides of triangle A are proportional to the sides of triangle B.
 x^{2} – y^{2} = (x + y)(x – y)
 (x + y)^{2} = x^{2} + 2xy + y^{2}
 (x  y)^{2} = x^{2}  2xy + y^{2}
 A function in the form of f(x) = 3x + 12 is the same as y = 3x + 12.
 The equation of the line in the slope/intercept form:
y = mx + b, where the slope = m, and the yintercept = b.  The equation of the line in standard form:
Ax + By = C, where the slope = A/B and the yintercept = C/B.  Slope – four ways to determine the slope:
 Slope = rise (vertical change)/run (horizontal change)
 Given two points on a line, (x_{1}, y_{1}) and (x_{2}, y_{2}), the slope = (y_{2} – y_{1})/(x_{2} – x_{1}).
 If the equation of the line is in the slope/intercept form, y = mx + b, the slope = m.
 If the equation of the line is in standard form, Ax + By = C, the slope = A/B
 The standard form of a parabola equation: y = ax^{2} + bx + c
 Vertex form of the parabola equation:
y = a(x – h)^{2} + k, where the vertex is the point (h,k).  Equation of a circle? (x – h)^{2} + (y – k)^{2} = r^{2} where the center of the circle is the point (h,k)
and the radius of the circle is r.  The quadratic formula:
For ax^{2} + bx + c = 0, the value of x is given by:
x = (−b ± √ b2 − 4ac ) / 2a  The key to solving average problems is to find the total of the items before doing anything else.
There are two ways to find the total:  Total= sum of the items
 Total = the average times the number of items. This method is usually required on SAT problems.
 Average speed = total distance / total time; Distance = (speed) x (time)
 SOHCAHTOA (applies to a right triangle)
 sine of an angle = side opposite the angle over the hypotenuse (SOH)
 cosine of an angle = side adjacent to the angle over the hypotenuse (CAH)
 tangent of an angle = side opposite the angle over the side adjacent to the angle (TOA)
 180 degrees = π radians
 Imaginary numbers
 i = √1
 i^{2} = 1
 i^{3} = i
 i^{4} = 1
 i^{5} = i
 i^{6} = 1
 i^{7} = i
 i^{8} = 1
etc.
 A present amount P increases at an annual rate r for t years. The future amount F in t years is:
F = P(1 + r)^{t}  A present amount P decreases at an annual rate r for t years. The future amount F in t years is:
F = P(1  r)^{t}  Item sold at discount: discount amount = original price x discount percent
 Item sold at discount: reduced price = original price x (1discount percent)
 Given two points, A(x_{1},y_{1}), B(x_{2},y_{2}), find the midpoint of the line that connects them:
Midpoint = the average of the x coordinates and the y coordinates:
(x_{1} + x_{2}) / 2, (y_{1}+y_{2}) / 2  Given two points, A(x_{1},y_{1}), B(x_{2},y_{2}), find the distance between them:
Distance = √[ (x_{2  }x_{1})^{2 }+ (y_{2  }y_{1})^{2}^{ }]
Actually, this is one formula you do not need to memorize, since you can simply graph your
points and then create a right triangle from them. The distance will be the hypotenuse, which
you can find by using the Pythagorean Theorem.  Probability of x = (number of outcomes that are x)/(total number of possible outcomes)
SAT Math Operations
Operations You Need to be Able to Perform
 Substitute values for a variable and simplify.
 Add fractions with different denominators, where the denominators are numbers.
 Add fractions with different denominators, where the denominators are variables.
 Know how to simplify complex fractions.
 In a fraction, the denominator cannot equal zero. If an equation is solved and the value of the variable makes the denominator = zero, then that value cannot be a solution to the problem.

When picking numbers, consider positive numbers, negative numbers, zero, decimals, and extreme numbers.

Understand the definitions of the terms digit, integer, number, prime number, factor, multiple, divisible, reciprocal of a number, absolute value of a number.

Know the absolute value sign.

Know the common fractiondecimalpercent equivalents.

Know how to change a fraction to a decimal or to a percent.

Know how to change a decimal to a percent.

Know how to change a percent to a decimal.

Understand the factorial concept.

Know how to compute permutations and combinations: n items taken x at a time.

Know when to use Venn diagrams.

When angles are formed when a line crosses parallel lines, several equal angles are created.

When a diagram is given in a geometry problem, consider adding one or more lines to create another figure.

Geometric figures are not necessarily drawn to scale; lines that look equal may not be equal; angles that look equal may not be equal.

In a triangle, the length of sides opposite equal angles are equal.

In a triangle, the length of a side opposite a larger angle is greater than the side opposite a smaller angle.

Know the third side rule for triangles: the length of any one side of a triangle must be less than the sum of the other two sides, and greater than the difference between the other two sides.

Two triangles are congruent if the sides of one triangle are equal to the corresponding sides of the other triangle and the angles of one triangle are equal to the corresponding angles of the other triangle.

Two triangles are similar if the angles of one triangle are equal to the corresponding angles of the other triangle and the sides of one triangle are not equal to the corresponding sides of the other triangle.

If two triangles are similar, their corresponding sides are proportional.

The measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc.

The length of an arc is a fraction of the circumference of a circle.

A line tangent to a circle produces a right angle at the point of tangency between the line and another line that connects the point of tangency to the center of the circle.

Know the exponent rules.

Know how to express a number with alternative bases using appropriate exponents; the most common problems involve changing a number to a base of 2 or a base of 3.

Know how to determine the three averages: mean, median, and mode.

Know how the normal curve, mean, and standard deviation interact.
 Read ratio problems carefully,
 A ratio can express a part to part relationship.
For example, a ratio of 1 to 2 = 1:2 = ½.  A ratio can express a part to whole relationship.
For example, a ratio of 1 to 2 has two parts and a whole (1 + 2 = 3). One part is ⅓, the other part is ⅔.  Solve linear equations when the answer is a number (one equation and one unknown.)
 Solve linear equations when one variable is in terms of other variables (one equation with all variables.)
 Solve simultaneous equations (two equations in 2 unknowns.)
 Solve quadratic equations by factoring, by using the quadratic equation, and by completing the square.
 Find the radius of a circle from the formula of a circle.
 Know how to write the formula of a circle in standard form.
 Factor an expression.
 Type 1: 3xy + 7x = x(3y + 7)
 Type 2: 2x^{2} + 13x + 15 = (2x + 3)(x + 5)
 Type 3: 2^{13} – 2^{11} = 2^{11}(2^{2} – 1) = 2^{11}(41) = 2^{11}(3)
 Solve inequalities.
 Find the price of an item after a sales tax is added.
 Find the price of an item after a percent increase.
 Find the price of an item after a percent decrease.
 Find the percent of a number.
 When one number is greater than another, find the percent greater.
 When an amount changes, find the percent change.
 Know the three averages: mean, median, and mode.
 In an average problem, the first thing to do is to find the total; there are two ways to find the total.
 Find the average of a set of numbers.
 Find the missing number in a set of numbers when the mean is known.
 From the equation of a line, determine the y intercept, x intercept, and slope.
 Understand positive slopes, negative slopes, and slope = zero.
 Equation of a parabola.
 Coordinate geometry: locate points in the xy plane.
 Know the I, II, III, and IV quadrants.
 Evaluate information in a chart.
 Word problems: write down each detail; proceed in a step by step fashion.
 Trigonometry: find the sine of an angle; find the cosine of an angle; find the tangent of an angle (remember SOHCAHTOA.)
The sine of an angle = the side opposite the angle divided by the hypotenuse (SOH)
The cosine of an angle = the side adjacent to the angle divided by the hypotenuse (CAH)
The tangent of an angle = the side opposite the angle divided by the side adjacent to the angle (TOA)  In right triangle ABC, if angle B is the right angle, then the sine of angle A = the cosine of angle C.