FTCE General Knowledge: Ultimate Guide and Practice Test
Preparing to take the FTCE General Knowledge test?
Awesome!
You’ve found the right page. We will answer every question you have and tell you exactly what you need to study to pass the FTCE General Knowledge test.
In fact, we will cover 4 key areas of the exam.
FTCE General Knowledge Test Overview
FTCE General Knowledge Overview
FTCE General Knowledge may be a required exam for anyone seeking teacher certification in any grade in Florida. It is a test of basic skills. The test ensures that teachers at all levels possess the necessary competencies and skills to effectively teach.
There are 4 subtests:
 Essay Subtest
 English Language Skills Subtest
 Reading Subtest
 Mathematics Subtest
You can register to take all or any combo of the four subtests in one session. You have to pass all subtests to earn a passing score for the exam.
The exam is a computerbased test, but don’t worry, you just need basic computer skills. If you made it to this point in your education and career, you have nothing to worry about.
Here is the subtest format and time allotment breakdown:
Subtest  Questions  Time 

Essay  1 Essay  50 Minutes 
English Language Skills  40 MultipleChoice  40 Minutes 
Reading  40 MultipleChoice  55 Minutes 
Mathematics  45 MultipleChoice  100 Minutes 
Frequently Asked Questions About the FTCE General Knowledge
Quick Facts
Cost: $130 (First attempt: any combination of subtests)
$150 (Retake: any combination of subtests)
Location: Tests are by appointment only, yearround. Click here to find a testing site near you.
What to Bring: You need to bring two valid, unexpired forms of identification in English. Click here for more information about identification requirements.
Number of Attempts: There are no limits on how many times you can take the test before you pass; however, you do have to wait 31 days between testing attempts.
Scoring: You must score at least 8 out of 12 points on the Essay Subtest to pass. For the English Language Skills, Reading, and Mathematics Subtests, you must score at least 200 points on each to pass.
When you finish taking the test, you will immediately get an unofficial pass/nonpass result based on the multiplechoice questions (unless they are experiencing score report delays). You can expect your official score within four weeks.
Click here to read more about testing policies.
Register for the FTCE General Knowledge exam here.
Frequently Asked Questions
What FTCE test(s) do I need to take?
The Bureau of Educator Certification (BEC) determines your testing requirements after you apply for certification. Click here for more info.
You may be able to demonstrate mastery of General Knowledge in another way. Click here for more info.
How long will the FTCE General Knowledge test take me?
The full test itself is 245 minutes but expect to be at the testing site longer. It takes time to get checked in and get started. Plan to arrive at least 30 minutes before your appointment time.
Do I get a break during the FTCE General Knowledge exam?
If you take all four General Knowledge subtests in a single session, you will receive a 15minute break.
What can I expect when I arrive at the testing site to take the FTCE General Knowledge test?
When you get there, expect to have your identification checked, your photo taken, your palm scanned, your eyeglasses checked, and to place your belongings in secure storage. You will be given an erasable notepad and pen. Before starting the test, you’ll have to complete a short tutorial and sign an agreement.
How do I pass the FTCE General Knowledge test?
To pass the FTCE General Knowledge test, you must first understand what is on the exam and what you will be expected to know. The best way is to review the 240Tutoring test breakdown materials and practice questions. Once you identify areas of weakness, you can begin targeting those areas with instructional content and practice questions.
Is the FTCE General Knowledge test hard?
Yea, it’s challenging. Take a look at these passing rates:
Source: Florida Department of Education, Division of Accountability, Research, and Measurement, Office of Assessment, Postsecondary. Data are provided by Evaluation Systems group of Pearson February 2018.
You have to study quality, trusted sources (like 240Tutoring).
FTCE General Knowledge 5 Top Tips

Make sure to answer every question (even if you guess)

Know how much time you have left

Eliminate incorrect answers first

Work through practice questions so you know what to expect

Study quality, trusted sources (like 240Tutoring)
Getting the Help You Need
And if this seems like a lot of information, it’s because it is. This is a test that decides if you can teach the next generation of leaders. But if you’re feeling overwhelmed, don’t be.
We’ve got the best study guides for the General Knowledge test. So, if you’re feeling overwhelmed and you don’t even know where to begin to figure out how to teach phonemic awareness or how to identify the different characteristics of the stages of writing, we’ve got you covered.
You see, our study guides are filled with hundreds of pages of instructional content and hundreds of authentic practice questions that are going to walk you through the exact concepts we’re talking about in this video in much more depth and detail. And it takes you from knowing what’s on the test to knowing what you need to know to be successful on the test and equipping you with that information so that you can be successful when you take this test.
So, if at any point, you’re just overwhelmed or you want to save a lot of time and a lot of headaches, hop over to 240tutoring.com, get the General Knowledge study guide, and make sure you’re prepared today.
FTCE General Knowledge: Essay
Overview
You will have 50 minutes to complete 1 essay question. You will get to choose between two topics. You must prepare, write, and edit your essay within the 50 minutes. All essays will be typed unless prior arrangements have been made.
Two raters will score your essay based on content and these elements:
 ideas
 focus
 organization
 style
 diction
 sentence structure
 mechanics
 capitalization
 punctuation
 spelling
 usage
Take a look at the official skills assessed via the essay:
Check out the 240Tutoring Constructed Response Questions page. It has some very good information that will help you on the test.
Overview
You will have 40 minutes to complete 40 multiplechoice questions.
The English Language Skills subtest can be neatly divided into three different sections. Those three sections are:
 Language Structure
 Vocabulary Application
 Standard English Conventions
So, let’s start with Language Structure.
Language Structure
This section tests your knowledge on how the English language works (or should work).
Language Structure questions make up about 25% of the English Language Skills subtest.
There are four big concepts you definitely have to know to get these questions correct:
 Modifiers
 Parallelism
 Effective Structures
 Patterns of Organization
The first big concept you should know is what a modifier is. Modifiers are words or phrases that change or clarify another word in the sentence. The purpose of a modifier is to add detail or explain something. These words are usually adjectives (describe nouns) or adverbs (describe verbs).
Here is an example. Look at this simple sentence:
They were running.
Now, let’s add a modifier:
They were running quickly.
The adverb quickly is a modifier of the verb running.
Get it? Good!
But, modifiers are commonly misplaced. Look at this sentence:
She purchased a car for my brother they call Lightning.
In this sentence, Lightning is the car’s name. But the placement of the modifier is all wrong, so it causes some confusion. Is Lightning the brother’s name? No! Let’s move the modifier closer to the noun it modifies:
She purchased a car they call Lightning for my brother.
See? All better.
Here’s a friendly tip: These are very simple sentences I just used. Expect the sentences on the test to be much more detailed.
The next big concept to know is parallelism. Very simply, parallel structure means that you use the same grammatical form within a sentence.
Let’s look at an example of a sentence without parallel structure:
Caroline enjoys dancing, the playground, and to take long walks.
Now, look at the same sentence but with parallel structure:
Caroline enjoys dancing, going to the playground, and taking long walks.
See how all the verbs end in –ing? That’s parallelism!
Again, these are simple sentences. Expect to see more detailed, complex sentences on the exam.
The third big concept to know is effective structures. This includes knowing how to identify and fix:
 fragments
 comma splices
 runon sentences
 syntax errors
I’ll talk about a couple of these in more detail in a little bit.
And the last big concept to know is patterns of organization. More specifically, you need to know what the modes of rhetoric are. Here, let me tell you. The most common modes are:
 narrative
 descriptive
 expositive
 argumentative
Now, those are the four broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you two specific concepts to be familiar with because they will most likely appear on the test.
Comma Splices
Comma mistakes happen. They happen a lot. A comma splice is a common comma error (wow, that was a mouthful). This error occurs when two independent clauses are joined together with a comma. It is a type of runon sentence. Let’s look at an example:
Tomatoes are not vegetables, they are a fruit.
These two independent clauses can be sentences on their own, so simply adding a comma between them just doesn’t work.
We can fix this comma splice error three ways:
By adding a conjunction:
Tomatoes are not vegetables, but they are a fruit.
By changing the comma to a semicolon:
Tomatoes are not vegetables; they are a fruit.
By making separate sentences:
Tomatoes are not vegetables. They are a fruit.
You can expect to have to correct a comma splice error on the test.
Sentence Fragments
A sentence fragment is a group of words that look like a sentence but aren’t. A sentence needs at least one independent clause, containing a subject and a verb. Here is an example of a fragment:
Bought the groceries.
This fragment begins with a capital letter and ends with a period, but it is not a complete sentence. Where is the subject? Who bought the groceries? Let’s fix it:
Jonathan bought the groceries.
There you go. Now it’s a complete sentence with a subject and a verb (independent clause).
You’ll more than likely need to identify and fix sentence fragments on the exam.
Vocabulary Application
Put simply, this section tests your knowledge about words.
Vocabulary Application questions make up about 25% of the English Language Skills subtest.
There are three big concepts you definitely have to know to get these questions correct:
 Determine Meaning of Words
 Correct Usage of Words and Phrases
 Diction and Tone
The first big concept you should know is how to use context to figure out what a word means. You will come across a word that you probably don’t know on the test. By using the context (the sentences around the word) and clues, you should be able to figure out what that word means.
Parts of words, like prefixes, roots, and suffixes, can really help you figure out what a word means.
The next big concept to know is how to correctly use words and phrases. On the test, you will definitely be given a sentence with a word missing. You will have to choose the most effective word or phrase within the context to place in the sentence.
And the last big concept to know is what diction and tone are and how to identify them in writing. Diction refers to the author’s choice and use of words and tone is the way the author expresses his or her feelings and attitudes through those words.
Those are the three broad concepts to be familiar with.
Specific Concept
Let’s talk about a specific concept that you need to be familiar with.
Commonly Misused Words
There are certain words that people just have a hard time with. Take a look at this list:
 affect/effect
 lie/lay
 you’re/your
 imply/infer
 comprise/compose
 farther/further
 fewer/less
 cite/site
 than/then
 to/too/two
 there/their/they’re
For each of the bullets above, make sure to know when the right time to use each word is. You will more than likely see at least one of them on the test.
Prefixes, Roots, and Suffixes
You can use a knowledge of prefixes, roots, and suffixes to figure out what a word means.
For example, let’s look at the word portable (I know, you probably already know what this word means, but it’s a good example). If you have a good understanding of prefixes and suffixes, you can gather a good idea about what portable means.
The prefix port means to carry and the suffix able means capable of. So, put them together and you can figure out that the word portable means capable of being carried or something like that.
Be familiar with the most common prefixes, roots, and suffixes. Check out this resource. It will help you on the test.
Standard English Conventions
This section tests your ability to identify and correct errors in sentences. These include tense, subject/verb agreement, parts of speech, spelling, punctuation, and capitalization errors.
Standard English Conventions questions make up about 50% of the English Language Skills subtest.
There are three big concepts you definitely have to know to get these questions correct:
 Parts of Speech
 Capitalization, Punctuation, and Spelling Conventions
 Agreement
The first big concept to know is the parts of speech. You definitely need to know what these are:
 noun
 pronoun
 verb
 adverb
 adjective
Be sure to know what these parts of speech are and how to correctly use them in sentences.
The next big concept to know is standard capitalization, punctuation, and spelling conventions. These are the rules of capitalizing, punctuating, and spelling. Take some time to review all of those rules you learned in grade school.
Remember, on the test, you’ll be finding errors in sentences.
And the last big concept is agreement. There are two types of agreement that will appear on the exam: subject/verb and pronoun/antecedent. Know what both of these are and how to fix sentences with agreement problems.
Now, those are the three broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you two specific concepts to be familiar with.
Pronoun Shifts
This is a common grammatical error that occurs when a writer starts a sentence using one type of pronoun and then suddenly shifts to another type of pronoun.
Let’s look at an example:
If you brush your teeth regularly, then most people can avoid cavities.
This sentence starts with the pronouns you and your (singular) but then suddenly shifts to people (plural). This is an error. Let’s fix it:
If you brush your teeth regularly, then you can avoid cavities.
See how it all matches now? No sudden shifts!
SubjectVerb Agreement
In sentences, subjects and verbs must agree in number. This means that if a subject is singular, its verb also needs to be singular. If the subject is plural, then its verb must also be plural. Let’s look at a sentence with incorrect subjectverb agreement:
Emily are at the pool.
The subject, Emily, is singular. Emily is one girl. The verb, are, is plural. Let’s fix this sentence:
Emily is at the pool.
Now, the subject and verb are both in singular form. They agree.
The trick 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.
And that’s some basic info about the English Language Skills 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.
FTCE General Knowledge: Reading
Overview
You will have 55 minutes to complete 40 multiplechoice questions.
All Reading questions are passage based. Reading passages will be both expository and narrative. Each test form will contain about five passages.
The Reading subtest can be neatly divided into three different sections. Those three sections are:
 Key Ideas and Details
 Craft and Structure
 Integration of Information and Ideas
So, let’s start with the biggest, Key Ideas and Details.
Kay Ideas and Details
This section tests your knowledge on drawing inferences and conclusions, identifying themes, and determining the cause and effect of events.
Key Ideas and Details questions make up about 40% of the Reading subtest.
There are three big concepts you definitely have to know to get these questions correct:
 Conclusions and Inferences
 Cause and Effect
 Central Idea and Themes
The first big concept is knowing what conclusions and inferences are and how they differ from each other.
A conclusion is a judgement or decision reached based on what you learned from the passage.
An inference is figuring out missing information by using clues and hints from the passage. When trying to make an inference, a good question to ask yourself is, “What does the passage suggest?” An inference is a type of conclusion.
Make sure your inferences rely on the author’s words rather than your own feelings or experiences.
You can 100% expect to be asked to draw a conclusion or make an inference after reading a passage.
The next big concept is understanding what cause and effect is. A cause/effect relationship describes or discusses an event or action that is caused by another event or action. This structure often uses words and phrases such as because, since, as a result, due to, consequently, and therefore.
Remember, one cause (or event) can have several effects. For example, crashing your car can cause broken bones, increased insurance premiums, and angry parents. This one event had three (negative) effects.
You can expect to see cause and effect questions on the test.
And the last big concept to know is what central ideas and themes are and how to identify them. Think of main ideas and central ideas as the same thing. They are what the story is mostly about. Main ideas are usually found in literary passages while central ideas are usually found in informational text.
The theme of a piece of text is the message or lesson the author wants to get across. It is usually a statement about life that readers can apply to their own lives.
You also need to know how to identify the central/main ideas and themes of reading passages. This will definitely be on the test. A great resource to have would be a very thorough study guide (I know of a great one!).
Now, those are the three broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you one specific concept that will be on the test.
Supporting Information/Evidence
The phrase “textual evidence” comes up several times in the Reading subtest competencies and skills.
Reading passages contain supporting information, or evidence, which includes facts, statements, or examples that guide you to a full understanding of the main idea. This evidence is used to clarify, illuminate, explain, describe, expand, and illustrate the main idea.
Sometimes a test question will ask you to choose which supporting evidence from a passage best proves the author’s claim.
Some examples of supporting information/evidence include:
 comparison one thing is shown to be like another
 contrast one thing is shown to differ from another
 statistics use of research to support an observation
 quotations use of the words of authorities to add weight to an argument
 vivid descriptions
Craft and Structure
This section tests your knowledge on how well you can identify and explain an author’s word choice, organization, point of view, and purpose.
Craft and Structure questions make up about 25% of the Reading subtest.
There are three big concepts you definitely have to know to get these questions correct:
 Word Choice and Meaning
 Organization and Text Structure
 Point of View and Purpose
The first big concept to know is word choice and meaning. Why did the author choose to use this word and what does it mean? Specific word choices can shape a text’s meaning or tone. Author’s carefully choose their words when writing a story. Authors may choose to use different types of language like figurative or connotative language.
For the test, you need to be able to figure out the meaning of words and phrases and how those specific word choices affect the meaning or tone of the passage.
The next big concept to know is about story organization and text structure. For the test, think of these words as synonyms. Organization is the act of putting things into a logical order, and can refer to writing, thoughts, or even your sock drawer!
In writing, organization is the arrangement of ideas, incidents, evidence, or details in a specific order. Writers use different organizational strategies, and you need to be able to recognize a few of the most utilized methods of organization like cause/effect, compare/contrast, and problem/solution.
And the last big concept is point of view and purpose. You need to be able to figure out how an author views something and why an author wrote the passage. On the test, you may be asked to compare the point of view of two or more authors on the same topic.
Know these purposes for writing:
 to persuade
 to inform
 to entertain
 to compare
 to express
Now, those are the three broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you two specific concepts to be familiar with because they will most likely appear on the test.
Figurative Language
Figurative language is language that uses words with meanings that are different from the literal interpretations. A writer using literal language simply states the facts as they are. A writer who describes something by comparing it with something else is using figurative language.
Writers use figurative language to be more effective and persuasive and to give the readers new insights. The most common figurative language are similes, metaphors, and personification.
Connotative Language
The emotion and association connected to a word is known as its connotative meaning. Since different people have different experiences, words can connotatively mean different things. Words can have a negative, neutral, or positive connotation.
A word’s dictionary definition is known as its denotative meaning.
Integration of Information and Ideas
This section tests your ability to evaluate, synthesize, and analyze information from texts.
Integration of Information and Ideas questions make up about 35% of the Reading subtest
There are really only three things you need to know how to do for this part of the test. You need to know how to:
 Evaluate a statement
 Synthesize information
 Compare two statements
The first thing you need to know how to do is evaluate an author’s statement for relevancy, sufficiency, and validity. The test may ask you to read an author’s statement from a passage and then determine if that statement is valid or invalid and why.
The next thing you need to know how to do is synthesize information. Basically, you need to take all of your background knowledge (the stuff you already know) and what you learn from a reading passage to form a better understanding of what the author is trying to say.
And finally, you need to be ready to compare two statements from a passage. On the test, you will for sure be asked to read two sentences from a passage and determine if the second sentence contradicts, explains, restates, clarifies, describes, or relates the first sentence.
And that’s some basic info about the Reading 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.
Getting the Help You Need
And if this seems like a lot of information, it’s because it is. This is a test that decides if you can teach the next generation of leaders. But if you’re feeling overwhelmed, don’t be.
We’ve got the best study guides for the General Knowledge test. So, if you’re feeling overwhelmed and you don’t even know where to begin to figure out how to teach phonemic awareness or how to identify the different characteristics of the stages of writing, we’ve got you covered.
You see, our study guides are filled with hundreds of pages of instructional content and hundreds of authentic practice questions that are going to walk you through the exact concepts we’re talking about in this video in much more depth and detail. And it takes you from knowing what’s on the test to knowing what you need to know to be successful on the test and equipping you with that information so that you can be successful when you take this test.
So, if at any point, you’re just overwhelmed or you want to save a lot of time and a lot of headaches, hop over to 240tutoring.com, get the General Knowledge study guide, and make sure you’re prepared today.
FTCE General Knowledge: Mathematics
Overview
You will have 100 minutes to complete 45 multiplechoice questions.
Reminder: The test center will provide an onscreen fourfunction calculator and an onscreen reference sheet.
The Mathematics subtest can be neatly divided into four different sections. Those five sections are:
 Number Sense
 Geometry and Measurement
 Algebraic Thinking
 Probability and Data
So, let’s start with Number Sense.
Number Sense
This section tests your ability to order numbers and correctly solve realworld problems using the four operations.
Number Sense questions make up about 17% of the Mathematics subtest.
There are three big concepts you definitely have to know to get these questions correct:
 Order of Operations
 Value of Real Numbers
 Word Problems
The first big concept and by far the most important is order of operations.
The order of operations, or PEMDAS, PEMDAS, is simply the process you follow to simplify and work an equation.
Let me give you an example. If you have an equation like this:
2(x – 3) + 3(x + 4)^{2}
You have to work the problem according to a specific order, the order of operations.
In this particular example, you would first solve for the parentheses, then you would solve for the exponents. Then going left to right, you do either multiplication or division then you would add or subtract in the same order (from left to right).
So that’s why we group the M and the D and the A and the S together.
Now, this is incredibly important because, on the test, you will be required to simplify an equation. So, you have to know the order of operations to get that question correct.
The next big concept to know is the value of real numbers. A real number is, really, any number you can think of. It includes whole numbers, rational numbers (fractions and decimals), and irrational numbers (π, √2, etc.). Real numbers can be negative or positive.
Now, the test will, and I mean will have you place different forms of numbers from greatest to least or least to greatest on a number line.
In a given data set, you might have two fractions, a decimal, pi, a negative integer, and a regular integer. You then must organize all of these from least to greatest (or greatest to least).
So, make sure you know how to translate decimals to fractions and fractions to decimals, so you can compare the two to figure out which one is greater or less than the others.
Oh, and also make sure you understand decimals to the hundredths place.
Now, the last major concept to know from number concepts is how to read, structure, and apply mathematical word problems. These problems will include all four operations (+, , x, ÷).
Now, my biggest tip to help you with this is simply to work through a lot of authentic practice questions, specifically, word problems in mathematics.
Now, while these questions aren’t going to be the most complex, it does take a lot of practice to learn how to read a question prompt, understand the question, and then solve the problem.
And really, it’s just one of those things you have to practice, practice, practice. So, find a great source of authentic practice questions that you can use.
Those are the three broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you two specific concepts to be familiar with because they will most likely appear on the test.
Prime Numbers
A prime number is a whole number that cannot be made by multiplying other whole numbers together. Examples of prime numbers include 2, 3, 5, 7, and 11. There are many more.
You should also know what prime factors are and how to find them.
Properties of Math
Think of a property as kind of like a rule you need to follow. Okay? There are quite a few of these properties:
 Commutative Property of Addition
 Commutative Property of Multiplication
 Associative Property of Addition
 Associative Property of Multiplication
 Distributive Property
 Additive Identity Property
 Additive Inverse Property
 Multiplicative Identity Property
 Multiplicative Inverse Property
Whew. Like I said, there’s a lot. You need to know what these are and how to solve problems using them. A really thorough study guide would be a great resource to have and use.
Geometry and Measurement
This section tests your ability to identify and classify shapes and solve measurement problems.
Geometry and Measurement questions make up about 21% of the Mathematics subtest.
There are three big concepts you definitely have to know to get these questions correct:
 Two and ThreeDimensional Shapes
 Ratio and Proportion
 Measurement Units and Quantities
The first big concept to know is how to identify and classify both two and threedimensional shapes based on their properties. Properties of twodimensional shapes can include sides, corners, and angles.
Properties of threedimensional shapes can include faces, edges, and vertices.
You also need to know how to find the perimeter and area of twodimensional shapes and the surface area and volume of threedimensional shapes.
The next big concept to know is what ratio and proportion are. On the test, you will be asked to solve ratio and proportion problems by looking at scaled drawings. Let’s talk about what these three words mean.
A ratio simply compares numbers. A ratio can be written in three different ways:
3:1
3 to 1
3/1
A proportion means that two ratios are equal. For example, 1/4 = 2/8. These ratios are equal because if we reduce 2/8, we arrive at 1/4.
A scaled drawing is a drawing that represents a really large object (too large to be drawn in its actual dimensions).
So, know these terms and do several practice problems to get ready for the test.
And the last big concept to know is measurement units and quantities.
You need to be familiar with units and quantities like:
 temperature
 time
 money
 length
 width
 height
 area
 mass
 weight
 volume
 speed
Now, just like with word problems and number concepts, this mathematical concept isn’t necessarily complex, you just need to make sure you’re familiar with those different types of measuring units and quantities.
Those are the three broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you two specific concepts to be familiar with because they will most likely appear on the test.
Pythagorean Theorem
The Pythagorean Theorem is used to find any length of a side of a right triangle (if you know the other two sides).
The equation of the Pythagorean Theorem is:
a^{2 }+ b^{2}= c^{2}
Where A and B are the two sides of the right triangle and C is the hypotenuse of the triangle.
And I guarantee you one thing, if you take anything from this, take this one thing: you will have a question about the Pythagorean Theorem on the test. That is an absolute guarantee. It will most likely be in some sort of word problem.
An example would be:
Billy walked three blocks west, and four blocks north. If Billy walked a straight line, how many blocks would Billy have walked?
Something like that will show up on the test.
Area
On the test, you will be asked to find the area of twodimensional shapes and the surface area of threedimensional shapes.
But don’t worry! Remember, I told you that you’ll be given an onscreen reference sheet for the Mathematics subtest. This reference sheet lists all of the formulas for finding area and surface area.
BUT, you do need to spend some time practicing these types of problems. It won’t be as easy as just finding the area of a rectangle (length x width). You might be asked to find the area of a trapezoid or the surface area of a cylinder.
And you can bet these skills will be tested with realworld word problems.
Algebraic Thinking
This section tests your ability to, you guessed it, solve algebra problems.
Algebraic Thinking questions make up about 29% of the Mathematics subtest.
There are three big concepts you definitely have to know to get these questions correct:
 Solving for x
 Slopeintercept form
 Creating an equation from a data set
The first big concept you need to know is how to solve for x. Solving for x is pretty straightforward. The test will give you an equation and then you have to solve for x. So, the test will give you an equation like:
4x^{2}– 4(3 + 2) = 16
And in this equation, we would just need to balance the equation for x, so you would simplify it as much as you can, balance the equation, and you’d find that x equals three.
4x^{2 }– 4(5) = 16
4x^{2 }– 20 = 16
4x^{2}= 36
x^{2}= 9
x = 3
Now, take note. You are more than likely going to be presented with a realworld word problem. Be able to take what you need from the problem, build the equation, and solve for x.
You are also going to have to solve inequalities. Solving inequality statements in one variable, such as 3/4x – 9 > 21, is much the same as solving equations like those addressed above.
The only major differences are that:
 the direction of the inequality sign will change after some operations are performed
 a finished final answer generally requires the variable to be written on the left
 the solution set is often presented on a number line.
And the second concept is slopeintercept form.
Now, the slopeintercept equation is simply:
y = mx + b
And in this equation, m is equal to the slope of the line on a graph and b is the yintercept, hence the name slopeintercept form.
So, for the equation:
y = 3x + 4
The slope of the line would be three and the yintercept would be four.
Now, the last major concept to know is how to create an equation from a data set. The test will give you a data set that looks something like this:
x  1  2  3  4 
y  1  3  5  7 
And you’re required to create a corresponding equation that matches the data set. For this data set, the corresponding equation is:
y = 1 – 2x
Now, if you look at the data set, anytime you plug the x value in, you get the corresponding y value if you solve for the equation. And while this kind of question can seem difficult, it’s one of the easier questions to answer if you just work backward.
All you need to do is look at the answer options, plug in the data set values into each equation, and see if they match.
Now, those are the three broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you two specific concepts to be familiar with because they will most likely appear on the test.
Distributive Property of Multiplication over Addition
There are a lot of properties (think: rules) in algebra. Knowing them will help you solve algebra problems quickly and correctly.
Take a look at one of these properties, the Distributive Property of Multiplication over Addition:
The product of a factor with a sum is the same as the sum of the products made by that Algebra factor and each number involved in the addition or subtraction. The reverse direction is also true.
Symbolically, then, the Distributive Property can be represented multiple ways:
a(b + c) = ab + ac
(b + c)a = ba + ca
ab + ac = a(b + c)
ba + ca = (b + c)a
As subtraction is properly understood as a form of addition, each statement above is also true for subtraction, such as a(b – c) = ab – ac.
FOIL
Remember the acronym FOIL from middle school algebra? The letters of
FOIL stands for the pairs of values to be multiplied during the distribution process before being added together.
For example, in the problem (a + b)(c + d):
F = First, the first quantity from each binomial = ac
O = Outer, terms towards the outside of the binomial multiplication problem = ad
I = Inner, the terms towards the inside of the binomial multiplication problem = bc
L = Last, the last term in each binomial = bd
And so, the product of (a + b)(c + d), obtained through the Distributive Property using FOIL, is the sum of the terms ac + ad + bc + bd.
Probability and Data
This section tests your ability to determine the likelihood of events occurring and analyze and interpret sets of data.
Probability and Data questions make up about 33% of the Mathematics subtest. It’s a big one.
There are three big concepts you definitely have to know to get these questions correct:
 Measures of Central Tendency
 Organizing and Displaying Data
 Probability
The first big concept to know is measures of central tendency. What does that mean?
It’s simply four concepts: mode, median, mean, and range.
Now, on the test, they’re going to give you a data set of about 8 to 12 numbers, and they’re going to ask you one or more of the following. What is the mode? What is the median? What is the mean? Or what is the range of the data set? They will also be embedded in realworld word problems.
So, you have to know what those central tendency measurements are and how to find them for a data set. And when you practice, work on a data set of about 8 to 12 doubledigit numbers.
The next big concept to know is the different ways to display and organize data. On the test, you will see data displayed in the following ways:
 histograms
 bar graphs
 circle graphs
 pictographs
 line plots
 tables
Know what each of these are and how the presentation of data can lead to different or inappropriate interpretations in the context of a realworld situation.
And, finally, the last big concept to know is probability. Probability is defined as the likelihood of an event occurring. Probability is the number of successful outcomes possible to the total number of outcomes possible.
Look at these examples.
If a sixsided die is rolled, what is the probability of landing on any one of the sides? The answer, of course, is one in six.
The next question you might get is: Billy flipped a coin 10 times. The coin landed on heads seven times, and the coin landed on tails three times. What is the probability of the coin landing on tails on the next flip?
You also need to know how to calculate probability using counting procedures, tables, and tree diagrams.
Now, those are the three broad concepts to be familiar with.
Specific Concepts
Right now, I’m going to give you two specific concepts to be familiar with because they will most likely appear on the test.
Standard Deviation
You need to what standard deviation is. The standard deviation of a data set is found by taking the (positive) square root of its variance. When the measures of central tendency are closely clustered so that the mean is approximately equal to the median, which is also approximately equal to the mode, and the data is dispersed symmetrically about the median, this is called a normal distribution and is often referred to as a bell curve. In a normal (bellshaped) distribution, about twothirds of the data lie between ±1 standard deviation of the mean.
Did that make your head hurt? Well, put more simply, standard deviation is a measure of how spread out numbers are.
Odds
So, people often use the terms “odds” and “probability” interchangeably. But, there is an important difference between the two.
Probability = the number of successful outcomes possible: total number of outcomes possible.
Odds = number of successful outcomes possible: number of unsuccessful outcomes
Know the difference between the two. It’s important.
And that’s some basic info about the Mathematics subtest.
Getting the Help You Need
And if this seems like a lot of information, it’s because it is. This is a test that decides if you can teach the next generation of leaders. But if you’re feeling overwhelmed, don’t be.
We’ve got the best study guides for the General Knowledge test. So, if you’re feeling overwhelmed and you don’t even know where to begin to figure out how to teach phonemic awareness or how to identify the different characteristics of the stages of writing, we’ve got you covered.
You see, our study guides are filled with hundreds of pages of instructional content and hundreds of authentic practice questions that are going to walk you through the exact concepts we’re talking about in this video in much more depth and detail. And it takes you from knowing what’s on the test to knowing what you need to know to be successful on the test and equipping you with that information so that you can be successful when you take this test.
So, if at any point, you’re just overwhelmed or you want to save a lot of time and a lot of headaches, hop over to 240tutoring.com, get the General Knowledge study guide, and make sure you’re prepared today.
FTCE General Knowledge Practice Test
Now, let’s look at a few practice questions in each area to see how these concepts might actually appear on the real test.
Ready? Let’s go!
Question 1
Both₁ of Janet’s children became a concert pianist₂ after they went to Julliard; she was unbelievably₃ proud of them.
Which of the following parts of the sentence is grammatically incorrect?
 1
 2
 No error
 3
Correct answer: B. Nouns that refer to the same item must agree in number: they must both be singular, or they must both be plural. Because the sentence states that Janet has two children, the number of concert pianists should be plural. The corrected sentence should read, “Both of Janet’s children became concert pianists.”
Question 2
Charles asked me to go to the movies with him₁, but Ashley and me₂ go to the movies together every Monday, so I had to disappoint him₃.
Which part of the sentence contains an error in pronoun usage?
 1
 3
 2
 No error
Correct answer: C. Pronouns must agree in case. In compound structures where there are both a noun and a pronoun, drop the noun for a moment. Then you can see which case you want. You wouldn’t say, “me go to the movies,” so the correction would read, “Ashley and I go to the movies together every Monday.”
Question 3
Famine and close living quarters₁ in cities was₂ to blame for the rapid spread of the Black Death₃ in Italy.
Which part of the sentence contains a grammatical error?
 3
 2
 1
 No error
Correct answer: B. The subject of the sentence is “famine and close living quarters.” Because this is a compound subject made up of two singular nouns joined by and, a plural verb is required. Therefore, “was” should be changed to “were.”
Question 4
Although the jeweler’s apprentice thought that the emeralds looked real, the master jeweler easily determined that they were counterfeit.
The underlined word “counterfeit” means:
 fake.
 unstable.
 genuine.
 reliable.
Correct answer: A. Antonyms are words with opposite or almost opposite meanings. When you see a word you don’t know, you can use antonyms as context clues to help figure out an unfamiliar word’s meaning. In the passage, the antonym “real” helps you figure out that “counterfeit” means fake or forged.
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?
 No error
 3
 2
 1
Correct answer: D. “Trying to fall asleep…” is a dangling modifier, or a modifier that appears to modify 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
Read this passage and then answer the following questions.
Excerpt from Inaugural Address by John F. Kennedy, January 20, 1961
^{1} “In your hands, my fellow citizens, more than in mine, will rest the final success or failure of our course. Since this country was founded, each generation of Americans has been summoned to give testimony to its national loyalty. The graves of young Americans who answered the call to service surrounds the globe.
^{2} Now the trumpet summons us again – not as a call to bear arms, though arms we need; not as a call to battle, though embattled we are – but a call to bear the burden of a long twilight struggle, year in and year out, ‘rejoicing in hope, patient in tribulation’ a struggle against the common enemies of man: tyranny, poverty, disease, and war itself.
^{3} Can we forge against these enemies a grand and global alliance, North and South, East and West, that can assure a more fruitful life for all mankind? Will you join in that historic effort?
^{4} In the long history of the world, only a few generations have been granted the role of defending freedom in its hour of maximum danger. I do not shrink from this responsibility – I welcome it. I do not believe that any of us would exchange places with any other people or any other generation. The energy, the faith, the devotion which we bring to this endeavor will light our country and all who serve it – and the glow from that fire can truly light the world.
^{5} And so, my fellow Americans: ask not what your country can do for you – ask what you can do for your country.
^{6} My fellow citizens of the world: ask not what America will do for you, but what together we can do for the freedom of man.
^{7} Finally, whether you are citizens of America or citizens of the world, ask of us the same high standards of strength and sacrifice which we ask of you. With a good conscience our only sure reward, with history the final judge of our deeds, let us go forth to lead the land we love, asking His blessing and His help but knowing that here on earth God’s work must truly be our own.”
Question 1
Which of the following best defines the word summons as it is used in paragraph 2 of the selection?
 A call to action
 A court order
 To make noise
 To draw away from
Correct answer: A. The word “summons” in this context is best defined as a “call to action”. The excerpt even defines the word, in a way, when it reads: “not as a call to bear arms, . . . but a call to bear the burden…”.
Question 7
The writer’s purpose in this speech is best described as:
 a defamatory denunciation of global powers.
 a stirring and inspiring call to patriotism.
 congratulatory remarks regarding the current transition of power.
 a complaint against indolent citizens.
Correct answer: B. This is the best answer. “Stirring and inspiring” best describe the effect this speech has on its intended audience, and “call” is certainly the purpose.
Question 8
The purpose of the rhetorical questions in paragraph 3 of the selection is:
 to cause the audience to question the speaker’s motives.
 to unite the listeners in a common goal.
 to call attention to the need for swift military action.
 to produce a divisive effect upon its audience.
Correct answer: B. The rhetorical questions in this selection are there to bring the audience toward a common consensus; rhetorical questions don’t need answers because the answer is always supposed to be obvious. By asking these questions rhetorically, the speaker brings his listeners to the same answer, thus uniting them in a common goal.
Question 9
The main idea of this passage can best be summarized as:
 other nations should rise up and help out.
 we the people should be asking ourselves what we can do for the common good.
 people should stop being so lazy and fix the world’s problems.
 too many have died fighting for national loyalty.
Correct answer: B. This is the best summary of the main idea. The speech applies to “the people” in a unified way; it calls for them to question themselves, and it applies these ideals to a general, human “good”.
Question 10
Simplify: 30 – 2 × 50 + 70
 0
 210
 570
 70
Correct answer: A. To simplify the given expression, follow the order of operations. The order of operations is often expressed by the acronym PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Within the equally ranked operations (the pair including Multiplication and Division, and also the pair including Addition and Subtraction), work left to right. Of the operations present in the problem (subtraction, multiplication, and addition), the first to be completed must be multiplication because “M” precedes “A/S” in the order of operations. Therefore, the expression 30 – 2 × 50 + 70 will be simplified to 30 – 100 + 70. The remaining operations (subtraction and addition) are equally ranked and so must be performed in the order in which they appear when reading the problem from the left to the right. First 30 – 100 + 70 becomes 70 + 70, and then finally 70 + 70 = 0.
Question 11
Yolanda is getting a new rug for her room. Her old rectangular rug is 5 ft by 7 ft. Her new rug is circular with a diameter of 7 ft. How is the size of the new rug related to the size of the old one?
 The new rug is about 3.5 ft² larger than the old one
 The new rug is about 4.5 ft² smaller than the old one
 The new rug is about 4.5 ft² larger than the old one
 The new rug is about 3.5 ft² smaller than the old one
Correct answer: A. The size of each of Yolanda’s rugs is determined by the rug’s area. The area for a rectangle is found by multiplying length and width (or base and height) of the rectangle. Therefore, Yolanda’s original rectangular rug has an area of 7 x 5 = 35 ft². The area of a circle is found using the formula A = πr², where A is the area and r is the radius of the circle. Because the diameter of a circle is twice the radius, the radius of Yolanda’s new circular rug must be 7 × ½ = 3.5 feet. Therefore, the area of Yolanda’s new rug will be A= π(3.5)² = π(12.25) ≈ 38.5 ft². The answer choices describing the relationships between the sizes of the rugs are all assessments of the difference in square footage of the two rugs. Therefore, subtraction should be applied. Because the new rug’s measurement of ~38.5 ft² is larger than the old rug’s 35 ft², the answer is that the new rug is about 38.5 – 35 = 3.5 square feet larger than the old one.
Question 12
Marty gets an allowance of $5 each week from his parents. He also can earn extra money by doing additional chores outside of his usual household responsibilities for $1.50 per chore. He has been working on saving his money to buy a new game and thinks he will be close this week. If he would like to get at least $20 from his parents at the end of the week, what is the minimum number of additional chores Marty needs to complete?
 17
 13
 14
 10
Correct answer: D. Let c = number of additional chores Marty must complete. Because Marty will earn $1.50 for each chore, the expression 1.5c represents the money Marty will earn from doing c additional chores. Marty gets $5 each week automatically from his parents, so the expression 5 + 1.5c represents the total amount of money that Marty can get from his parents at the end of the week. Marty wants to have at least $20, and so 5 + 1.5c ≥ 20 expresses Marty’s goal of attaining at least $20. To solve this inequality statement, subtract 5 on each side to get 1.5c ≥ 15. Then, divide both sides of the inequality statement by 1.5 in order to isolate c. Neither of these steps require a change in direction of the inequality symbol because neither one is multiplication or division by a negative number. The final result, therefore, is c ≥ 10, indicating that Marty must complete at least 10 additional chores over the course of the week in order to get at least $20 from his parents at week’s end.
Question 13
The inequality statement, 9x – 8 > 24 – 7x, can be fully simplified to which expression?
 x < 16
 x < 2
 x > 2
 x > 16
Correct answer: C. Simplification of the expression 9x – 8 > 24 – 7x can begin in multiple ways, but the simplest is to add 7x to each side. Adding a quantity never causes a change in direction of the inequality sign, so the resulting statement is 16x – 8 > 24. Next, 8 can be added to each side of the problem, resulting in 16x > 32. Finally, x will be isolated when 16 is divided from each side. Division by a positive number does not result in a change in the direction of the inequality sign, and so the final answer is x > 2.
Question 14
7.5, 7.2, 7.1, 8.0, 7.9, 8.3, 7.5, 6.9, 8.2, 7.6
Aaron runs on a treadmill for an hour each day. He recorded the number of miles completed on each run for the last ten days. The length of each run, in miles, is given above. What is the range of the length of Aaron’s runs during this period, in miles?
 0.1
 1.6
 7.5
 1.4
Correct answer: D. To find the range of the length of Aaron’s runs, one strategy would be to order the list of the lengths given from least to greatest. The ordered list is: 6.9, 7.1, 7.2, 7.5, 7.5, 7.6, 7.9, 8.0, 8.2, 8.3. From this list, it is clear that Aaron’s shortest run was 6.9 miles and his longest run was 8.3 miles. The range of a set of data is the difference between the highest and lowest values in the set, and so 8.3 – 6.9 is calculated to get 1.4, the range of the lengths of Aaron’s runs for this tenday time period.
FTCE General Knowledge: English Language Skills