ILTS Test of Academic Proficiency (TAP) 2018-11-09T23:00:06+00:00

ILTS Test of Academic Proficiency (TAP)

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ILTS Test of Academic Proficiency (TAP)

ILTS TAP Overview

The Test of Academic Proficiency (TAP) tests an Illinois teaching candidate’s knowledge of reading comprehension, language arts, mathematics, and writing. It is designed to draw upon up-to-date and relevant expectations for those seeking employment as new teachers.

The Test of Academic Proficiency (TAP) tests an Illinois teaching candidate’s knowledge of reading comprehension, language arts, mathematics, and writing. It is designed to draw upon up-to-date and relevant expectations for those seeking employment as new teachers.

The TAP is computer based. Candidates schedule to sit for the test at a Pearson Testing Center. Some candidates may be entitled to a TAP exemption based on certain ACT or SAT scores.

Information and screen shots obtained from the Illinois Licensure Testing System website: http://www.il.nesinc.com/Home.aspx

Information and screen shots obtained from the Illinois State Board of Education website: https://www.isbe.net/Documents/TAP_PassRates400_20170101_20170331.pdf https://www.isbe.net/Documents/act-sat-testing-in-lieu-of-tap.pdf

Quickfacts

Cost: All subtests: $113. Individual subtest: $68. It can become quite expensive to sit for multiple components, multiple times. It pays to be prepared!

Scoring: You need to have a scaled score of 240 or higher on each subtest. You only need to pass each subtest once.

Pass rate: Typically, the pass rate hovers around 26% for the test as a whole. Candidates tend to perform best on the Writing subtest but poorest on the Mathematics subtest. The Reading and Language Arts subtest is also challenging.

Best Attempt Rate

Total Reading Comprehension Language Arts Mathematics Writing
26% 42% 38% 34% 93%

Study time: Required study time will vary from examinee to examinee. Some test takers (who had been away from math for a while) reported success after spending 10 days reviewing the mathematics content.

The best approach to studying is to find a great, thorough program that includes practice tests and study guides (I know a great one!).

SAT/ACT exemption:

Candidates are exempt from the TAP if one of the following is applicable:

Scores must be sent to the Illinois State Board of Education in a sealed envelope. When ordering, use code 3001 for ACT and 6773 for SAT.

What test takers wish they would’ve known:

  • Test takers report that knowing the content isn’t enough; candidates must be able to apply their knowledge.
  • Candidates who had not taken a major math course since high school suggests spending a lot of time reviewing the mathematical concepts covered on the TAP.
  • Preparation is also key to overall success. Some examinees, who took the entire test without studying, could not complete all of the subtests.

ILTS TAP: Reading Comprehension

Overview

If the subtest is taken individually, you will have 150 minutes to answer 60 multiple-choice questions.

The Reading Comprehension subtest has six standards:

  • Meaning of Words and Phrases (17%)
  • Main Idea and Supporting Details (17%)
  • Inference and Interpretation (17%)
  • Relationships Among Ideas (17%)
  • Critical Reasoning (16%)
  • Outlining and Summarizing (16%)

So, let’s start with Meaning of Words and Phrases.

Meaning of Words and Phrases

If the subtest is taken individually, you will have 150 minutes to answer 60 multiple-choice questions.

The Reading Comprehension subtest has six standards:

  • Meaning of Words and Phrases (17%)
  • Main Idea and Supporting Details (17%)
  • Inference and Interpretation (17%)
  • Relationships Among Ideas (17%)
  • Critical Reasoning (16%)
  • Outlining and Summarizing (16%)

So, let’s start with Meaning of Words and Phrases.

This section tests your knowledge on vocabulary, phrases, and figures of speech.

Candidates will need to be able to define specific words isolated from a wider passage, recognize the differences between homonyms, explain the significance of phrases that may be natural to native speakers but challenging when taken word by word and understand synonyms and antonyms.

Let’s discuss some concepts that will more than likely appear on the test.

Figurative Language

Figurative language is typically used to boost or intensify writing. It can include hyperbole, metaphors, personification, similes, and symbolism. It addresses readers by bringing to mind ideas that may not be directly stated but draw upon the reader’s knowledge, experience, and feelings. Easily stated – it refers to any writing that goes above the normal meaning of words.

Context Clues

Context clues are the hints or evidence within a sentence or passage that help to give the reader a sense of the meaning of an unusual or difficult word or phrase. Sometimes the words can be jargon, typical to specific fields but not often used in a wider context. A common TAP exam question asks you to choose a definition for a word based on its context.

Main Idea and Supporting Details

This section tests your knowledge on synthesizing the fundamental claim or expression of the writing and the items that support it. Typically, the main idea is general and applies to the passage in its entirety instead of a very specific answer related to a sentence or small portion. The introductory and conclusion paragraphs should establish the main idea and other paragraphs will contain supporting details.

Here are some concepts that you may see on the test.

Main Idea

This is the central point of a paragraph or entire passage. It often is presented at the beginning of a paragraph or passage; the remainder of the paragraph or passage provides support and explanation. A typical test question asks you to choose a statement that best expresses the main idea of a paragraph or passage.

Sequence of Events

The sequence of events refers to the actual chronology or order of a story. Authors may begin a narrative at a later point and go back or present side notes from points that precede the general narrative. Consider how before, during, after, then, and similar words can change the placement of events in chronology.

Inference and Interpretation

This section tests your knowledge on contextualizing, or placing, a written source. The answers are not direct and require the reader to read between the lines.

Here are some things you may see on the test.

Author’s Purpose

This is what the author of a passage intended to accomplish with their writing. For example, sometimes the author is attempting to inform readers or put forth a certain viewpoint or perspective on a topic.

Author’s purpose is usually related to the main idea. One type of question on the TAP exam lists several ideas and asks you to identify the author’s main purpose.

Point of View

This refers to the angle through which the narrative unfolds. In recollections, for example, narrators will refer to themselves in the first person using the pronouns “I” or “we.”

A narrative may also use third person perspective in which the events are recorded by a third party, present or omniscient, indicated through the pronouns “he,” “she,” “it,” and “they.”

Though not common, second person perspective directly draws the reader into the text through the use of the pronoun “you”.

Relationships Among Ideas

This section tests your knowledge on the connection between ideas in a passage. Recognizing cause and effect, similarity or difference, or other means that drive a narrative or provide description is important. It is crucial to be able to identify the anchors that tie ideas together.

Here is something you may see on the test.

Drawing Conclusions

This is related to making inferences and interpretations. Thinking through a passage and its details (while making inferences) allows a reader to reach conclusions or judgements. On the exam, you will be asked to make a comparison based on the relationships presented.

Critical Reasoning

This section tests your knowledge on decoding the validity, credibility, strengths, and weaknesses of a piece of writing. You will need to be able to recognize opinion from fact and what assumptions, stated or unstated, the writing depends on.

Here are some things you may see on the test.

Qualifying Language

These are sort of like the terms that serve to make statements more or less certain. Reread that last sentence without the qualifying language “sort of like.” Qualifying language serves to strengthen or weaken action and can make claims more concrete or vague.

Let’s take a look at another example:

It appears that it will snow during the night, so be careful driving.

Appears acts as qualifying language to introduce confident uncertainty. Weather prediction is not 100% accurate, and the qualifying language reminds us that, though it is likely, it is not certain.

Bias

A bias is a particular preference or dislike for someone or something. In writing, this may be very apparent when directly stated, or it may be revealed by the vocabulary, phrases, or tone a writer uses. An exam question may ask you to analyze why an author makes a particular claim.

Outlining and Summarizing

This section tests your knowledge on the arrangement and content of a passage. Passages will typically include a distinct introduction, body, and conclusion. Closely examine what the author writes in each to be able to create an outline or summary of the main ideas.

Here is something you may see on the test.

Summary

A summary is a condensed and to-the-point shortening of a passage or portion of a passage. Try to match exact details from an answer choice with components of the passage. One typical question type for this standard asks you to choose a correct outline that corresponds to the main ideas presented in the passage.

And that’s some basic info about the Reading Comprehension subtest.

Now, let’s look at a few practice questions in each area to see how these concepts might actually appear on the real test.

ILTS TAP: Reading Practice Questions and Answers

Reading Comprehension Practice Questions & Answers

Use the following passage to answer questions 1-4.

(1) Determining which foods are junk and which aren’t can be confusing. Is fast food junk? What about high-calorie or convenience-store foods? Think of it this way: If the food has very few vitamins, minerals, (3) and other nutrients that you need for optimal health, it’s probably junk. The main principle to remember is that food classified as junk will have a lot of sugar, fat, or salt.

(5) The effects of junk food are no laughing matter. Junk food can lead to obesity, heart disease, and diabetes. But you may not realize how much it can immediately make you feel like, well, junk. The fat in (7) those foods can build up on your blood vessel walls, Dr. Harold Jayne explains, which “makes it harder for your blood vessels to circulate blood around your body.” That buildup can quickly affect how well (9) you are able to perform during sports and other exercise.

Question 1 

Which of the following statements best expresses the main idea of paragraph 1 of the selection?

  1. Nutritious food contains vitamins and minerals
  2. All fast food can be classified as junk food
  3. It is easy to tell which foods are junk and which foods are nutritious
  4. Junk foods have low nutritional content and high amounts of sugar, fat, or salt

Correct answer: 4. This is the correct answer.

Question 2

Which of the following statements best expresses the main idea of paragraph 2 of the selection?

  1. Heart disease is the leading cause of death in women
  2. Eating nutritious food can boost your athletic performance
  3. Eating junk food can be harmful to your lungs
  4. Eating junk food can negatively affect your health

Correct answer: 4. “Negative health effects” is correct because the author stresses how eating junk food can be harmful to your health.

Question 3

Which of the following is the best definition of the expression no laughing matter as it is used in line 5 of the selection?

  1. A humorous concept
  2. A serious issue
  3. A controversial issue
  4. A debatable issue

Correct answer: 2. A serious issue is correct because the colloquial phrase “no laughing matter” means “not something to joke about.” Clearly, the author wants the reader to know that the effects of junk food are serious because multiple healthy warnings are included.

Question 4

Which underlined word or phrase is used incorrectly in the selection?

  1. It’s
  2. Effect
  3. No laughing matter
  4. Principle

Correct answer: 2. Effect is the correct answer choice. In the sentence, “That buildup can quickly effect how well you are able to perform during sports and other exercise,” the author should have used the verb affect, not the noun effect. Affect and effect are quite different in meaning, although they are frequently confused. Affect is primarily a verb meaning “have an effect on or make a difference to.” Effect, on the other hand, is used both as a noun and a verb, meaning “a result” as a noun or “bring about a result” as a verb.

Use the following passage to answer questions 5-7.

(1) While most people can name plenty of their favorite artists, ask someone what makes an artist great, and you’ll likely get a different answer from each person you ask. Try to compare the greatness of (3) different artists and you might start an argument. That’s because feeling connected to a work of art is an incredibly personal experience. The same piece of work may affect two people in very different (5) ways, ranging from delight to indifference to disgust. Some works of art end up in the trash, some incite riots, and some are put on the cover of magazines. Still, the art that ends up in the trash could be (7) discovered and treasured years later, while the art on the magazine cover can end up forgotten. No matter what happens to the art, as long as it exists, it always has the potential to inspire others.

Question 5

The author probably uses the word “indifference” in line 5 to mean:

  1. lack of interest
  2. concern
  3. bias
  4. compassion

Correct answer: 1. Lack of interest is correct. The author has given context clues to help the reader, creating a spectrum of ways people view art: from positive (delight) to negative (disgust). The definition of indifference, or lack of interest, lands right in the middle.

Question 6

The author’s main purpose in this selection is:

  1. to show that responses to art are subjective and personal.
  2. to show which qualities make art great.
  3. to show that artistic standards don’t change.
  4. to show that people don’t care about art.

Correct answer: 1. “Responses to art are subjective…” is correct because the author explicitly states that responses to art are personal. In addition, the author shows that art is subjective, or influenced by personal feelings, tastes, or opinions, by stating that “the same piece of work may affect two people in very different ways.”

Question 7

According to the information presented in the selection, people disagree on the greatness of art and artists because:

  1. feeling connected to art is a personal experience
  2. art is irrelevant in society today
  3. art has the potential to inspire others
  4. the standards of great art haven’t changed since the Renaissance

Correct answer: 1. “Art is a personal experience” is correct because the author explicitly states in the selection that “feeling connected to a work of art is an incredibly personal experience.”

Use the following passage to answer questions 8-10.

1          Americans spend about 1.5 billion dollars a day on groceries, but supermarkets and grocery stores want shoppers to spend even more. A typical grocery store has about 50,000 products to sell to customers. Grocery stores have found creative and clever methods to make sure that shoppers buy more of these products.

2          Some stores use heat maps to track which aisles customers linger in, looking at products. This helps supermarket owners and managers figure out where people spend the most time in the store. Many stores provide discount cards that not only offer reduced prices to shoppers but also can electronically track products that customers purchase. At the checkout counter customers will be offered coupons for items similar to their purchases. One supermarket has started giving customers a handheld self-checkout device linked to the store’s discount card. This device alerts customers to sales as they walk by or scan certain products. This may sound convenient, but researchers like Joseph Turow of the University of Pennsylvania worry about customer privacy and the possibility of stores selling the shopping details of their customers to other companies.

3          Store owners know that milk and eggs are common items on many grocery lists, so these items should be at the front of the store, right? Actually, most stores place those items deeper into the store so that shoppers have to pass tantalizing products on their way to get the needed items. Florists, bakeries, and produce sections are usually at the front of the store because the items in them will appeal to shoppers’ senses, enticing customers to make purchases. Managers know that red signs get the attention of shoppers and that yellow and white signs have a calming effect. They also know that the human eye is likely to focus on products that are at eye level, so that is where the most expensive products are placed on the shelves. Less expensive products are placed higher or lower. Some companies negotiate with the supermarket to ensure that their products are in prime locations to make them more appealing than a competing brand’s products.

4          While the customer is trying to spend the shortest amount of time and the least amount of money while shopping, the supermarket is trying to encourage the shopper to do the opposite. A study by a food marketing group showed that about 60% of the items bought at the supermarket were not on the customer’s original list. If it sounds sneaky, it is! But an informed customer can see through these gimmicks and avoid coming home with extra items.

Question 8

Which of the following is the best summary of the above selection?

  1. Technology has become one of the most successful methods that supermarkets employ to study customer buying trends
  2. Supermarkets use some tricky techniques to get their customers to spend more time and buy more things in their stores
  3. Supermarkets set up their stores in a very specific way in order for their shoppers to have the best possible experience
  4. Customers should be informed about supermarket strategies that entice them to buy more items than were originally on their list

Correct answer: 2. This passage focuses on the various methods used by supermarkets to ‘trick’ their customers into spending more and buying more, and thus, staying longer in their stores. This is the best answer.

Question 9

Which of the following is the best summary of the purpose of paragraph 2?

  1. The use of technology in supermarket analysis has many positive outcomes for both the supermarket and the customer
  2. Customer privacy is an important factor to think about when it comes to using technology to track customer habits
  3. Supermarkets have begun employing technology in their strategy to not only track, but also attract customers who shop in their stores
  4. Supermarkets should use caution when employing technology in collecting data for customer analysis

Correct answer: 3. Paragraph 2 details a few different ways supermarket utilize technology to collect and analyze data about their customers. Thus, this option is best.

Question 10

Which of the following is an opinion stated in the passage?

  1. “They also know that the human eye is likely to focus on products that are at eye level, so that is where the most expensive products are placed on the shelves.”
  2. “Some stores use heat maps to track which aisles customers linger in, looking at products.”
  3. “A study by a food marketing group showed that about 60% of the items bought at the supermarket were not on the customer’s original list.”
  4. “This may sound convenient, but researchers like Joseph Turow of the University of Pennsylvania worry about customer privacy and the possibility of stores selling the shopping details of their customers to other companies.”

Correct answer: 4. The study done by Turow also involves Turow’s opinion. He “worries,” and his worry is based on his opinion. Although his opinion is based on his research, he still forms an opinion. Thus, this choice is best.

Getting the Help You Need

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ILTS TAP: Language Arts

Overview

If the subtest is taken individually, you will have 150 minutes to answer 60 multiple-        choice questions.

The Language Arts subtest has seven standards:

  • Command of Standard Usage (17%)
  • Mechanical Conventions (17%)
  • Purpose and Audience (17%)
  • Unity, Focus, Development, and Organization (17%)
  • Editing and Revision (17%)
  • Communication (16%)
  • Writing Assignment

So, let’s start with Command of Standard Usage.

Command of Standard Usage

This section tests your fluency and command of the particular English spoken in the United States of America.

Let’s discuss some concepts that will more than likely appear on the test.

Subject-Verb Agreement

This refers to matching the correct number form of a verb with a subject. If the subject is singular, then the verb should be singular, too. If the subject is plural, then the verb must also be plural, as well. A question for this standard may ask you to identify an incorrect usage. Let’s take a look at a sentence with incorrect subject-verb agreement.

My sisters enjoys eating pizza.

The subject, sisters, is plural – sister and sister. The verb, enjoys, is singular. Let’s fix this sentence:

My sisters enjoy eating pizza.

The key to making sure your subjects and verbs agree is knowing the singular and plural forms of subjects and verbs. There are some rules that are helpful to know.

Modifiers

Modifiers are the words or phrases that change or clarify another word in the sentence. They add more detail or explanation. Most commonly these are adjectives (describing nouns) or adverbs (describing verbs).

Modifiers change a portion of the sentence but can be removed without otherwise affecting the grammar. This makes them dependent. A typical test question may ask for necessary changes for a particular paragraph to smooth the writing or make it correct.

Here is an example:

The home team won the game.

Simple, but let’s add a modifier that better describes this hypothetical game:

The home team unquestionably won the game.

The adverb unquestionably is a modifier of the verb won.

There are rules for the placement of modifiers, but typically they come before the word they modify.

Mechanical Conventions

This section tests your knowledge on the particular spelling, capitalization, and punctuation of English in the United States.

Here is a concept that you may see on the test.

Standard Capitalization

All sentences begin with a capital letter, and all proper words and titles are also capitalized. Let’s examine this in action:

The city of berlin was divided during the Cold War.

This sentence is incorrect. Cold War is properly capitalized as a proper noun, but Berlin is also a proper noun.

As a test taker, you will be asked to determine if a sentence needs correcting. Test questions may also ask whether a particular change is necessary, or you may be prompted to choose a more precise or appropriate word.

Purpose and Audience

This section tests your knowledge on the particular spelling, capitalization, and punctuation of English in the United States.

Here is a concept that you may see on the test.

Writer’s Purpose

This is what drives the writing – what the author is hoping to achieve or accomplish. A question for this standard may give you a spot in the passage to add a sentence. You will have to choose which answer choice would be most consistent with the author’s purpose and audience.

Unity, Focus, Development, and Organization

This section tests your knowledge of recognizing an author’s level of efficiency. Thesis and organization need to be evaluated as effective or not. You will need to recognize good writing and determine when there may be parts that cloud the narrative or are not necessary.

Here is a concept that you may see on the test.

Writing Organizational Methods

This refers to the type of structure a piece of writing follows. It can be chronological, order of importance, problem and solution, or compare and contrast. The test will ask you to identify which structure is used in a passage.

Editing and Revision

This section tests your knowledge on improving imprecise or bulky writing. You will need to be able to edit writing to bring clarity and consistency. It will be helpful to recognize unnecessary words or phrases, as well as suggest more precise words.

Let’s discuss some concepts that will more than likely appear on the test.

Imprecise Words and Phrases

Using imprecise words and phrases undermines writing by introducing vagueness or obscurity. By substituting precise words, a reader will have a greater sense of the specific ideas of a piece of writing. Test questions may ask you to consider a more appropriate word choice for one indicated in a passage.

Let’s take a look at an example:

Ernest Hemingway is a strong writer whose works are well-known.

Strong is vague. A more precise word could reveal more about his writing or its effects. The test will give alternative choices; all but one would shift the meaning of the sentence without adding precision. The best choice for this example may be something like:

Ernest Hemingway is an influential writer whose works are well-known.

Transition Words

In writing, these are the words or phrases that act as links between ideas and signal how they relate to one another. They act to remove confusion between ideas. A typical test question will ask you which transition words can be inserted into a sentence to better understand the sequence of the writer’s ideas.

Communication

This section tests your knowledge on the usage and employment of recognized and effective writing mechanics.

Let’s discuss some concepts that will more than likely appear on the test.

Topic Sentence

This is a sentence that explains what a paragraph is about (like a summary of the focus). A test question may ask you to identify a portion of writing that should be revised to avoid repetition.

Sentence Fragments

Sentence fragments are a group of words that look like a sentence but aren’t. They are actually missing a subject or a verb and can’t stand on their own. They do not have an independent clause, which all sentences need.

On the test, a typical question will ask you to indicate the portion of a numbered paragraph that is not a standard sentence. Here is an example of a fragment:

British soldiers in the American Revolution.

This begins with a capital letter and ends with a period but does not have any action – there is no verb. What about these soldiers? What did they do? Let’s fix it:

British soldiers in the American Revolution are sometimes called redcoats.

There it is! With a subject and a verb (independent clause), we now have a complete sentence.

Writing Assignment

The writing assignment asks you to prepare an organized and thoughtful piece of writing in English, as it is used in the United States. The instructions will ask you to account for content, purpose, and audience.

You will take a position on an issue then support it with details in a composition that follows standard conventions of organization, spelling, grammar, and punctuation. Test takers tend to do very well on the writing component.

And that’s some basic info about the Language Arts subtest.

Now, let’s look at a few practice questions in each area to see how these concepts might actually appear on the real test.

ILTS TAP:Language Arts Practice Questions and Answers

Language Arts Practice Questions & Answers

Question 1 

Ansel Adams was₁ a famous photographer who enjoyed₂ photographing nature. The Ansel Adams Gallery currently sells₃ not only his original photographs, but also reproductions of his classic work.

Which part of the sentence contains a grammatical error?

  1. No error
  2. 1
  3. 2
  4. 3

Correct answer: 2. The sentence contains no error.

Question 2

It bothers me when Casey₁ says that she₂ is inarticulate, because she₃ is more articulate than me₄.

Which part of the sentence contains an error in pronoun usage?

  1. 4
  2. 1
  3. 2
  4. 3

Correct answer: 1. Pronouns must agree in case. Problems of case can occur with comparisons, because they are really shorthand sentences which usually omit words. Complete the above comparison in your head, and you can choose the correct case for the pronoun. You wouldn’t say, “She is more articulate than me is.” You would say, “She is more articulate than I am.”

Question 3

Many₁ people do not see the importance of continuing to educate oneself₂, but teachers are known to be life-long learners₃.

Which part of the sentence above contains an error?

  1. 1
  2. No error
  3. 3
  4. 2

Correct answer: 4. Because of the plural noun “people,” the pronoun in agreement should also be plural. Thus, “oneself” should be changed to “themselves”.

Question 4

My band has been rehearsing daily₁. Because we have a concert in two weeks₂. It is our first paid gig, so we are all looking forward to it₃.

Which part of the passage is a fragment?

  1. 1
  2. No error
  3. 3
  4. 2

Correct answer: 4. A sentence is a group of words that has a subject, a verb, and expresses a complete thought; a sentence fragment is a group of words that does not express a complete thought. The word “because” makes “2” a fragment. The corrected sentence would read, “My band has been rehearsing daily, because we have a concert in two weeks.”

Question 5

Trying to fall asleep in the uncomfortable bunk₁, the sheets felt uncomfortably hot₂ and the breeze refused to blow₃.

Which part of the sentence contains a misplaced modifier?

  1. No error
  2. 2
  3. 3
  4. 1

Correct answer: 4. “Trying to fall asleep…” is a dangling modifier, or a modifier that modifies the wrong word or phrase because the word or phrase that it should modify is missing from the sentence. A corrected version of the sentence would read, “Trying to fall asleep in the uncomfortable bunk, I felt uncomfortably hot in the sheets and the breeze refused to blow.”

Question 6

Lasagna is a delicious comfort food, it can be made healthier with the addition of vegetables₁. Although it is time consuming to make, it is my favorite dish to prepare₂. Maybe it’s my favorite because my grandmother passed down her recipe to me₃.

Which part of the passage contains a comma splice?

  1. 1
  2. No error
  3. 2
  4. 3

Correct answer: 1.  A comma splice error occurs when two complete sentences are joined by only a comma, like in answer “1”. In order to fix the comma splice, the writer could change the comma to either a semicolon or a period. Alternatively, the writer could insert the coordinating conjunction and after the comma.

Question 7

Mark₁ your music is so poignant₂ and original, and I love how it reflects your passion. We will probably hear you on the radio₃ someday!

Where should a comma be inserted to make the sentence grammatically correct?

  1. After “poignant”
  2. No comma is needed
  3. After “Mark”
  4. After “radio”

Correct answer: 3. Use commas to separate the name of a person being spoken to from the rest of the sentence. The name “Mark” at the beginning of the sentence should be followed by a comma.

Question 8

Low₁ introductory credit card rates₂ usually revert back₃ to standard interest rates after the initial period is complete₄.

Select the word or phrase that is redundant and can be removed without changing the meaning of the text.

  1. 2
  2. 3
  3. 1
  4. 4

Correct answer: 2. Redundant words and phrases needlessly repeat information that is given elsewhere in the sentence. “Back” and “revert” are redundant. “Back” can be removed without changing the meaning of the sentence, so it should be taken out.

Question 9

Plastic bags have come under fire recently, with some cities even banning them altogether. ___________, paper bags are not necessarily more friendly to the environment than plastic bags. _________, a recent study showed that a paper bag has to be used three times before it can be said to have a lower impact on global warming than a plastic bag.

Complete the passage with the transitions that help the reader progress logically from one idea to the next.

  1. However, As a result
  2. However, In fact
  3. For instance, Likewise
  4. Therefore, In fact

Correct answer: 2. “However, In fact” is correct. The first blank requires a transition of opposition (however) to show the contrast between the thoughts about plastic bags being bad for the environment with the fact that paper bags are no better. The second blank requires the transition in fact to introduce an example that substantiates the claim that paper bags are not friendlier to the environment than plastic bags.

Question 10

Sports are a wonderful means for mankind to exercise one of its most basic principles: competition with our fellow man. Surrounding all types of sports is the concept of sportsmanship – the respect and ethical behavior shown to all participants of a contest. The spirit of the game, in many cases, is more important than the outcome of the match; a true competitor understands this. This is why many of our most beloved athletes are not always the most talented performers—it is the players who play with the purest motive, for the sake of the team, and with respect for all opponents, who gain the respect and admiration of the fans.

There are greater lessons to be learned from sports than being well liked by fans. Sports, and by extension, the athletes who play them, extend beyond cultural differences; surely styles of play can vary between countries and regions, but in general, sports are played the same everywhere. Similarly, fans of a sport are able to appreciate incredible athletic feats or displays of true sportsmanship regardless of the player. Simply put, in a day and age when settling cultural differences is of utmost importance, sports are a reasonably viable way to bring the world closer together.

Lastly, international events such as the Olympic Games or World Cup are perfect opportunities to show the world that international cooperation and peace are possible. Sports can and should be used as instruments of change in an uncertain world. They can also be proponents of peace.

The Olympic Creed says it best: “The most important thing in the Olympic Games is not to win but to take part, just as the most important thing in life is not the triumph, but the struggle. The essential thing is not to have conquered, but to have fought well.”

The passage above discusses the importance of sports. Select the best evidence from the passage to support the author’s belief that sports can connect different cultures.

  1. “The essential thing is not to have conquered, but to have fought well”
  2. “Sports are a reasonably viable way to bring the world closer together”
  3. “The spirit of the game, in many cases, is more important than the outcome of the match”
  4. “There are greater lessons to be learned from sports than being well-liked by fans”

Correct answer: 4. The study done by Turow also involves Turow’s opinion. He “worries,” and his worry is based on his opinion. Although his opinion is based on his research, he still forms an opinion. Thus, this choice is best.

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ILTS TAP: Mathematics

Overview

If the subtest is taken individually, you will have 150 minutes to answer 50 multiple-choice questions.

Calculators are not allowed, but a formulas sheet is provided. This contains definitions of mathematical symbols, units of measurement abbreviations and conversions, and perimeter, volume, and area formulas for geometry.

Check out the formulas sheet here.

The Mathematics subtest has five standards:

  • Integers, Fractions, Decimals, and Units of Measurement (20%)
  • Reasoning (20%)
  • Algebra and Geometry (20%)
  • Data Analysis and Statistics (20%)
  • Applied Problems (20%)

So, let’s start with Integers, Fractions, Decimals, and Units of Measurement.

Integers, Fractions, Decimals, and Units of Measurement

This section tests your ability to solve problems with numbers written with and without fractions or decimals. This may include very large integers or very small fractions.

Here are some concepts that you may see on the test.

Dividing Fractions by Fractions

Dividing fractions is the same as multiplying fractions once you flip the numerator (the top number) and the denominator (the bottom number) of the second fraction.

For example:

(2/3)/(4/1)

First, flip the second fraction.

(2/3)/(4/1)

Then, use multiplication instead of division.

(2/3)(4/1)

You’ll find the answer to be 8/3.

Test questions will involve multiplying and dividing fractions as well as converting percentages to fractions (within the same problem).

Scientific Notation

This allows very large numbers or very small numbers to be written in a shorter form. It takes advantage of powers of ten (ten multiplied by itself the number of times indicated with an exponent).

This can also be used to express very small fractions by dividing by ten instead of multiplying. This is indicated with negative exponents. 

Let’s look at this in action.

Look at the number 0.0000000018.

That’s a lot of zeros.

It can then be expressed as -1.8 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 or simplified with scientific notation:

1.8 x 10-9

The exponent tells us how many places the decimal point should be moved. In this example, the decimal will move to the left.

Reasoning

Inductive Reasoning

This type of reasoning starts with a specific scenario and makes conclusions that are general. It is small example or scenario that lends itself to a wider conclusion or theory.

These can be wrong, but the process comes from valid logic or pattern recognition. A typical test question will present a continuing pattern and ask you to select the next, most likely figure.

Deductive Reasoning

This refers to the process of reaching a conclusion through logic from given statements. This will always involve justification.  Test questions will involve selecting a statement that must be true based on established truths.

Algebra and Geometry

This section tests your knowledge on the mathematics of unknowns and the properties and relationships of figures and shapes.

Here are some concepts that you may see on the test.

Solving for x

In algebra, “x” stands for an unknown number. Using inverse (opposite) operations to manipulate equations will help you find x.  It is pretty straightforward. Let’s go through an example:

– 3(1 +2) = 23

The goal is to isolate x and simplify as much as possible.

– 3(3) = 23

– 9 = 23

= 32

= 16

x = 4

Though the formulas sheet will be useful for many algebra problems, you should be comfortable with linear algebra expressions.

The test will present a real-world word problem, so take what you need from it to build an equation and solve for x.

Volume

Volume is the measurement of the space inside a three-dimensional object. The formulas sheet will provide you with the formulas you need to solve these problems.

Data Analysis and Statistics

This section tests your knowledge on the collection, analysis, and interpretation of sets of numbers.

Here is a concept that you may see on the test.

Measures of Central Tendency

Statistics can be used with large sets of numbers to determine what single number best represents the set of data. Measures of central tendency include mean, median, mode, and range. Typical test questions ask you to compare two presented distribution curves or find the mean, median, mode, or range of a given data set.

Applied Problems

This section tests your ability to use mathematics in everyday practice, specifically relating to fields with specialized knowledge like business or science.

Here is a concept that you may see on the test.

Word Problems

These are mathematical problems expressed in writing rather than in typical math notation. They can be considered “real world” problems in which you will need to determine the proper operations and set up any models or equations.

And that’s some basic info about the Mathematics subtest.

Now, let’s look at a few practice questions in each area to see how these concepts might actually appear on the real test.

ILTS TAP:Mathematics Practice Questions and Answers

Mathematics Practice Questions & Answers

Question 1 

Gracie helped put together gift bags for each graduate for her dance school’s graduation party. Each dance school graduate received a gift bag with either a figurine of a ballet dancer or a keychain with a miniature pair of ballet slippers attached to it. The ratio of ballet dancer figurines to gift bags was 3 to 8. If there were 88 gift bags for the dance school graduates, how many received ballet slipper keychains?

  1. 24
  2. 33
  3. 55
  4. 64

Correct answer: 3. The ratio of ballet dancer figurines to gift bags was 3 to 8. Therefore, out of every 8 gift bags, 3 had ballet dancer figurines and 5 (because 8 – 3 = 5) bags contained ballet slipper keychains. Therefore, the ratio of ballet slipper keychains to the total gift bag count is 5:8. If the total number of gift bags is 88, then the number of bags that contain ballet slipper keychains is 5/8 of 88, or 55.

Question 2

Some friends had a contest to guess the number of M&M’s in a jar. Tina guessed 270, Terry guessed 50% more than Tina, Twyla’s guess was twice Tina’s, and Toby guessed 500. There were actually 450 M&Ms in the jar.  Which friend guessed closest to the correct number?

  1. Toby
  2. Tina
  3. Terry
  4. Twyla

Correct answer: 3. Tina guessed 270. The difference between her guess and the actual number of M&Ms is 450 – 270 = 180. Terry guessed 50% more than Tina: 270 + 0.5(270) = 270 + 135 = 405. The difference between Terry’s guess and the actual number of M&M’s is 450 – 405 = 45. Twyla guessed 2 x 270 = 540. The difference between Twyla’s guess and the actual number of M&Ms is 540 – 450 = 90. Toby guessed 500. The difference between Toby’s guess and the actual number of M&Ms is 500 – 450 = 5. With differences of 45, 50, 90 and 180, Terry’s difference of 45 M&Ms is the closest guess.

 

Question 3

The Parent Teacher Organization at Douglass Elementary baked cookies. The ingredients to make each batch of cookies cost $3. Each batch made 20 cookies. The PTO sold each cookie for $0.50. They produced b batches of cookies and sold every single one of them. What is a valid expression, in terms of b, for the profit that the PTO made for their cookie sale?

  1. [(0.5)(3) + 20]b
  2. [(0.5)(20) + 3]b
  3. [(0.5)(20) –3]b
  4. [(0.5)(3) – 20]b

Correct answer: 3. In general, Profit = Revenue – Expenses. The revenue that the PTO brought in from their bake sale was $0.50 for every cookie sold. There were 20 cookies in each of b batches of cookies made and sold. Therefore, there were a total of 20b cookies produced and sold. With each cookie selling for $0.50, the total revenue from the sale was 0.50 × 20b, which can also be expressed as (0.5)(20b) or (0.5)(20)b. The expense to produce the cookies was $3 for every batch. Therefore, expenses = 3b. Profit can now be expressed as the difference between revenue and expenses: (0.5)(20)b – 3b. The answer choices show b factored out, and so the answer [(0.5)(20) –3]b can be selected.

Question 4

Which of the following equations correctly models the relationship in the table?

  1. y = 3x + 1
  2. y = 3x – 5
  3. y = x – 2
  4. y = 2x

Correct answer: 2. The equation y = 3x – 5 correctly models the relationship in the table. The x-values in this table all increase by 2 units while the y-values in the table increase by 6 units. The consistent changes in x and y illustrate that the data is linear. Accordingly, a slope can be calculated by using the formula slope = (y2 – y1)/(x2 – x1) and the coordinate pairs from any two points in the table. For example, (10 – 4)/(5 – 3) = 6/2, which reduces to a slope of 3/1, or simply 3. Of the answer choices, only two options include a slope of 3. Given the trend of the data in the table, y = 3x + 1 cannot be the answer (because the table in the data shows negative y-values for x < 1, and so it cannot have a y-intercept of +1). Therefore, y = 3x – 5 is the correct answer. Alternatively, the answer choices can be tested. Coordinate pairs from the table can be substituted into the appropriate positions for x and y and the equation that makes true statements for at least two points is the best answer. In this case, the points (5, 10) and (3, 4) are tested and shown to be true here: 10 = 3(5) – 5 and 4 = 3(3) – 5.

Question 5

A pole broke 15 feet from its base. The base remains perpendicular to the ground. The break was not complete, however, so the top portion of the pole extends to the ground while still remaining attached to its base, as shown in the diagram above. The top portion of the pole hits the ground 8 feet from the place where the base of the pole enters the ground. How tall, in feet, was the pole before it broke?

  1. 32
  2. 25
  3. 17
  4. 23

Correct answer: 1.  Because the pole is perpendicular to the ground, the pieces of the pole form one leg and the hypotenuse of a right triangle. The space on the ground between the base of the pole and the (former) top of the pole is the other leg of the right triangle. The two legs of the right triangle, then, are 15 feet and 8 feet. Therefore, the length of the top portion of the pole is the length of the hypotenuse of the right triangle and can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle will equal the square of the hypotenuse of that triangle. The formula for the Pythagorean Theorem is written a² + b² = c², where a and b are the leg lengths and c is the length of the hypotenuse. In this case, then, the equation to solve is 8² + 15² = c². Following the order of operations correctly makes the equation 64 + 225 = c², and then 289 = c². The equation is solved for c by taking the square root of each side and using only the positive version of the square root of 289, which is 17. [Also note that “8, 15, 17” is a Pythagorean Triple, and so the missing side could have been found without actually making the calculations for the Pythagorean Theorem.] Because the top portion of the pole has a length of 17 feet, the total height of the pole before it broke would have been the 15-foot portion still in the ground, plus the additional 17 feet, or 15 + 17 = 32 feet.

Question 6

The cement pipe used in a storm drain system is an 8-foot long right circular cylinder with a wall thickness of 3 inches and an outside diameter of 24 inches. Which of the values below best approximates the volume, in cubic feet, of the interior of the pipe? (The formula for the volume, V, of a right circular cylinder with radius r and height h is V = πr²h.)

  1. 1
  2. 2,034.7
  3. 113.0
  4. 14.1

Correct answer: 4.  If the diameter of the pipe is 24 inches, then the radius of the pipe is 12 inches (because d = 2r, where d = diameter and r = radius). If the wall of the pipe has a thickness of 3 inches, then the interior of the pipe has a radius of 12 – 3 = 9 inches. Because the calculation is to be performed in cubic feet and not in inches, 9 inches must be converted to feet. This can be done using the conversion factor 1 foot/12 inches to cancel inches and bring in feet. 9 inches × 1 foot/12 inches = 9 feet/12, which reduces to ¾ feet, or 0.75 feet. Therefore, the radius to use in the volume calculation is 0.75 feet. The length of the cement pipe was given as 8 feet. Accordingly, the value to use as the height of the right circular cylinder is 8 feet. Finally, substitutions can be made, and the appropriate calculations performed, using 3.14 as an approximation for π in the formula V = πr²h so that the volume of the interior of the pipe is discovered to be approximately 14.13 cubic feet. The best answer to select from the options, therefore, is 14.1. V = π(0.75)²(8)= π(0.5625)(8)= π(4.5)≈14.13 cubic feet.

Question 7

If 15 milliliters (mL) is equivalent to ½ ounce (oz.), which equation could be used to find n, the number of mL in 1 cup?

  1. n = 15 × ½ × 8
  2. n = 15 × 8 ÷ ½
  3. n = 15 ÷ ½ + 8
  4. n = 15 ÷ 8 × ½

Correct answer: 2. There are 8 ounces in 1 cup. Because the problem references ½ oz., it must be determined that there are 8 ÷ ½ = 8 × 2 = 16 portions with a volume of ½ ounce in a single cup. Each of these ½ ounce portions is the equivalent of 15 mL. Therefore, n = 15 × 8 ÷ ½ is the number of milliliters in 1 cup.

Question 8

The dot plot above shows the shoe size of the 25 students in Ms. Redmond’s kindergarten class. What is the median of these shoe sizes?

  1. 5
  2. 11
  3. 9
  4. 13

Correct answer: 1. The median of a set of data is the middle value (in a data set that contains an odd number of pieces of data) when the data is ordered. The dot plot given in the prompt shows the data of the students’ shoe sizes organized from least (size 9) to greatest (size 13). Each dot represents a single student with that size shoe. With 25 pieces of data, the 13th piece of data is the median (with 12 values that are smaller than or equal to it, and 12 values that are greater than or equal to it). In this case, the 13th piece of data is in the column for size 10.5, and so the median of the set is 10.5.

Question 9

A bag of marbles contains 3 red marbles, 5 blue marbles, and 2 yellow marbles. Edgar draws a marble from the bag, replaces it, gives the bag a good shake, and draws again. Which calculation should be used to determine the probability that Edgar drew a red marble both times?

  1. 3/10 + 2/9
  2. 3/10 + 3/10
  3. 3/10 × 2/9
  4. 3/10 × 3/10

Correct answer: 4. The situation of selecting two marbles with replacement (a marble is drawn, it is replaced/put back in the bag, and another marble is drawn) creates two independent events (the outcome of one event does not impact the outcome of the other event because the first marble selected is back in the bag before the second marble is chosen). Therefore, the probability for both Event A and Event B to occur is found by multiplying the probability for Event A with the probability for Event B. The probability of each event is found by comparing the number of successful outcomes possible in the situation to the total number of possible outcomes. In this case, a successful outcome (for each draw) is selection of a red marble. There are 3 red marbles in the bag. The total number of possible outcomes is found by counting each of the marbles in the bag (3 red + 5 blue + 2 yellow = 10 marbles). Therefore, P(red) = 3/10 each time Edgar pulls a marble out of the bag full of red, blue, and yellow marbles. The probability of drawing red on both draws, then, is found by multiplying each probability: 3/10 × 3/10.

Question 10

Which of the following equations is written in slope-intercept form?

  1. 3y – 5x = 10
  2. y + 5 = 3x
  3. y = 3x + 5
  4. x = 3y + 5

Correct answer: 3. Slope-intercept form of the equation of a line is y = mx + b where m and b are numbers representing the slope of the line and its y-intercept, respectively. Only the answer choice y = 3x + 5 is presented in this format (with the slope of the line being 3 and its y-intercept being 5).

Getting the Help You Need

Feeling overwhelmed? Don’t worry! We have you covered.

Go to 240tutoring.com and sign up for our ILTS TAP study guide.

It comes with a 48 hour no questions asked refund policy, so if you don’t like it, you can request a full refund within 48 hours.

Also, it comes with the 240Tutoring Guarantee. If you score a 90% or higher on our practice test, but fail the real exam, you’re entitled to a money-back refund.

Get the Study Guide
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