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CBEST 2017-10-19T19:58:10+00:00

The Ultimate Guide to the CBEST

Want to prepare for the CBEST but don’t know where to start? We’ve got the prep materials you need, including:

  1. Need-to-know Details:  This includes all of the important test info, how much it costs, and explains a passing score.
  2. Test Breakdown: Wanna know what’s on the CBEST? Each test covers specific concepts, skills and ideas. We’ll tell you what it takes to pass.
  3. Practice Test: Measure your readiness for the CBEST Mathematics test by taking our free practice test!

CBEST Overview

CBEST, or California Basic Educational Skills Test, is a required exam for anyone seeking teacher certification in California.

If you have:

  • A high school diploma or GED
  • College credit toward a career in education
  • Applied or are applying for an alternative teaching certification program

Then you can register to take the CBEST.

There are three parts to the test:

  • Mathematics
  • Reading
  • Writing

You can take one, two or all three sections at a time and you can pass them individually.

The math and reading sections are both made up of 50 multiple-choice questions, and the writing section includes two short essays.

Quick Facts

Cost: $102 for the computer-based test or $41 for the paper-based test*

Location: The CBEST offers computer-based tests (CBT) and paper-based tests (PBT). CBTs are offered year-round daily (except Sunday) and PBTs are offered at set times throughout the year.

For more information on testing dates and details, check out the CBEST Test Info Page.

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 45 days between testing attempts.

Scoring: CBEST scores each subject on a range from 20-80. A passing score for each CBEST subject is 41.

But:

if you score a 123 overall, you can pass with a single subject score of 37 or higher.

CBEST releases preliminary scores for Mathematics and Reading at the testing site, but official results aren’t released for 2 weeks if you take the Computer-Based Test or 3 weeks if you take the Paper-Based Test.

Overall

The test gauges your ability to solve mathematical problems, comprehend information presented in reading passages, tables and graphs, and assesses your ability to write effectively.

Is the CBEST hard? Not if you understand the test structure and know what types of information the questions want you to answer – which is what we’re here for!

CBEST: Mathematics Breakdown

The mathematics portion of the CBEST is made up of 50 multiple choice questions. Most of the questions will be scenario based problems, or word problems.

You have 4 hours to complete the CBEST, no matter how many sections you take.

There are no calculators are allowed for any part of the exam.

The First Step

While mathematics can seem intimidating, the concepts covered in the CBEST test are, for the most part, basic math skills with practical applications. The mathematics section of the CBEST focuses on three main skill factors:

  • Estimation, measurement and statistics
  • Computation and problem solving
  • Numerical and graphical relationships

That might not seem too bad, but each of these skill factors also has subcategories. We’ll cover them in detail below.

Estimation, Measurement and Statistical Principles

Estimation, Measurement and Statistical Principles make up 30% of the questions on the test.

Estimation and Measurement requires you to know:

    • How to estimate the amount of time it will take to complete a project
    • How to estimate the result of a problem before computing it
    • Standard U.S. units of measurement for length, temperature, weight and capacity
    • How to measure length and perimeter

Statistical Principles tests your knowledge of ratios, probability and percentages. You need to remember:

    • How to use data to find the average, proportion or percentage
    • How to predict an outcome based on probability
    • How to determine student performance in a classroom based on test scores

Computation and Problem Solving

Computation and Problem Solving make up 35% of the test. Not having a good foundation of mathematics will cause these questions to be more difficult to answer, so make sure you feel confident in:

  • How to add/subtract/multiply/divide whole numbers, and how to add/subtract positive and negative numbers
  • How to solve practical math problems: can you determine a total based on unit price?
  • How to solve for one unknown
  • How to recognize if a given problem has enough information to be solved or if there are alternate ways to solve a problem

Numerical and Graphical Relationships

Numerical and Graphical Relationships questions also make up 35% of the test.

Here you’ll be tested on your ability to use data from tables, spreadsheets and graphs as well as whether you can recognize that .25 and ¼ mean the same thing.

You need to know:

  • How to organize numbers on a number line, like knowing -7 < -4
  • How to use greater than/less than/equal to and other mathematical symbols
  • How to identify mathematically equivalent numbers, formulas and expressions
  • How to apply the meaning of logical connectives (if/then) and quantifiers (some, all, none) to solve problems
  • How to use tables, spreadsheets and graphs (bar, line, circle) to solve math problems

And Remember!

All of the questions are worth the same amount of points and there’s no penalty for wrong answers. If you don’t know, do your best to make an educated guess by eliminating the obviously wrong answers.

And you can always use the “guess and check” method – plugging the answer options into the problem to see which one works best!

Now it’s your turn to put all your new knowledge to good use. Try going through our free practice test below:

CBEST: Reading Breakdown

The reading portion of the CBEST is made up of 50 multiple choice questions, which vary in their difficulty, complexity and subject matter.

You have 4 hours to complete the CBEST, no matter how many sections you take.

The test measures two skill factors, and all of the questions can be answered based solely on the information given in the passages.

The First Step

The reading section of the CBEST has two skill factors:

  • Critical Analysis and Evaluation
  • Comprehension and Research Skills

There are 50 questions, and not all of them come from reading passages. The test looks at your ability to understand information that comes from written passages, tables and graphs.

The questions cover multiple subjects with different degrees of difficulty and complexity,

But:

You can answer all of the questions based only on the information given in the test.

Critical Analysis and Evaluation – 40%

Analysis and Evaluation covers your knowledge of identifying, recognizing, and determining the central ideas, author’s point of view, and intended audience from the passage you read.

These questions cover:

  • Identifying what supports a writer’s main idea, and inconsistencies or differences in the point-of-view from a passage or two sources
  • Recognizing the writer’s viewpoint, persuasive techniques, audience and how the specific words used communicate the correct/incorrect tone
  • Determining relevant information in the writer’s argument, what strengthens/weakens it, and what statements are facts and what are opinions

Comprehension and Research

Comprehension and Research questions test your ability to logically and accurately read the text and make conclusions about specific words and ideas.

These questions cover:

Words – using context clues, syntax and structure to determine meaning of unknown words, figurative or colloquial language, how context changes a word’s meaning or how words can have different interpretations or meanings.

Ideas – identifying the relationship between general/specific ideas, arranging ideas into an outline, recognizing the main idea or purpose statement, identifying accurate paraphrases or summaries of ideas and recognizing implied relationships between people, ideas and events.

And Remember!

With the reading questions, there’s no penalty for wrong answers – so even if you don’t know, make your best guess!

If you’re ready to see how you’ll do on the exam, check out our free CBEST Reading Test.

CBEST: Writing Breakdown

The writing portion of the CBEST is made up of two writing topic prompts that measure your ability to write effectively.

You have 4 hours to complete the CBEST, no matter how many sections you take.

The First Step

The writing test is just that – writing!

You’re given two different writing prompts. The prompts ask you to write from your perspective, and don’t require that you have any specialized knowledge.

The first prompt is to analyze a statement or situation:

This might look like agreeing or disagreeing with a given quote from a well-known author or analyzing opposing viewpoints on a particular political or educational opinion.

The second prompt is to write about a specific personal experience:

This could be something like sharing a time you overcame adversity and what you gained from it, or imagining being able to change something from your past and how it could affect your life now.

The Essays

The essays are scored on a scale of 1-4.

A score of 4 means you effectively communicated to your audience with:

  • Clear central ideas and point-of-view
  • Clearly arranged ideas and discussion points
  • Good choice of words and understanding of their meanings
  • Well-laid out paragraphs and sentence structure
  • A response that adresses the topic and uses language/tone meant for the audience

A score of 1 means you failed to communicate with your audience by:

  • Not stating or staying focused on a central idea and point-of-view
  • Unclear meaning and poorly organized writing
  • Using the wrong words and/or spelling them incorrectly
  • Having errors in the sentences, paragraphs and writing mechanics
  • Not understanding and providing what the writing prompt asks for

Because of the way the test is scored, it’s important to be able to state your central idea and point of view clearly.

Make sure your ideas are organized clearly and logically – does your writing have a good flow?

Stay on topic – what you write needs to relate to the prompt and your supporting information should make sense.

Pick the right words and use them well – make sure what you say is written for an educated audience. No slang, swearing or otherwise unnecessary language should be in your essay.

And make sure your writing mechanics – like spelling, punctuation and capitalization – are up-to-date.

To test your readiness to write a 4-point essay, work through our free practice questions!

And Remember!

With the reading questions, there’s no penalty for wrong answers – so even if you don’t know, make your best guess!

If you’re ready to see how you’ll do on the exam, check out our free CBEST Reading Test.

Writing Practice Test

Think you’re ready for the real deal? Try working through this free writing practice test:

Locate the error, if any. 

Mark was very1 tired after the soccer game and angrily2 shut the door because he didn’t play good3 that day.

a. 1
b. 2
c. 3
d. no error

Correct Answer: C

“Good” should be changed to “well,” as “well” is an adverb describing the verb “play,” whereas “good” is an adjective. “Very” is correctly used before the adjective “tired,” and “angrily” is an adverb used correctly to describe the verb “shut”.

Neither Cindy nor her friends wants1 to miss2 the chance to purchase concert tickets early; Cindy especially hopes3 to get great seats.

a. 1
b. 2
c. 3
d. No error

Correct Answer: A

The subject must agree with the nearest noun in a paired conjunction. Therefore, the verb “wants” should be changed to the plural form—“want”—in order to agree with the plural subject closest to it, “friends”.

“Miss” is used correctly here. What do they want? Not to miss the chance to purchase tickets. Also, the second clause following the semi-colon employs the verb “hopes,” which correctly agrees with the single subject “Cindy.”

Last week, Felicity went1 to the store, but she should have went2 yesterday since the same store was having3 a sale on the items she purchased.

a. 1
b. 2
c. 3
4. no error

Correct Answer: B

Rationale: Although “have went” is in the past tense, which correctly reflects the main past tense verb “went,” the past participle should be written “have gone”.

Rationale: The past participle “was having” is the correct verb form here, and the fact that “Felicity went” just “last week” correctly uses the past form of the verb “go.”

The rainy weather really effected1 the outcome of the game; being from the desert2, the team wasn’t accustomed3 to playing in such weather4.

a. 1
b. 2
c. 3
d. 4

Correct Answer: A

This sentence brings about a number of commonly confused words. “Effect” is almost always a noun, whereas “affect” is most often a verb. One easy way to remember this is that the action word “affect” starts with an “a,” like “action.” Change “effected” to “affected” to correct this sentence.

The rest of these commonly confused words are spelled and used correctly.

Jana, my oldest sister1, needs to find a new veterinarian in the area. For2 she has recently moved to a new city3.

a. 1
b. 2
c. 3
d. no error

Correct Answer: B

Replace the period between “area” and “for,” and replace it with a comma to connect these two clauses. The second sentence standing by itself is a fragment and must be connected to the first part of the sentence.

“My oldest sister” is correctly punctuated between commas, as it clarifies the person of “Jana,” but is not a necessary part of the sentence. And “to a new city” is another distractor that clarifies where Jana has moved.

On your way to the store, please1 pick up a gallon of milk ours2 is expired and tastes3 strange.

a. 1
b. 2
c. 3
d. No error

Correct Answer: B

This run-on sentence consists of two separate thoughts: “Please pick up a gallon of milk,” and “Ours is expired and tastes strange.” There are many ways to correct this sentence. You could simply put a period after “milk” and begin a new sentence with “Ours…” Or, you could use a semi-colon between “milk” and “ours” to indicate a connected thought. Also, you could place the word “because” in between “milk” and “ours”.

The comma after “store” is used correctly to set off the introductory phrase. Also, no change is needed for “expired and tastes”—this is a simple distractor.

While taking a test1, people who tap their pencils can be very distracting to others around them2, which could result3 in faulty test score results.

a. 1
b. 2
c. 3
d. no error

Correct Answer: B

This run-on sentence consists of two separate thoughts: “Please pick up a gallon of milk,” and “Ours is expired and tastes strange.” There are many ways to correct this sentence. You could simply put a period after “milk” and begin a new sentence with “Ours…” Or, you could use a semi-colon between “milk” and “ours” to indicate a connected thought. Also, you could place the word “because” in between “milk” and “ours”.

The comma after “store” is used correctly to set off the introductory phrase. Also, no change is needed for “expired and tastes”—this is a simple distractor.

As we floated down the Amazon river1, Alexa thought she saw a snake2 moving along the river’s3 edge and following our canoe.

a. 1
b. 2
c. 3
d. no error

Correct Answer: A

“Amazon River” is a proper noun, thus “River” should also be capitalized in this sentence.

The use of “snake” here is not a proper noun, so it should not be capitalized, as with the word “river’s” at the end of the sentence. The writer isn’t using “river” here as specifically referring to the Amazon River, but as a simple noun locating where the snake is on that specific river.

Ronald’s lawyer was able to advice him1 that she would not lose2 the case and that she could prove whose fault3 the car accident really was.

a. 1
b. 2
c. 3
d. no error

Correct Answer: A

The lawyer would “advise” Ronald, not “advice” him. Advise here is used as a verb, whereas “advice” is a noun.

The other distractors are commonly confused words: lose/loose and whose/who’s. They are used correctly in this case.

They1 always say to avoid leaving a plastic water bottle out in the heat because it2 will melt, leaking chemicals into the contents3 of the bottle.

a. 1
b. 2
c. 3
d. no error

Correct Answer: A

The pronoun “they” is vague—who are “they”? The answer is unclear from the sentence. Therefore, “A” is the correct answer. “They” should be replaced with a more specific noun, such as “scientists” or “researches,” perhaps.

Choice “B” does not contain an error because “it” correctly refers to the plastic water bottle. Also, “C” is not a good choice since “contents” is a plural noun addressing the liquid that is present inside the bottle.

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?

a. 1
b. 2
c. 3
d. No Error

Correct Answer: B

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.”

The two instances of the pronoun “him” are distractors because although they are pronouns, they are used correctly in the sentence.

I was supposedto meet₂ Jack at the movies before six o’clock. He arrived₃ early, but I arrived earliest₄.

Which part of the sentence contains a grammatical error?

a. 1
b. 2
c. 3
d. 4

Correct Answer: D

The comparative form should be used when comparing or contrasting two different objects, places, situations, etc. Because this sentence is comparing arrival times of only two people, the comparative form should be used.  The corrected sentence should read: “He arrived early, but I arrived earlier.”

The past tense verbs “was supposed” and “arrived” are used correctly, as well as the infinitive phrase “to meet.”

There₁ thinking about selling their₂ house; it’s the one with the red door over there₃.

Which part of the sentence contains a grammatical error?

a. 1
b. 2
c. 3
d. 4

Correct Answer: A

There, their, and there are commonly confused words. The sentence should begin with “they’re,” which is a contraction for they are.

“Their” is used correctly as a possessive, showing ownership of the house. At the end of the sentence, “there” is used correctly to show the location of the house.

Drivers veered₁ dangerously close to the edge of the winding road, attempting to bypass₂ the cows that were congregating, honking their horns₃.

Which part of the sentence contains a grammatical error?

a. 1
b. 2
c. 3
d. no errors

Correct Answer: C

“Honking their horns” is a misplaced modifier, or a modifier that is placed in the wrong order or location. Its placement at the end of the sentence incorrectly suggests that the cows are honking their horns, not the drivers. A corrected version of the sentence would read: “Drivers veered dangerously close to the edge of the winding road, honking their horns and attempting to bypass the cows that were congregating.”

Both “drivers veered” and “attempting to bypass” are used correctly.

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?

a. 1
b. 2
c. 3
d. no error

Correct Answer: B

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 answer choice B a fragment. The corrected sentence would read, “My band has been rehearsing daily because we have a concert in two weeks.”

Answer choices A and C are complete sentences that each have subjects, verbs, and express a complete thought.

Jack and Diane are an example of the belief that opposites attract₁. He loves going to the movies, she loves reading books₂. In addition, she is an introvert while he is an extrovert₃. Lastly, she loves vacationing at the beach; he loves vacationing in the mountains₄.

Which part of the passage contains a comma splice?

a. 1
b. 2
c. 3
d. 4

Correct Answer: B

A comma splice error occurs when two complete sentences are joined by only a comma, like in answer choice B. 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 but after the comma.

Answer choices A, C, and D are punctuated correctly.

It’s₁ time for the football game to begin, but the home team can’t find its₂ football. Did pranksters take it? Its₃ difficult to know exactly what happened.

Which part of the sentence contains a grammatical error?

a. 1
b. 2
c. 3
d. no error

Correct Answer: C

The word “it’s” is a contraction for it is. The word “its” is possessive, or shows ownership, but doesn’t need an apostrophe. “Its” in answer choice C should be revised to it’s and used as a contraction, because the writer intends to say, “It is difficult to know exactly what happened.”

Answer choice A uses “it’s” correctly as a contraction, while answer choice B uses “its” correctly as a possessive.

Mathematics Practice Test

Think you’re ready for the real deal? Try working through this free mathematics practice test:

12π ÷ 9 is approximately equivalent to:

a. 4/3
b. 4
c. 4π
d. Π

Correct Answer: B

4 is the correct answer.  Recall that a good estimation for π is 3.  So, 12π ≈ 12(3)

A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate. Which of the following did the student perform?

a. Rotation
b. Reflection
c. Refraction
d. Translation

Correct Answer: D

A translation is simply moving the object from one point on a plane to another point on the plane. The shape of the object remains the same; the object is simply moved along the plane.

If angle DEF is congruent to angle GHI, which of the statements is true?

a. ∠ E and ∠F are complementary
b. ∠D ≌ ∠I
c. ∠G and ∠F are complementary
d. Side DE ≌ Side EF

Correct Answer: C

If two triangles are congruent, then corresponding sides (sides that are in the same position) and corresponding angles (angles that are in the same position) are also congruent.  In the figure, this means that DE = GH, DF = GI, and EF = IH and m∠D ≌ m∠G, m∠F ≌ m∠I, m∠E ≌ m∠H.  The symbol in the corner of ∠E and ∠H tells us that E and H are right angles and are each equal to 90°.  Since the sum of the angles in any triangle is 180°, this means that since m∠H = 90°, then m∠G + m∠I = 180 – 90 = 90° and would, therefore, be complementary.  But what about ∠G and ∠F?  Well, since ∠F and ∠I are corresponding angles, they are congruent and their measures can be substituted for each other.  So, m∠G + m∠F = 90°.  Therefore, this option is a true statement.

In the expression 3x² + 6x +3, how many terms are in the equation?

a. 1
b. 2
c. 3
d. 4

Correct Answer: C

A term is either a single number, a variable, or numbers and variables multiplied together. The equation 3x² + 6x +3 has three terms: 3x², 6x, and 3.

Which of the following geometric objects has five faces, eight edges, and five vertices?

a. A pentagonal pyramid
b. A rectangular pyramid
c. An octagonal prism
d. A triangular prism

Correct Answer: B

A rectangular pyramid is the correct choice.

Tim rolls a pair of dice 25 times and records the sum of the numbers shown. How many different sums are possible?

a. 10
b. 11
c. 12
d. 36

Correct Answer: B

The possible sums when rolling a pair of dice are: 2, 3, 4, 5, 6, 7, 8, 9 10, 11, 12. There are 11 possible sums.

In the parallelogram above, what is the measure of angle G?

a. 100°
b. 110°
c. 220°
d. 120°

Correct Answer: A

A parallelogram’s angles have a sum of 360°. By definition, the opposite sides are parallel meaning that side GH and FI are parallel, and sides GF and HI are parallel.  When lines are parallel, their same side interior angles are supplementary: their sum is 180°.  This means that angle H and angle G have a sum of 180°.  So, if the measure of angle H is 80°, then angle G has a measure of 100°.  This problem requires an understanding of the properties of parallel lines as well as of the properties of parallelograms.

Which expression best represents y in terms of x?

a. y = x ­­– 2
b. y = 2x – 3
c. y = 1 – 2x
d. y = -(x + 4)

Correct Answer: C

The expression y = 1 – 2x is the only expression that satisfies ALL of the possibilities on the chart.

Mrs. Azul had each of her first graders separate a small bag of M&Ms into groups by color, arrange the groups into side by sidebars, and determine which color they had the most of. What concept is Mrs. Azul introducing to her first-grade class?

a. Range
b. Mean
c. Median
d. Mode

Correct Answer: D

Mrs. Azul is having her students arrange their data (M&Ms) into bars in order to compare the heights or lengths of the bars.  This is a visual representation of the bar that is the longest or has the most M&Ms – the mode.  A good way for students to remember mode is to think about the word most.  The mode is the piece of data (M&Ms in this case) that occurs the most frequently.

Order the following numbers from greatest to least: -2, ½, 0.76, 5, √2, π.

a. 5, π, √2, 0.76, -2, ½
b. 5, π, √2, 0.76, ½, -2
c. -2, 0.76, ½, √2, π, 5
d. -2, ½, 0.76, √2, π, 5

Correct Answer: B

This is correctly ordered from greatest to least.  The largest number is 5, which rules out answer choices C and D. The biggest issue here might be deciding which is larger: π or √2.  It is important to know that a good estimate for π is » 3; it is good to know that √2, the square root of 2, is some irrational number slightly bigger than 1.  So π > √2 and so far, we have: 5, π, √2.  0.76 is close to 0.75 or 3/4, which is bigger than 1/2. -2 is the smallest, the only number less than 0.  So, the correct order is 5, π, √2, 0.76, 1/2, -2.

The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500?

a. $500 = $2b + $0.75b
b. $500 + $2b = $0.75b
c. $500 = $2b – $0.75b
d. $500 – $0.75b = $2b

Correct Answer: C

The profit is equal to the selling price minus whatever costs are applicable.  So, if the profit is to be $500, then enough buttons must be sold to reach that profit.  If we are selling the buttons for $2 each, but it costs $0.75 to make each one, then there is a profit of $2 – .75 or $1.25 on each button.  How many buttons will we have to sell to reach $500 profit:  $500 = $1.25b.  This is: $500 = $2b – 0.75 c = 1.25b. So, the Booster Club will have to sell 400 buttons.

Susan surveyed the people leaving Mama Mia’s Pizza Palace to determine America’s favorite food when eating out. What is the best explanation for why the results of Susan’s survey might NOT be valid?

a. The survey is biased because it did not include everyone in America
b. The survey should have been conducted in front of a different restaurant
c. The survey is biased because it only interviewed people who had just eaten at a specific restaurant
d. The survey should have been conducted online

Correct Answer: C

This gives the best explanation of why this survey is invalid:  it only interviewed people who had just eaten at a specific restaurant, so the sample surveyed was definitely not random.

A sixth-grade class is asked to estimate the answer to the following question:
75.8 + 326.79 + 488.92 ÷ 11 = _____.

Which of the following would be the best answer?

Correct Answer: C

For 900, the sums of the first three numbers were estimated, but no division by 11 happened. For 80, this reflects that the total sum was divided by 11 (incorrect since only the last added 488.92 is to be divided by 11) and rounded to the nearest 10. For 82, this reflects that the total sum was divided by 11 (incorrect since only the last added 488.92 is to be divided by 11) and rounded to the nearest whole number.

This question checks for understanding of the order of operations. Since this problem involves both addition and division, division MUST be done first. The correct order of operations is parenthetical expressions, exponents, multiplication/division (left to right, whichever comes first), and finally addition/subtraction (left to right, whichever comes first).  So, the 488.92/11 is performed first. Since this is an estimation problem, it would be about 500 / 10, which is 50.  Then 75.8 + 326.79 is about 400.  Adding the 50 and 400, we get about 450.

Mrs. Fields’ science class takes care of a plant at school. The class is responsible for watering the plant and measuring its growth. The students’ measurements are charted in the table.

Which of the following equations relates the height of the plant, h, and the number of months, m, assuming a constant rate of growth?

a. 5m + 3 = h
b. 4m = h
c. 8m – 5 = h
d. 3m + 5 = h

Correct Answer: A

The difference between the growth of each month is 5 inches; looking at the growth of each month, the plant’s height increases 5 inches each month. If the rate of growth is constant, then the beginning height of the plant is 3 inches; the height at the first month (8 inches) minus the growth of that month (5 inches) would equal 3 inches. If the growth of each month is 5 inches, then one can find the height of the plant by the growth of each month (5 inches) multiplied by the month (m) and then add 3 inches to account for the initial height. 5m + 3 = h.

Mr. Andrews is in a city whose street grid can be represented by a coordinate plane. Mr. Andrews wants to walk from his current location at a local barbershop, represented on the coordinate plane as (1, 2), to his apartment. Mr. Andrews walks 5 blocks east, or to the right, and 1 block south, or down. Which of the following ordered pairs correctly depicts the location of Mr. Andrews’ apartment?

a. (6, 1)
b. (2, 7)
c. (0, 7)
d. (6, 0)

Correct Answer: A

The first number in the coordinates represents the X-axis, the second number represents the Y-axis. The X-axis runs horizontally and the Y-axis runs vertically. If Mr. Andrews walks 5 blocks east, or right, then it would be correct to add 5 to 1, which would be 6. If Mr. Andrews walks 1 block south, or down, then it would be correct to subtract 1 from 2, which would be 1. The correct answer is (6, 1).

What equation describes the linear relationship shown in the table?

a. y = 3x + 1
b. y = 2.5x
c. y + 1 = 3x
d. y + 3x = 1

Correct Answer: A

The table above is correctly represented by the equation y = 3x + 1.

Triangle ABC will be reflected across the line x = y. What are the coordinates of the reflection image of point A?

a. (-2,-1)
b. (2,1)
c. (1,2)
D. (1,-2)

Correct Answer: D

(-2,- 1) is the reflection of A over the x-axis (or y = 0). (2,1) is the reflection of A over the y-axis (x = 0). (1,2) is the result of a 90° clockwise rotation of A about the origin. While most are familiar with reflecting over a horizontal or vertical line, reflection over any line is permissible. The line y = x is used frequently in mathematics to find inverses of graphs. The inverse of a graph is its reflection over the line x = y. The reflection of the point over the line x = y of point B (-1,1) becomes (1,-1) or B; the x and y values are simply swapped. The same is true for point A (-2,1): the reflection is the point A’ which becomes (1,-2) and point C (-2,3), the reflection is the point C(3,- 2).

Tosha has 8 coins in her pocket. She has a mixture of pennies, nickels, dimes and quarters, but she has no more than 3 of any coin. What is the largest amount of money she could possibly have?

a. $1.11
b. $1.07
c. $1.23
d. $1.21

Correct Answer: A

To satisfy the prompt given, there must be a minimum of $.08 in pennies and a maximum of $2.00 in quarters. She will need to have the most number of the coins with the greatest value: quarters and dimes. So, that would be 3 quarters, 3 dimes, 1 nickel, and 1 penny. This totals $1.11

A runner is running a 10k race. The runner completes 30% of the race in 20 minutes. If the runner continues at the same pace, how long will it take to complete the race?

a. 67 minutes
b. 60 minutes
c. 85 minutes
d. 62 minutes

Correct Answer: A

To find the answer to this question, set up a ratio; remember that 30% = .3 and 100% = 1. (20 / .3) = (x / 1) When you cross multiply to solve for x, you get the equation .3x = 20. Divide each side by .3 to isolate x and the answer is 66.66666. The best answer choice is 67 minutes.

10, 8, 5, 3, 7, 4, 5, 9, 2, 3, 7, 3, 8, 6, 4, 1, 2, 1, 10, 3, 20.

What is the range and mode of the data set?

a. Range: 9; Mode: 3
b. Range: 10; Mode: 3 and 4
c. Range: 10; Mode: None
d. Range: 9; Mode: 3 and 4

Correct Answer: A

Remember that before you can find the median, the data must be arranged in order from least to greatest or greatest to least. Then the median is simply the middle term. In this set, however, there are 20 terms so the middle two terms are 4 and 5. The median, in this case, is the average of the two middle scores: (4 + 5) ÷ 2 = 4.5. The mean is the sum of all of the numbers in the data set divided by 20, the number of items in the data set: 101 ÷ 20 = 5.02. The mean is about 5.0. The mean is written as 5.0 because the value has been rounded to the nearest tenth; writing the mean as 5 would indicate that it is an exact whole number, 5.

There are 5 children in the Drake family.  The oldest children are 12-year-old twins, and the youngest child is 4 years old. If the sum of all the children’s ages is 47, what could be the ages of the other 2 Drake children?

A. 8 and 11 years old
B. 9 years old
C. 3 and 6 years old
D. 7 and 11 years old

Correct Answer: A

The sum of the ages of the five children is 47. The twins are 12 (2 x 12 = 24) and the youngest child is 4 years old. So, for these three children, we have used 24 + 4 = 28 of the sum of 47, leaving 19 as a sum of the ages of the two remaining children when each of the two children must be between the ages of 4 and 12. The only choice that sums to 19 is 8 and 11.

Which of the following best describes the polygon above?

a. A regular pentagon
b. A convex pentagon
c. A concave pentagon
d. A hexagon

Correct Answer: B

A convex polygon has no angles greater than 180°. Another way to think of how to identify a convex pentagon is that it has no angles pointing inward. A pentagon has 5 sides. The shape above is a convex pentagon.

Mrs. North’s front yard is in the shape of a pentagon. The measure of 4 of its angles are: 90°, 110°, 120°, and 90°. What is the measure of the fifth angle?

a. 128°
b. 88°
c. 28°
d. 130°

Correct Answer: D

To solve this problem, you need to know the sum of the angles of a pentagon. The sum of the angles of a pentagon is 540°. Therefore, the equation for the solution would be 540 – (90 + 110 + 120 + 90) = N. N, being the solution of the fifth angle, would be 130°.

Simplify: 30 – 2 * 50 + 70

a. 0
b. 570
c. -210
d. -70

Correct Answer: A

To simplify the equation, follow the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (PEMDAS) and work left to right. The steps to simplify the expression would be: 30 – 2 * 50 + 70 = 30 -100 + 70 = -70 + 70 = 0. PEMDAS can be slightly deceiving. The order of operations is: Parentheses, then exponents, then multiplication and division, then addition and subtraction. When performing multiplication/division, you perform the actions as they appear left to right; multiplication does not necessarily come before division – they have equal priority. The same goes for addition and subtraction.

Mrs. Harris writes all the numbers from 4 to 24 on slips of paper and places them in a hat. She then asks a student to pick a number from the hat. What is the probability that the number chosen by the student will be a prime number?

a. 1/24
b. 3/10
c. 1/3
d. 9/20

Correct Answer: C

Mrs. Harris writes down 21 numbers (4-24). This number set has 7 prime numbers (5, 7, 11, 13, 17, 19, and 23). That leaves 7 numbers out of 21 being prime. A student has 7 chances in 21 to choose a prime number. This can be simplified to 1 out of 3, or 1/3.

Reading Practice Test

Think you’re ready for the real deal? Try working through this free reading practice test:

Use the following passages to answer the 4 questions below. Passage 1 is by Dorothy Sayers; Passage 2 is adapted from a work by Raymond Chandler. 

Passage 1

The detective story does not and cannot attain the loftiest level of literary achievement. Though it deals with the most desperate effects of rage, jealousy, and revenge, it rarely touches the heights and depths of human passion. It presents us with an accomplished fact, and looks upon death with a dispassionate eye. It does not show us the inner workings of the murderer’s

mind—it must not, for the identity of the criminal is hidden until the end of the book. The most successful writers are those who contrive to keep the story running from beginning to end upon the same emotional level, and it is better to err in the direction of too little feeling than too much.

Passage 2

I think what was really gnawing at Dorothy Sayers in her critique of the detective story was the realization that her kind of detective story was an arid formula unable to satisfy its own implications. If the story started to be about real people, they soon had to do unreal things to conform to the artificial pattern required by the plot. When they did unreal things, they ceased to be real themselves. Sayers’ own stories show that she was annoyed by this triteness. Yet she would not give her characters their heads and let them make their own mystery.

Which of the following best paraphrases the main idea in Passage 1?

a. Detective stories are not great literature
b. Detective stories don’t have relatable characters
c. Detective stories may someday be improved upon
d. Detective stories have plots without direction

Correct Answer: B

Passage 1 makes the argument that detective stories “cannot attain the loftiest level of literary achievement.” In other words, detective stories “are not great literature.” So, choice “A” is correct.

Although the passage does mention how characters in detective stories aren’t really well-developed, that detail falls under the larger reason proving why detective stories are not great literature. So, choice “B” is incorrect. This reasoning applies to choice “D” as well. Choice “C” is off-topic

Which of the following statement would the author of Passage 2 most likely agree with?

a. Dorothy Sayers writes formulaic and predictable detective stories
b. Detective story writers should ensure that the characters are not too deeply develope
c. Dorothy Sayers’ writings have inspired a new type of detective story
d. Detective writers should hold on tightly to their plots and characters’ actions.

Correct Answer: A

The author in Passage 2 makes it clear that the reason why Dorothy Sayers (author of Passage 1) finds fault with the detective genre is that she comes to it with the assumption that it is prescribed. Thus, choice “A” is correct. Given the author’s opinion in Passage 1, choices “B” and “D” are incorrect and contradict the writer’s opinion. Choice “C” is off-topic.

Which of the following best describes the relationship between the two passages?

a. Passage 1 highlights the merits of the genre; Passage 2 downplays its faults
b. Passage 1 focuses on the uniqueness of the genre; Passage 2 focuses on its weaknesses
c. Passage 1 discusses the limitations of the genre; Passage 2 discusses the uniqueness of the genre
d. Passage 1 relates the details the particulars of the genre; Passage 2 generalizes the limitations

Correct Answer: C

Choice “C is the best answer because the first passage focuses on the limitations of writing in the detective genre, while Passage 2 focuses on how the detective genre is unique and has merit.

For an answer to be correct, all parts much be correct. Answer choice “D” is partially correct, but the second half of the answer is incorrect, thus making the entire answer incorrect. Choice “A” is completely incorrect—the passage expresses the opposite views as expressed in this answer choice. This reasoning applies to answer choice “B” as well.

Which of the following best describes the relationship between the two passages?

a. Passage 1 highlights the merits of the genre; Passage 2 downplays its faults
b. Passage 1 focuses on the uniqueness of the genre; Passage 2 focuses on its weaknesses
c. Passage 1 discusses the limitations of the genre; Passage 2 discusses the uniqueness of the genre
d. Passage 1 relates the details the particulars of the genre; Passage 2 generalizes the limitations

Correct Answer: A

The author in Passage 2 makes it clear that the reason why Dorothy Sayers (author of Passage 1) finds fault with the detective genre is that she comes to it with the assumption that it is prescribed. Thus, choice “A” is correct. Given the author’s opinion in Passage 1, choices “B” and “D” are incorrect and contradict the writer’s opinion. Choice “C” is off-topic.

Which of the following would the author of Passage 1 most likely agree with?

a. The detective genre involves a creative and unpredictable writing style
b. The plot of a detective story is formulated
c. Detective story writers soon be known as world-class writers
d. The characters in detective stories are well-developed and have deep inner worlds

Correct Answer: B

Choice “B” is correct because Dorothy Sayers, author of Passage 1, describes the predictable, strict, and formulaic writing style that characterizes the detective genre, in her opinion. Rationale: Choices “A,” “C,” and “D” contradict the expressed opinion of the author of Passage 1, so those choices are incorrect.

Use the passage below to answer the following 3 questions. 

1          Deep beneath the permafrost about 600 miles from the North Pole, a concrete chamber is keeping a treasure safe. The vault is hidden 390 feet inside a mountain in Norway’s remote Svalbard Islands. This isolated location ensures that the treasure concealed in the vault will remain untouched by any human or natural disaster. The vault was built to withstand bomb blasts and earthquakes, but the treasure it shields is not what you might expect. This vault was not built to store precious gems or gold bars. It was designed to store something even more valuable and critical to our very survival—food. This vault is sometimes called the Fort Knox of food.

2          The idea of storing seeds has been discussed by global organizations since the 1980s. Dr. Cary Fowler, who was president of the Global Crop Diversity Trust at the time of the vault’s creation, explained that construction plans for such a vault began to come together shortly after several natural disasters devastated global food crops. Fowler and his agency want to collect and safely store seeds to make sure they do not disappear in the future. He and other scientists are concerned that plant diversity is rapidly diminishing. “We are losing biodiversity every day,” Fowler explains. “It is kind of a drip, drip, drip—it’s also inevitable. We need to do something about it.” When a type of food is no longer grown because of a natural disaster, such as a flood, or because it becomes unpopular or too expensive to grow, it can disappear from stores and kitchens forever. The Global Crop Diversity Trust wants to prevent this by preserving as many varieties of seeds as possible. The assortment at the vault ensures that food supplies can be maintained or replenished if necessary.

All of the following are factors listed in paragraph 1 that help to protect the ‘treasure’ within the vault EXCEPT:

a. the fact that it is made out of concrete.
b. the fact that it was built on an isolated island.
c. the fact that it is located deep inside a mountain.
d. the fact that it is heavily guarded.

Correct Answer: D

Choice “D” is the correct answer because the passage mentions all of the other choices as protective factors associated with the vault except choice “D”—nothing in the paragraph hints at it being guarded. The fact that it’s located on a remote island in freezing temperatures deep within a mountain probably negates the need for any physical guard.

Paragraph 1 of the selection mentions that the food storage vault is built out of concrete and is located deep within a mountain on a “remote” island. Therefore, the first three choices do reflect an accurate reading of the text and so do not apply to the exception.

In paragraph 2, it can be inferred that Dr. Fowler:

a. has a distaste for seed storing.
b. is concerned about the inevitable food shortage.
c. wants farmers to grow a larger variety of crops.
d. is overwhelmed by the amount of seed varieties.

Correct Answer: B

Dr. Fowler’s tone indicates a hint of anxiety. The fact that “we need to do something about it” seems imminent from his speech. Therefore, choice “B” is the best option.

Choice “A” is incorrect in its tone. Choices “C” and “D” are off topic and not mentioned in the text.

In paragraph 2, what is the best definition for the word “replenished”?

a. Filled up again
b. Wasted
c. Distributed
d. Protected

Correct Answer: A

Choice “A” is correct because “replenished” means to refill or restock. The fact that the vault holds many varieties of seeds means that, if something occurred to threaten crop production, one could draw seeds from the vault and “replenish,” or “restock” the supply of seeds for that particular crop.

This question requires the use of context clues to discover word meanings. Paragraph 2 discusses how seeds can be kept in these vaults in order to have extra supplies to maintain or “replenish” the supply. Choice “B” is close to the opposite of the meaning of the word in question, so it is incorrect. “Protected” and “distributed” may seem like close substitutes, but distributing is what one would do after the seeds had been “replenished,” and protecting them is what the vault does do, but it does that in order to “replenish” the seeds. So, choices “C” and “D” are incorrect.

Use this passage to answer the following two questions. 

(1) Landscapes, images of natural scenery, remained a popular subject in early modern art. Driven in part by their dissatisfaction with the modern city, many artists sought out places resembling untouched (3) earthly paradises. In these areas, away from the bustle of the modern city, artists were able to focus on their work and observe nature firsthand. Because of this, many radical artistic experiments occurred (5) in the most rural and least “modern” of settings. These ranged from the use of unexpected, non-naturalistic colors, to the unusual application of paint.

Which of the following best states the main idea of this passage?

a. Similar to previous artists, modern artists enjoyed painting landscapes
b. Inspired by the modern city, artists experimented with new techniques
c. Early modern artists avoided the modern world and embraced nature, causing new techniques to be developed in old settingsEarly modern artists          used new techniques in color choice and application
d. Early modern artists used new techniques in color choice and application

Correct Answer: C

Option C is correct. The passage discusses artists’ desire to leave the modern city and focus on nature to create art, which caused new “modern” techniques to be created in settings that weren’t modern at all.

Answers A and D are stated in the passage but don’t give a complete sense of what the passage is about. Answer B is only partly correct, as artists experimented with new techniques but were not inspired by the modern city.

 

The author probably uses the word “dissatisfaction” in line 2 to mean:

a. contentment.
b. unhappiness.
c. unkempt.
d. misery.

Correct Answer: B

Option B is correct. Artists expressed their “dissatisfaction,” or unhappiness, with the city, so they went to the country to create.

Option A is an antonym of the correct answer. Option C is completely unrelated; it means “misery.” Option D is an overstatement; the artists were unhappy, not miserable.

Use this passage to answer the following 3 questions. 

(1) When you go on vacation, it is often customary to send friends and family members postcards from the places you visit. The postcards not only let them know where you are and how you’re doing, but (3) they provide them with a keepsake from your vacation. Today, the ritual of sending postcards has been somewhat replaced by posting vacation pictures on Facebook, Instagram, and other social media (5) sites. In a recent survey of vacationers, 75% said that they are more likely to post on Facebook than to send a postcard. Not long ago, however, it was not uncommon for people to amass many hundreds of (7) postcards received from acquaintances. As these collections grew, a hunger for more postcards arose, and some people became amateur postcard collectors.

The author probably uses the word “amass” in line 6 to mean:

a. purchase.
b. gradually gather.
c. achieve.
d. surrender.

Correct Answer: B

Option B, “gradually gather,” is correct because people collect, or gather, postcards that they receive from friends and family.

Option A, “purchase,” is incorrect because people receive the postcards from their friends and family, they don’t buy them. Option C, “achieve,” is incorrect because it means “to accomplish,” and doesn’t make sense in the sentence. Option D, “surrender,” is incorrect because it is an antonym meaning “to give up.”

Which of the following would be an antonym for the word “customary” as it is used in line 1 of the selection?

a. Expected
b. Ordinary
a. Unusual
d. Common

Correct Answer: D

Option D, “common,” is correct because it is a synonym for “customary,” and means “of frequent occurrence; usual.”

Option A, “unusual,” is incorrect because it is an antonym of “customary.” Option B, “ordinary,” is incorrect because it’s meaning (of no special quality or interest; unexceptional) doesn’t make sense in the sentence. Option C is incorrect. Although it is closer to the correct meaning than answer choices A and B, “common” is still closer to the meaning of “customary” than “expected,” which means “to regard as likely to happen.”

Which of the following details most supports the author’s view that vacationers prefer social media to postcards?

a. The use of the word “customary” in line 1
b. The statistics used in line 5
c. The reference to postcard collectors in line 8
d. The mention of “hundreds of postcards” in lines 6 and 7

Correct Answer: B

Option B is correct because the author has used a fact as statistical evidence to prove his point.

Option A is incorrect because it mentions use of postcards, not social media. Option C is incorrect because it focuses on postcard use in the past, not social media use in the present. Option D is incorrect because the fact that people used to collect postcards in the past has no bearing on the fact that people currently prefer social media.

Use the map below to answer the following two questions. 

According to the map, Brazil:

a. Is a country located to the east of Peru.
b. Is a city located to the east of Peru.
c. Is a city east of Chile.
d. Is a country south of Argentina.

Correct Answer: A

This question requires a reader to carefully study the map and the map key. It requires one to follow geographical directions and carefully locate directions on a map. “A” is the correct answer choice here because it accurately describes the location in question.

This question requires you to carefully study the map and be able to read and use the map key. Choices “B” and “C” are incorrect because Brazil is not a city. Choice “D” is incorrect because Brazil is north of Argentina.

According to the map, the Sechura Desert:

a. Runs south of Bolivia.
b. Is west of the Pacific Ocean.
c. Runs down the west coast of Peru.
d. Runs the border of Peru and Brazil.

Correct Answer: C

This question requires a reader to carefully study the map and the map key. It requires one to follow geographical directions and carefully locate directions on a map. “C” is the correct answer choice here because it accurately describes the location in question.

According to the map, the Sechura Desert runs the western border of Peru, off the coast of the Pacific Ocean. It is north of Bolivia and is on the east side of the Pacific Ocean, so choices “A” and “B” are not correct. And it does not border Brazil, so choice “D” is not correct.

The following is an excerpt from a speech delivered by Frederick Douglass to the International Council of Women in Washington, D.C., April 1888 on the topic of Women’s Suffrage.

Use the passage to answer the following two questions. 

All good causes are mutually helpful. The benefits accruing from this movement for the equal rights of woman are not confined or limited to women only. They will be shared by every effort to promote the progress and welfare of mankind every where and in all ages. It was an example and a prophecy of what can be accomplished against strongly opposing forces, against time-hallowed abuses, against deeply entrenched error, against worldwide usage, and against the settled judgment of mankind, by a few earnest women, clad only in the panoply of truth, and determined to live and die in what they considered a righteous cause.

In the above passage, Douglass arrives at the logical conclusion that if women are given equal rights, then:

a. women won’t have to die for the cause anymore.
b. a prophecy can come true.
c. these few earnest women can have the satisfaction of knowing their effort was not in vain.
d. many other good causes will benefit from this gain as well.

Correct Answer: D

Douglass claims that “all good causes are mutually helpful”; in other words, by winning the cause of women’s rights, many other good causes will be won as well. Therefore, “D” is the best answer.

The other answer choices, though some may be generally true (like “C”), they don’t support Douglass’ main claim: that this cause is linked to other causes.

Which of the following statements would the speaker MOST likely agree with?

a. Making a gain for one cause in human rights furthers the rights of all mankind
b. The government should focus its efforts solely on Women’s Rights
c. Many abuses are solved simply by a few good people
d. We must work diligently to correct one need at a time

Correct Answer: A

Douglass makes it clear that one advancement for society is an advancement for us all; these human rights violations are all connected. Therefore, “A” is the best choice.

Answers “B” and “D” both lean toward isolating causes; this claim contradicts Douglass’ assertion that all violations and all civil rights wins are connected. Choice “C” goes against Douglass’ inferred idea that we should all be working together—Douglass would not simply want a small number of people working on a goal, but his aim is to unite the people in these causes. Although its way is historically true in some cases that a “few good people” have worked toward winning a cause, Douglass would not want that to necessarily be the case.

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