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Praxis® Core
Ultimate Guide
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Preparing to take the Praxis®
Core?
Table of Contents
Awesome!
We will answer every question you have and tell you exactly what you need to study to pass the
Praxis® Core.
• Quick Facts
• Reading
• Mathematics
• Writing
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Overview:
The Praxis® Core Academic Skills for Educators exam tests individuals in reading, writing, and
mathematics. Its purpose is to measure the skills and content knowledge of individuals entering into
teacher preparation programs.
Format:
Be mindful of newly updated test numbers. Listed below are the changes for the current exam:
• Reading 5713 (new) same as 5712 (old)
• Mathematics 5733 (new) same as 5732 (old): the content categories have changed for the
new mathematics exam
• Writing 5723 (new) same as 5722 (old)
• Combined test 5752 (new) same as 5751 (old)
It is important to note that while the test codes changed for the Reading and Writing test, the
Cost:
$90 for each subtest or
$150 for the combined exam
Scoring:
The score range is 100-200. The passing rate varies per state but generally, you need a 156 on the
reading exam, 150 on the mathematics exam, and a 162 on the writing exam.
Pass rate:
Quick Facts
Test Number of Questions Time Limit
Reading 56 selected-response 85 minutes
Mathematics 56 selected-response 90 minutes
Writing
40 selected-response
2 essays
40 minutes 30
minutes per essay
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46% pass rate across all subtests
Study time:
It is important to set goals to know how much time you need to devote to studying each day. Start
off assessing how well you know the content by taking a practice sample test. Use the information
you are not familiar with to create a study plan. Stick to your developed plan and make sure to cover
all material thoroughly. Take the practice sample test again to gauge if you’re ready to take the real
exam.
What test takers wish they’d known:
• What the test covers
• How to use the computer-based calculator
• To arrive early to have adequate time for the tutorials on how to take the test
• To check test numbers to ensure registering for the correct test
• That test numbers have changed recently
• How important practice sample tests are
Information obtained from the ETS website: https://www.ets.org/praxis/about/core/
Quick Facts
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Overview
The Core Reading test (5713) has 56 selected-response questions. You will have 85 minutes to
complete this test.
There are three content categories on the Core Reading test:
Main Idea and Primary Purpose
The main idea is what the text is mostly about. The main idea may be clearly stated in a topic
sentence, or a reader may need to read the text in detail and decide what it is mostly about. The
primary purpose is the reason the author wrote the text. It could be to persuade a reader, to inform
a reader, or simply to entertain a reader. The main difference between the two is that the primary
purpose focuses on the author’s intention and the main idea focuses on the content of the text. So
When you come suddenly upon the porcupine in his native haunts, he draws his head back and
down, puts up his shield, trails his broad tail, and waddles slowly away. His shield is the sheaf of
larger quills upon his back, which he opens and spreads out in a circular form so that the whole body
is quite hidden beneath it. The porcupine’s great chisel-like teeth, which are quite as formidable as
those of the woodchuck, he does not appear to use at all in his defense but relies entirely upon his
quills, and when those fail him he is done for.
Throughout the passage, details on how a porcupine defends himself are bolded. These details
support the conclusion that the main idea = the defense mechanisms of the porcupine.
Reading:
Content Category # of Questions % of Test
Key Ideas and Details 17-22 35%
Craft, Structure, and Language Skills 14-19 30%
Integration of Knowledge and Ideas 17-22 35%
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the reader about the defense mechanisms of the porcupine.
Draw Inferences
Inference is using your background knowledge and what you read in a text to make a logical
answer the inferencing question:
It has been seen that ames have been prominent sources of articial light; and although of low
luminous efciency, they still have much to commend them from the standpoints of portability,
convenience, and subdivisions. The materials which have been burned for light, whether solid
or liquid, are rich in carbon and the solid particles of carbon by virtue of their incandescence are
responsible for the brightness of a ame.
According to the information provided in the passage, which of the following inferences can be
A.
B.
C.
D. The more carbon, the brighter the light.
D is the correct answer because the boldface words in the passage help to support the fact that
Analyze Organization
You will be asked to identify how an author constructed a passage or how paragraphs are related to
one another. Here are some examples of how text can be organized:
• Sequential order puts events or ideas in order based on logic.
• Chronological order puts events in order based on time.
• Order of importance puts events or steps in order based on their importance. They can be
ordered from least important to most important or vice versa.
• Spatial order puts objects in order based on physical or directional location.
• Cause and effect explains the reasons something happens and the results of it happening.
• Problem and solution
• Compare and contrast lists and explains the similarities and differences between two or
more things.
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Fact vs. Opinion
The same piece of writing can include both facts and opinions. Often in an argumentative or
persuasive piece, the author will use facts and details to prove his opinion is correct. Remember
that facts are details that can be proven. Opinions are more emotional statements that represent the
author’s beliefs about the topic. Here are some examples:
Fact: The atmosphere is about 78% nitrogen gas.
Opinion: Van Gogh is by far the greatest painter of his time.
Interpret Graphs
Graphs are often included in informational texts to supplement the main idea or provide a visual
depiction of the data provided. Some features to look for in a graph are headings, captions, a key,
a scale, and labels. The reader should read all text presented with the graph, determine the type of
graph used, and identify what relationship the data is showing. Using the graph below, let’s look at
some of these features to analyze the type of graph and its data.
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The graph shown is a bar graph that has a key to show the color-coding of each company: Company
A is orange and Company B is green. The graph also shows bar labels, indicating the years from
2015 to 2020.
The horizontal axis title is Years, referring to the bar labels listed. The vertical axis has a title of
Number of Cans Produced (in thousands). The vertical axis also has a numbered scale that correlates
to the vertical axis title indicating how many cans were produced by each company each year.
Meaning of Words
You will be asked to identify the meaning of a given word based on how it is used in a passage.
choices.
• Context clues are hints that the author gives within the text. They can be in the same
sentence as the unfamiliar word or in the surrounding sentences.
•
sentence in which the word appears.
• Replace the answer choices in the passage to see if it makes sense.
Let’s look at the example problem below and use the strategies suggested.
A picture is worth a thousand words. When you go on vacation, it is often customary to send friends
and family members photo postcards from the beautiful places you visit. The postcards not only let
them know where you are and how you’re doing, but 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 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 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” to mean:
A. achieve.
B. surrender.
C. purchase.
D. gradually gather.
D is the correct answer. The boldface words in the passage are context clues that help to clarify the
meaning of the word amass. Grew means that they started out small and got bigger, and collection
indicates many. Both of these words help the reader to understand that amass means to gradually
gather.
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You also could replace amass with the various answer choices to see which one makes sense
semantically or syntactically.
And that’s just some very basic information about the Core Reading test.
Now, let’s look at a few practice questions.
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Question 1
Consider the following passage:
Most reading will be for the content. It is desirable that the reading be easy and rapid, and that one
gathers in all the ideas as one reads. Because of the fact that oral reading is slower, more laborious
for both reader and listener, and because of the present easy accessibility of printed matter, oral
reading is becoming of steadily diminishing importance to adults. No longer should the central
educational purpose be the development of expressive oral reading. It should be rapid and effective
silent reading for the sake of the thought read.
Which of the following statements about expressive oral reading can best be inferred by this
A. Oral reading allows for a wider sharing of ideas.
B. Oral reading was an educational mainstay in the past.
C. Expressive oral reading is educationally effective.
D. Oral reading is faster than silent reading.
Correct Answer: B. The passage states that the central educational purpose should “no longer” be
oral reading, inferring that it used to be a mainstay.
Question 2
Consider the following passage:
In all probability no student of mycology has any one query more frequently or persistently pressed
after all.
This passage is primarily concerned with:
A. dispersing false ideas about mushrooms and toadstools being separate groups.
B. the different levels of toxicity of mushrooms and toadstools.
Reading Practice Questions
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C. how to tell toadstools and mushrooms apart.
D.
Correct Answer: A. The primary purpose of this passage is to relate that the two designations are
actually one group.
Question 3
Consider the following passage:
The light of the Crescent Moon, like some fairy boat suspended in the sky, is bright enough to cast
changing and dancing sparkles of silver upon the ocean. The Evening Star declines slowly in its turn
toward the western horizon. Our gaze is held by a shining world that dominates the whole of the
occidental heavens. This is the “Shepherd’s Star,” Venus of rays translucent.
A. A bizarre image is used to illustrate a ridiculous claim.
B. A metaphor and highly sensory language is used to convey awe for the night sky.
C.
D.
Correct Answer: B. This is the way the author is conveying the information.
Question 4
Consider the following passage:
Nature has so strongly marked the wild and the tame hog with the same characters, that no
hesitation arises in pronouncing the former to be the stock from whence we have derived the latter.
In common, however, with all other free and domesticated animals, there is a prolongation of muzzle
in the wild species, which is not to be found in those of our sties.
A. Wild hogs and tame hogs look very similar to one another.
B. Wild hogs have a longer muzzle as they need to smell out their food.
C. Wild hogs are more aggressive than domesticated ones.
D. Domesticated hogs are easy to tell apart from wild ones.
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Correct Answer: A. The passage supports this inference by stating that wild and domestic hogs have
“the same characters.”
Use the following passage to answer questions 5-7:
The Black Death, or, as it has been known, the Oriental plague, the bubonic plague, or in England,
such as have been seen in no other febrile disease. All the symptoms were not found in every case,
of the plague, some patients recovered.
and fell into a deep sleep, or became speechless from palsy of the tongue, while others remained
beverage could assuage the burning thirst, so that suffering continued without alleviation until
death, which many in their despair accelerated with their own hands. Contagion was evident, for
attendants caught the disease from their parents and friends, and many houses were emptied of
their inhabitants.
Question 5
This passage is primarily concerned with:
A. the plague’s many symptoms and its effects on individuals.
B. the effects of religion on those who chose suicide over suffering.
C. the widespread contamination by those treating the disease.
D. the false assumptions about the disease that lead to hysteria.
Correct Answer: A. This is the main idea of the passage.
Question 6
The author mentions “death, which many in their despair accelerated with their own hands” to show:
A. the loss of faith in the victims.
B. the dissemination of false beliefs.
C. the desperation of those suffering.
D. the strict religious expectations.
Correct Answer: C. The author mentions this in order to show how desperate victims were to
alleviate their pain.
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Question 7
The passage suggests that the Black Death was hard to detect because:
A. not all patients exhibited all or similar symptoms.
B. it was highly contagious and proved fatal almost from the onset.
C. there were no more people to treat patients and detect symptoms.
D. people were too scared to be around plague patients.
were not found in every case.”
Question 8
Consider the following passage:
The hopeless pessimism of the past, that saw in the unmerciful progress of organic evolution
no escape for the human animal from the grip of fate, is about to give way to the enthusiasm of
has discovered that he can not only change his environment, but that by this change he can modify
himself. The hope of the future lies in the moulding of man’s surroundings to his needs.
A. Humankind was happier before the age of machines.
B. Humankind created machines to change the environment.
C. It is most natural for humans to live in harmony with nature.
D. Humankind should accept its fate as a creator of machines.
Correct Answer: B. The passage presents the ability to change one’s environment as positive by
Question 9
Consider the following passage:
cases for a short time, it manifests itself most frequently by far over a period of years, or even a life-
time. It represents a trait rather than an episode. Extensive, very complicated fabrications may be
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A. a rebuttal of a claim about the pathology of lying
B. a summary of recent progress in studying pathological liars
C.
D.
Question 10
Consider the following passage:
convenience, and subdivisions. The materials which have been burned for light, whether solid
or liquid, are rich in carbon, and the solid particles of carbon by virtue of their incandescence are
According to the information provided in the passage, which of the following inferences can be
A.
B. The more carbon, the brighter the light.
C.
D.
Correct Answer: B. The passage explains that “solid particles of carbon...are responsible for the
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Overview
The Core Writing test (5723) has 40 selected-response questions and two essays. You will have 100
minutes to complete this test (40 minutes on selected-response questions and 30 minutes on each
essay).
There are two content categories on the Core Writing test:
Pronoun-Antecedent Agreement
Pronouns need to match their antecedent (noun) in person, number, and gender.
Susan called her husband to remind her to pick up bread, eggs, and milk.
In this sentence the pronoun her does not match its antecedent her husband. The pronoun him
should have been used instead.
The teacher wanted the boy to bring their book to class.
Their is the incorrect pronoun because it refers to more than one noun. “The boy” refers to only one
noun. The pronoun he should have been used instead of their.
Writing:
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Misplaced and Dangling Modiers
sentence.
Let’s look at some examples:
Incorrect: Paul was exhausted after mowing, and he fell right onto the bed covered in sweat.
Correct: Paul was exhausted and covered in sweat after mowing, and he fell right onto the bed.
covered in sweat after bed
instead of after Paul, the subject it is modifying.
Correct: Having broken his right hand, Paul
Paul. Changing it and
rewording the clause helps make the sentence clear about who the his
clause.
Parallelism
Parallelism, also called parallel structure, is when a series of components in a sentence are written in
a similar manner. The repetition creates balance and rhythm in the text.
He came, he saw, he conquered.
Like father, like son.
Sophia’s favorite activities include running, biking, and skiing.
Credible Sources
Credible sources are those that readers can trust. What are some things to look for when deciding if
• Check for the source of information.
• Check for the URL extension. A URL extension is the notation at the end of a web
address that categorizes the website type. The most credible online sources often end in
“.edu” (educational institution) or “.gov” (government resource), but not always. Other URL
extensions like “.com”, “.org” and “.net” can be purchased by anyone.
• Evaluate the credibility of the author. Check to see if any other accredited sources have
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that might suggest bias or hidden agenda.
• Check to see when the information was published. New research can quickly make the
information outdated.
• Professional website design shows the source has spent money or time in their marketing
and can show that a source is or isn’t credible just by appearance.
• Check for citations and verify that any cited source information is correct.
Essay Tips
You will be required to write two essays for part of the writing exam. One essay will be an
argumentative essay and the other one will be source-based. The selected-response questions and
the two essays will be scored together for a total score.
Tips for organizing these essays:
1. Write a thesis statement. It is important to have a clear thesis in order to get full credit for
the essays. Make sure to clearly state your point when writing the argumentative essay
and insightfully explain why the topic is important on the source-based essay.
2. Create an outline of the body paragraphs. This will help you to structure your essays so
you are able to express your ideas clearly.
3. Fill in paragraphs with details to support your opinions and facts.
4.
5. Read carefully through the essay, checking the grammar, punctuation, and mechanics of
your sentences. Check for subject-verb agreement throughout the essay and make sure
the tone of your essay is appropriate for the style of writing.
6.
And that’s just some very basic information about the Core Writing test.
Now, let’s look at a few practice questions.
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Question 1
We love everything about our new house aside from the fact that one of the neighbors have a dog
that is constantly barking.
A. the neighbors have (no change needed)
B. the neighbor’s have
C. the neighbors has
D. the neighbors’ have
E. the neighbor’s has
Correct Answer: C. This correctly changes the conjugation of the verb have. Neighbors is plural, but
we are referring to “one of our neighbors,” which is a singular subject, so we must use the singular
verb form, “has.”
Question 2
Identify the error in the sentence below.
I purchased a new bed for my dog, Peaches, but she chewed it up almost immediately, which leads
me to believe that she would prefer to sleep on the couch. No error.
A. I purchased
B. she chewed it up
C. leads me to believe
D. she would prefer
E. No error.
Correct Answer: E. Although there are multiple subjects and verbs in this sentence, there are no
errors.
Question 3
Identify the error in the sentence below.
After a grueling soccer practice in the excessively hot sun, I was hungry and thirsty my mom took me
home for dinner. No error.
Writing Practice Questions
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A. grueling soccer practice
B. excessively hot
C. sun, I
D. thirsty my
E. No error.
Correct Answer: D. This is a run-on sentence, and the two independent clauses should be separated
by a period, a semicolon, or a coordinating conjunction between “thirsty” and “my” (which should
now be capitalized).
Question 4
Identify the error in the sentence below.
Josh and Nick couldn’t hardly wait for the bell to ring on Friday so they could go home and play their
new video game. No error.
A. hardly
B. Friday
C. so
D. their
E. No error.
Correct Answer: A. This double negative is incorrect. Either the word “hardly” should be deleted or
“couldn’t” should be changed to “could.”
Question 5
When deciding a vacation spot, the Johnson family considered cost, weather, and how close it was to
a beach.
A. how close it was to a beach (no change needed)
B. how close to a beach
C. where a beach was
D. proximity to a beach
Correct Answer: D. This correctly changes the second part of the sentence so that the noun phrase
“proximity to a beach” completes the list. This ensures that the sentence is parallel.
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Question 6
A. My Life with Chimpanzees by Jane Goodall
B. a news article written based on an interview with Goodall
C. a biography of Goodall provided on the Jane Goodall Institute website
D. a documentary providing a broad overview of her life
Correct Answer: A. Since this is Jane Goodall writing about her own experience, it would be a
primary source.
Question 7
United States Holocaust Memorial Museum. “Introduction to the Holocaust.” Holocaust Encyclopedia.
https://encyclopedia.ushmm.org/content/en/article/introduction-to-the-holocaust. Accessed on 4 Apr.
2019.
listed tells us that:
A. this is the name of the website.
B. this is a primary source with an unknown author.
C. the individual name of an author was not provided.
D. this is the title of the source and indicates that “Introduction to the Holocaust” is the
subtitle of the article.
Correct Answer: C. When an individual author is not known, the organization publishing the material
can be used instead for citation purposes.
Use the following passage to answer questions 8-10.
The excerpt below is from a 1918 cookbook encouraging Americans to conserve wheat.
(1) A slice of bread seems like an unimportant thing. (2) One good-sized slice of bread weighs an
20,000,000 homes wastes on the average only one such slice of bread a day, the country is throwing
for over a million one-pound loaves a day. (6) For a full year at this rate there would be a waste of
wheat on the average are raised per acre. (9) It would take the product of some 470,000 acres just to
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provide a single slice of bread to be wasted daily in every home.
(10) Some say, “a full slice of bread is not wasted in every home.” (11) Very well, make it a daily
Small changes made on a large scale would have made an impact on the amount of wheat used in
every housekeeper who permits a slice of bread to be wasted in her home.
Question 8
One good-sized slice of bread weighs an ounce. It contains
A.
B.
C. an ounce, but it contains
D. an ounce because it contains
Correct Answer: A. Of the available options, this would be the most logical choice because the
semicolon connects the two related sentences.
Question 9
But some suggest that this is an exaggeration.
A. following sentence 9, at the end of the paragraph
B. following sentence 5
C. before sentence 10, at the beginning of the paragraph
D. following sentence 10
Correct Answer: C. This would be the best location to include this sentence. It would serve as a
transition into the main idea of the paragraph, since the paragraph goes on to refute this idea.
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Question 10
who permits a slice of bread to be wasted in her home.
A. move it to the end of paragraph 1
B. remove the sentence completely
C. move it to the beginning of the passage
D. leave it as is
Correct Answer: D. This sentence works well at the end of this passage to wrap up and provide
context for the previous facts and information.
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Overview
The Core Mathematics test (5733) has 56 selected-response and numeric entry questions. You will
have 90 minutes to complete this test. An on-screen calculator will be provided for you.
There are three content categories on the Core Mathematics test:
Scale Factor
Scale factors are used to help create models and drawings of extremely large or small items. The
steps to using a scale factor:
1. Convert the measurements to decimals or to the same units
2. Set up a ratio using scale factor
3. Cross multiply and simplify
4. Divide both sides to isolate x
Example: A woman is 5 feet 4 inches tall and her shadow is 4 feet 2 inches long. A girl is standing
First, convert the height and shadows to inches. Then set up a ratio of height to shadow for each
person:
Woman:
Mathematics:
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Girl:
Now, combine the two ratios into a proportion:
Cross-multiply:
64(39) = 50x
2496 = 50x
Divide both sides by 50 to isolate x:
x = 49.92 inches
So the girl’s height is about 4 feet and 1.92 inches
Percent Change
The percent change is the amount of increase or decrease between two numbers, compared to the
original number, written as a percent.
percent change = 100% x change divided by original
Find the difference or the change in the two values being compared
Divide the value of the change by the original number
Multiply by 100
Gabrielle is a babysitter who charges an hourly rate for her services. She has recently increased her
First, subtract: 15 - 12.50 = 2.50
Second, divide: 2.50 / 12.50 = .2
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Fractions, Decimals, and Percents - Conversions
To convert a fraction to a decimal, divide the numerator by the denominator.
Example: Write as a decimal.
Divide 4 by 5 to get 0.8
To convert a decimal to a fraction, determine the place value of the last digit, such as tenths,
hundredths, thousandths, etc. The base 10 number of the last value will be the denominator, so if it
ends in the tenths position, the denominator will be 10, or if the last digit is in the thousandths place,
the denominator will be 1000. Then place the number without the decimal in the numerator position
and simplify.
The last digit is in the thousandths place, so the denominator will be 1000
The number without the decimal is 325, so the fraction is
Simplify: =
Multiply the decimal by 100, then put the number over 100 and simplify if necessary.
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Multiply 0.32 by 100: 0.32
x
100=32
Now write 32 over 100:
Simplify: =
To write a percent as a decimal, divide the percent by 100 and remove the percent symbol. This will
move the decimal point over to the left by two places.
37.4% divided by 100 becomes 0.374
To convert a decimal to a percent, multiply the decimal by 100 and add the percent symbol.
This will move the decimal point two places to the right.
Multiplying 0.632 by 100 moves the decimal point two places to the right: 63.2%
To convert a fraction to a percent, convert the fraction to a decimal, then multiply by 100.
Example: What is
First, convert ¾ to a decimal by dividing the numerator by the denominator: 3
÷
4 = 0.75
Next, multiply the decimal by 100 and add the percent symbol:
¾ = 0.75 = 75%
To convert a percent to a fraction, remove the percent symbol, and then write the number over 100.
Simplify this fraction if necessary.
First, write 60% as a fraction over 100:
60% =
Then simplify:
=
Measures of Central Tendency
Mean, median, and mode are all measures of central tendency. They are different ways of describing
the center of a series of data points. Range is also a measurement used to describe data.
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The mean is the average of all of the data points in the set. It is found by adding the values of all of
the data points and dividing by the number of data points.
The median is the middle number of a set of numbers. It is found by ordering the numbers from
least to greatest and selecting the number in the middle. If there is an even number of numbers, the
median is the average of the two middle numbers.
The mode is the data point in the set that occurs the most often.
The range is the difference between the highest and lowest values in the data set.
Probability
the number of possible outcomes.
Probability =
Example:
Score Number of Students
A 3
B 15
C 11
D 7
The table above shows the number of students who earned an A, B, C, or D on a test. If a student
In the table, 15 students earned a B. A total of 36 students took the test.
Solving for x in Linear Equations
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To solve for x in linear equations, it is important to use inverse operations to isolate the variable.
Example: Solve for x in the equation 3x - 4 = 8
3x - 4 + 4 = 8 + 4
3x = 12
x
/=
x = 4
Circle Measurements
circumference of a circle.
The diameter is a line segment that runs from one point on the circle to another by passing through
the center of the circle.
The radius is a line segment that runs from any point on the circle to its center.
The circumference of a circle is the perimeter around the circle. It is found by multiplying the
diameter by or multiplying 2 radius.
The area of a circle is the area inside of the circle and is found by multiplying by the radius squared.
Example: Find the circumference and area of a circle with radius 4 inches.
C
A
And that’s just some very basic information about the Core Mathematics test.
Now, let’s look at a few practice questions.
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Question 1
A circle is divided into 5 sections and 4 of them are labeled with the fraction of the circle they
represent.
A. 1/5
B. 1/12
C. 1/6
D. 1/8
Correct Answer: B. The entire circle can be assumed to have an area of 1. Using the principle of the
least common denominator, the area represented by fractions equals:
+ + = + + + =
This can be reduced to , which means the remaining fraction represents .
Mathematics Practice Questions
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Question 2
Bill went to the store to purchase new clothes for the upcoming school year. Bill purchased 8 shirts,
A. 32
B. 16
C. 42
D. 48
Correct Answer: D. The answer can be found by multiplying the number of shirts by the number of
pairs of shorts and pairs of pants. This would create the equation (8 shirts) × (4 pairs of shorts + 2
pair of pants) = 8 × (4 + 2) = 8 × 6 = 48.
Question 3
When Joshua moved into a new apartment, his monthly rent decreased from 35% of his budget to
A. $1,920
B. $160
C. $960
D. $1,120
Correct Answer: A. Joshua will save 5% of $3200 each month, which is $160. To determine the
annual savings, multiply 160 by 12: 160 x 12 = $1920.
Question 4
This graph shows the temperature in Chicago on a spring afternoon.
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A. 3%
B. 1%
C. 9%
D. 10%
multiply by 100%.
In this case, it was 294K at 1pm and 297K at 3 pm.
x 100% = 1%
Question 5
A. 45 minutes
B. 1 hour, 5 minutes
C. 1 hour, 21 minutes
D. 55 minutes
Correct Answer: D. One option to determine the length of the class period is to see how long it is
from the start of class to the next full hour (from 10:43 am to 11:00 am), and then add the minutes
part of the end time. In this case, 11:00 am can be thought of as 10:60 am so that subtraction with
10:43 is easy: 10 – 10 = 0, so 0 hours and 60 – 43 = 17, so it is 17 minutes until 11 am. Then, from
11:00 am to 11:38 am is 38 – 0 = 38 minutes. The total length of the class is 17 + 38 = 55 minutes.
Another option to determine the length of the class period would be to reason that if it were an hour
before 11:43 am (43 – 38 = 5), and so this class is 5 minutes shorter than 1 hour, or 55 minutes long.
Question 6
that 60 of them read the local newspaper. Based on this sample, which of the following is the best
A. 450
B. 45
C. 4500
D. 5
Correct Answer: C. Of the 200 people sampled, 60/200 or 30% read the paper. 30% of the town’s
population is (0.30)(15200) = 4560. Therefore about 4500 people read the local paper.
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Question 7
drew a total of ten cards. His draws were as follows: 10, J, 10, K, 1, 2, 6, 10, 11, 4.
A. 3/10
B. 1/13
C. 1/4
D. 3/8
should ignore the extra information of what he drew so far.
Since there are four 10s in a standard deck of 52 cards, the probability of drawing a 10 is 4/52, or
1/13.
Question 8
A. Marty earns $12 for typing a paper. If her rate is $54 per hour, what is x, the number of
B. Marty collected 12 dozen eggs every day for 54 days. What is x, the total number of
C. Marty had 54 minutes left on her cell phone plan. If she uses 12 minutes, what is x, the
D. Marty made car payments on her car for 54 months until it was paid off. What is x, the
Correct Answer: D. To get the total months, 54, multiply the number of years, x, by the number of
Question 9
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A. v° = y°
B. x° + y° + z° = 180°
C. x° + y° = u°
D. w° = 90°
Correct Answer: D. There is no indicator that this is a right angle, so even if it appears this way, do
not assume so unless it is stated or there is a box in the corner.
Question 10
The Trout family just purchased a large table in the shape of a perfect circle. It is 600 cm across. John
helps set one side of the table for dinner and walks exactly halfway around the table. Which of the
A. 1,900 cm
B. 1,000 cm
C. 950 cm
D. 600 cm
Correct Answer: C. Since John walked halfway around the table, we are solving for half of the
