Solving Linear Equations and Graphing Linear Equations, Exams of Advanced Education

A variety of topics related to solving linear equations and graphing linear equations. It includes questions on solving for an unknown variable when given an equation with fractions, identifying the equation of a line parallel to another line, finding the equation of a line given a point and the slope, simplifying polynomial expressions, and ordering letters to create a new sentence. Practice problems and explanations to help students develop their skills in these areas of mathematics. By studying this document, students can gain a deeper understanding of linear equations, their properties, and how to work with them effectively.

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2024/2025

Available from 10/24/2024

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ACCUPLACER PRACTICE TEST
If a ≠ b and 1/x + 1/a = 1/b, then x =
A. 1/b - 1/a
B. b - a
C. 1/ab
D. a - b/ab
E. ab/a - b - E
The graph of which of the following equations is a straight line parallel to the graph of y = 2x ?
A. 4x - y = 4
B. 2x - 2y = 2
C. 2x - y = 4
D. 2x + y = 2
E. x - 2y = 4 - C
An equation of the line that contains the origin and the point (1, 2) is
A. y = 2x
B. 2y = x
C. y = x -1
D. y = 2x +1
E. y/2 = x - 1 - A
An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for
$360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950.
What is the number of two-bedroom apartments?
A. 3
B. 4
C. 5
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ACCUPLACER PRACTICE TEST

If a ≠ b and 1/x + 1/a = 1/b, then x = A. 1/b - 1/a B. b - a C. 1/ab D. a - b/ab E. ab/a - b - E The graph of which of the following equations is a straight line parallel to the graph of y = 2x? A. 4x - y = 4 B. 2x - 2y = 2 C. 2x - y = 4 D. 2x + y = 2 E. x - 2y = 4 - C An equation of the line that contains the origin and the point (1, 2) is A. y = 2x B. 2y = x C. y = x - D. y = 2x + E. y/2 = x - 1 - A An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of two-bedroom apartments? A. 3 B. 4 C. 5

D. 6

E. 7 - E

If θ is an acute angle and sin θ = 1/2, then cos θ = A. - B. 0 C. 1/ D. √3/ E. 2 - D 5y(2y - 3) + (2y - 3) = A. (5y + 1) (2y + 3) B. (5y + 1) (2y - 3) C. (5y - 1) (2y + 3) D. (5y -1) (2y - 3) E. 10y (2y - 3) - B One ordering of the letters T, U, V and W from left to right is UTVW. What is the total number of orderings of these letters from left to right, including UTVW? A. 8 B. 12 C. 16 D. 20 E. 24 - E From 5 employees at a company, a group of 3 employees will be chosen to work on a project. How many different groups of 3 employees can be chosen? A. 3

D) apart, but would still be dependent - (A) In the modern world, groups of people may live thousands of miles APART AND STILL BE DEPENDENT on each other politically, culturally, and economically JOSE WANTED TO STUDY HE TRIED TO KEEP his roommates quiet; but he did not succeed. A) Jose wanted to study he tried to keep B) Jose wanted to study, he tried to keep C) Because he wanted to study, Jose tried to keep D) Jose wanting to study, and trying to keep - (C) BECAUSE HE WANTED TO STUDY, JOSE TRIED TO KEEP his roommates quiet; but he did not succeed. PREDICTIONS TWENTY YEARS AGO that the phonograph record was about to become obsolete have proven to be true. A) Predictions twenty years ago that B) Predictions twenty years ago, C) Twenty years ago, predictions that D) Predictions, twenty years ago - (A) PREDICTIONS TWENTY YEARS AGO that the phonograph record was about to become obsolete have proven to be true. WHEN YOU MOVE OUT OF AN APARTMENT BEFORE THE CONTRACT EXPIRES, THIS is an example of breaking a lease. A) When you move out of an apartment before the contract expires, this B) You move out of an apartment before the contract expires, this C) Moving out of an apartment before the contract expires D) The fact that you move out of an apartment before the contract expires - (C) Moving out of an apartment before the contract expires is an example of breaking a lease KNOCKED TO HIS KNEES, THE QUARTERBACK LOOKED as if he were in pain.

A) Knocked to his knees, the quarterback looked B) The quarterback was knocked to his knees, looked C) The quarterback looked knocked to his knees D) The quarterback, looking knocked to his knees, - (A) KNOCKED TO HIS KNEES, THE QUARTERBACK LOOKED as if he were in pain YESTERDAY THE PRESIDENT ANNOUNCED THAT HE WOULD RETIRE FROM POLITICAL LIFE, TO AMAZED REPORTERS A) Yesterday the President announced that he would retire from political life, to amazed reporters. B) Yesterday the President announced that he would retire from political life, amazing reporters. C) The President, to the amazement of reporters, announced that he would retire from political life yesterday. D) Yesterday the President announced to amazed reporters that he would retire from political life. - (D) Yesterday the President announced to amazed reporters that he would retire from political life. Mr. Wilson PLANNNG to teach a course in physics next fall a. planning b. are planning c. with a plan d. plans - plans Using the spell checker, she eliminated a number of errors on her paper. rewrite Whole sentence, beginning with..

These BOOKS, WHICH WAS PUBLISHED IN THE LATE EIGHTEENTH CENTURY, are very valuable. a. books which was published in the late eighteenth century b. books in the late eighteenth century c. books which were published d. books, which is published, in the eighteenth century - books which were published

  1. The hikers were at the bottom of the canyon, and they discovered an abandoned mineshaft. Rewrite, beginning with ----After the hikers were... The next words will be a. at the bottom of the canyon, and they discovered an abandoned mineshaft. b. at the bottom of the canyon, they discovered an abandoned mineshaft. c. at the bottom of the canyon they discovered an abandoned mineshaft. d. at the bottom of the canyon when they discovered an abandoned mineshaft. - at the bottom of the canyon, they discovered an abandoned mineshaft. Good money managers control their present expenses, and they invest surplus dollars to meet their future needs. Rewrite the sentence using -------BECAUSE

The best choice will be a. Good money managers, because they control their present expenses, they invest surplus dollars to meet their future needs. b. Because good money managers control their present expenses, they invest surplus dollars to meet their needs. c. Because good money managers control their present expenses they invest surplus dollars to meet their needs. d. Good money managers control their present expenses, because they invest surplus dollars to meet their future needs. - b. Because good money managers control their present expenses, they invest surplus dollars to meet their needs. In a large city, you may have massive traffic jams on your daily commute to work. Rewrite this sentence omitting YOU. a. In a large city, a person may have massive traffic jams on your daily commute to work. b. In a large city, a resident may have massive traffic jams on his daily commute to work. c. In a large city, massive traffic jams may be part of the daily commute to work. d. In a large city, massive traffic jams may be part of the everyday commute on the way to work. - In a large city, massive traffic jams may be part of the daily commute to work. PANTING, THE CAB PULLED AWAY just as Judy arrived. a. Panting, the cab pulled away b. The cab pulled away panting

  1. Tornadoes are winds which rotate in a counterclockwise direction and look like a funnel at the bottom of a cloud, as anyone who is familiar with Oklahoma weather knows. Rewrite, beginning with Anyone who is ... Your new sentence will include a. knowing tornadoes b. and knows tornadoes c. has knowledge of tornadoes d. knows that tornadoes.... - (d) anyone who is familiar with Oklahoma weather Knows that tornadoes are winds which rotate in a counterclockwise direction and look like a funnel at the bottom of a cloud.
  2. Our supervisor, Betty White, handles all of the personnel problems that arise because she is an extremely diplomatic person in working with people. Rewrite, beginning with: Being extremely diplomatic in working with people, The next words would a. all of the personnel problems.... b. our supervisor, Betty White, .... c. and that .... d. problems arising with personnel.... - (B) Being extremely diplomatic in working with people, our supervisor, Betty White, handles all of the personnel problems that arise Chief Harrigan was invited to our safety meeting, he can demonstrate the correct use of

fire extinguishers. "PICK LETTER" a. Chief Harrigan was invited to our safety meeting, he can demonstrate the correct use of fire extinguishers. b. Chief Harrigan was invited to our safety meeting, therefore, he can demonstrate the correct use of fire extinguishers.. c. Chief Harrigan was invited to our safety meeting; therefore to demonstrate the correct use of fire extinguishers. d. Chief Harrigan was invited to our safety meeting so that he can demonstrate the correct use of fire extinguishers. - d

  1. Coming in from Fourth Street, the STUDENT UNION IS SEEN BY STUDENTS WHO ARE ARRIVING CAMPUS "PICK LETTER" a. Student Union is seen by students who are arriving on campus. b. students who are arriving on campus see.... c. the students having seen the Student Union.... d. the Student Union is being seen .... - b Because modern machinery can function unattended, the unemployment rate may increase, THIS COULD POSSIBLY CAUSE THE POVERTY RATE TO BE HIGHER "PICK LETTER' a. this could possibly cause the poverty rate to be higher. b. possibly causing a higher poverty rate. c. the possible raising of the poverty rate will be the result d. this causes the poverty rate to increase. - B

Rewrite, beginning with WE TOURED GENERAL GRANT'S ... The next words should be a. home, it is in Illinois. b. home, and it is in Illinois. c. home; in Illinois. d. home visiting in Illinois. - (B) We toured General Grant's home, and it is in Illinois.

  1. Tornadoes are made up of winds with speeds of 30 or 40 miles an hour or higher, and they cause the most deaths. Rewrite, beginning with Because tornadoes are made up of winds with speeds of 30 or 40 miles an hour or higher, ... The next words should be a. and they cause the most deaths. b. causing the most deaths. c. the tornadoes causing the most deaths. d. they cause the most deaths. - (D) Because tornadoes are made up of winds with speeds of 30 or 40 miles an hour or higher, they cause the most deaths
  2. If you want to create a beautiful room, having a large sum of money is not nearly so important to the finished setting AS IS THE KNOWLEDGE OF BASIC DECORATING.

"PICK LETTER"

a. as is the knowledge of basic decorating. b. as knowing the basics of decorating. c. but the knowledge of basic decorating. d. like the knowledge of basic decorating. - B

  1. The smaller a group is, the more opportunities we have to get to know other people well and to establish close ties with them.
  2. Two-person groups are the setting for many of our most intense and influential relationships.
  3. In three-person groups, coalitions become possible, with two members joining force against a third member.
  4. Five-person groups are large enough so that people feel they can express their emotions freely and even risk antagonizing one another, yet they are small enough so that members show regard for one another's feelings and needs. Which statement best expresses the unstated main idea of the above sentences? a. Two-person groups are an important part of our lives. b. A five-person group is better than a two-person group. c. The number of people in a group affects relationships within the group. d. Groups play a central part in every human activity, within family, the workplace, and the - C Consider how this passage reflects the relationship between cause and effect: In 1970 about sixty small and medium-sized factories in the United States adopted a four-day workweek.

-Most people collect Star Wars toys for sentimental reasons. -Some people collect them strictly to make money. What is the relationship between the two sentences? A. Cause & Effect B. Contrast C. Repetition D. Statement & Example - B

  1. Answer the question based on what is stated or implied. There are two kinds of jewelry that I do. There is commercial jewelry - class rings, necklaces, the kinds of things most people wear. I sell these items to meet my expenses for raw materials, supplies, and to make my living. The other, more creative work I do makes me feel that I am developing as a craftsperson. The author of this passage implies that: A. Artists are poor. B. There is no market for creative work. C. Rings and necklaces cannot be creative. D. Commercial and creative work fulfill different needs for the artist - D
  2. Read the passage below and choose the one organizational pattern from the lettered choices following the passage that best describes the way the author organized this paragraph. Did you know that the U.S. postal service handles 40% of the world's mail volume? Japan is the second largest carrier of cards and letters, but it handles only 8% of the world's mail. Perhaps the reason that

the U.S. handles such a large volume of mail is the large number of personal letters American citizens write. Personal letters do not require a strict format, but they do have a few guidelines. The date should be written at the top of the letter, either in the center or in the right-hand corner. The salutation, "Dear ____," should begin the letter and should be followed by a comma instead of a colon which is used in the salutation of a business letter. The body of the letter should sound like you, and say the things you intend to say. - C

  1. Read the statements below and then choose the best answer to the question from the list of lettered choices that follows. -Jenny does not like cake. -She does not like to bake it, to ice it, or to eat it. What does the second sentence do? A. It states the cause of the first. B. It emphasizes what is stated in the first. C. It compares the three things Jenny does not like about cake. D. It draws a conclusion about Jenny. - B
  2. Read the sentences below and then choose the best answer to the question from the list of lettered choices that follows. When we write a check that we know is going to "bounce", we are in fact performing a criminal act. It is a crime to knowingly write a "hot" check, one we know we don't have sufficient funds to cover. What does the second statement do? A. It provides supporting evidence for the first statement. B. It draws a conclusion from the first statement. C. It restates the central idea of the first sentence.

Scuba diving is the most exhilarating experience I have ever had. The first time I went, the dark mirror of the water beckoned me to drop from the side of the boat. I jumped feet first and entered a brightly colored world populated with fish, plants, and objects I had never dreamed of. Which of the following best describes the mood of the author after having this experience? A. Bored B. Anxious C. Excited D. Serena - C

  1. Read the passage below and then choose the best answer to the question from the list of lettered choices that follows. Did you know that a half-gallon milk container holds about $50.00 in pennies? While all investment counselors realize that we must accumulate money in order to save, most recommend different kinds of investments for people who are in different stages of life. Older investors, those with limited funds to invest, or people with greater financial and family commitments, should take fewer risks. Younger, wealthier, and unmarried investors can afford to venture into the unknown. Which of following best describes the main idea of this passage? A. A penny saved is a penny earned. B. Our ages and stages of life are part of what determines the investments that are best for us. C. Old people have the most money. D. Young people should concentrate on collecting pennies. - B
  2. Read the passage below and choose the best answer to the question. Answer the question on the basis of what is stated or implied in this passage.

Experienced truck drivers often travel in a convoy - a group of trucks that are traveling to the same part of the country. Convoys can help truckers to stay alert. The author implies that professional long-distance truck drivers may avoid traveling alone because: A. They might drive too fast. B. They want to arrive before anyone else. C. Accidents happen more frequently to lone truck drivers than to car drivers who travel alone. D. Long-distance travel can cause drowsiness. - D

  1. Read the passage below and choose the best answer to the question. Huge beasts such as the dinosaur have never really become extinct. Mothra, a giant caterpillar who later becomes a moth, destroys Tokyo, and stars in the 1962 Japanese film named for him. Mothra is born, dies, and reborn regularly on classic movie channels. In Japan Mothra is one of the most popular films ever made. Mothra has survived the creation of more current scary creatures such as giant apes, extraterrestrial beings and swamp creatures. More than 30 years after his creation, Mothra still lives. The main subject of the passage is: A. The reasons that fads do not endure. B. The lasting appeal of Mothra. C. The difficulty of marketing good horror movies. D. Old models for creatures are still used because making new monsters is expensive. - B
  2. Two underlined sentences are followed by a question or statement. Read the sentences, and then choose the best answer to the question or the best completion of the statement. Anxious to ensure that America would depart from European traditions regarding religion and royalty, the early U.S. could be described as a place that focused more on work than on the entertainment