Digital SAT Toughest Questions Math and English

Digital SAT Hardest Questions

Students frequently desire to ready themselves for the most challenging questions they may encounter on the SAT to enhance their confidence during the actual test. We have compiled a selection of the most difficult questions and will guide you on how to approach and solve them.

These questions are sourced from the complimentary SAT practice tests to ensure that we present you with examples reflective of those encountered on the official test. While we've included various question types, it's important to note that this compilation doesn't cover all Math and English topics or encompass every question type found on the SAT.

 What constitutes a "hard" question is, undoubtedly, subjective. What might be a formidable challenge for one student could be a walk in the park for another. Yet, through our extensive experience working with numerous students, we've discerned certain patterns and complexities that tend to leave many scratching their heads.

In the realm of SAT Math, the difficulty tends to crescendo, revealing its true colors in the second half of each section. As you delve into the latter questions, you'll notice a subtle but perceptible shift—a gradual ascent into the realm of more intricate problem-solving.

For every question presented, we've demystified the underlying concepts at play and clarified whether or not a calculator can be your trusty ally. We encourage you to take a stab at solving these conundrums independently before peering into our suggested solutions. Remember, there's rarely a solitary path to the correct answer—each problem is a puzzle with multiple routes to resolution.

Join us on this subjective odyssey through the complexities of SAT Math & SAT English . Challenge your preconceptions, hone your problem-solving skills, and discover the multitude of ways to conquer the mathematical terrain that awaits. Your adventure begins now.

Explore the SAT Course   Book a Free Trial Session 

 

Digital SAT Math Topics 

Heart of Algebra: Accounting for a formidable 33% of the test, this segment spans 19 questions. Brace yourself for an exploration of linear equations, inequalities, their graphical representations, and the art of maneuvering through systems.

Problem Solving and Data Analysis: Comprising 29% of the test with 17 questions, this section thrusts you into the world of ratios, proportions, percentages, and units. Navigate through the complexities of analyzing graphical data, probabilities, and statistics with a keen eye.

Passport to Advanced Math: With 28% of the test dedicated to 16 questions, this category challenges you to identify and craft equivalent expressions. Brace for the quadratic and nonlinear equations/functions and the intriguing landscapes of their graphs.

Additional Topics in Math: While constituting 10% of the test, this category is a wildcard with 6 questions. From geometry and trigonometry to radians, the unit circle, and complex numbers, expect the unexpected in this diverse mathematical realm.

Grid-in Questions: A unique challenge found at the end of each portion of the math test—both with and without a calculator. These questions transcend the safety net of multiple-choice tactics, demanding a deeper understanding of the material. With no answer choices to lean on, your mathematical prowess takes center stage. Fear not, though; armed with honed math skills, you'll find these grid-in questions to be conquerable peaks on your SAT journey.

 Book Your Free Demo Now

Here are most SAT toughest Questions with Correct Answers:

Question 1:

Ans. Choice A is correct. It’s given that Tilly earns p dollars for every w hours of
work. This can be represented by the proportion p

w . The amount of money, x , Tilly
earns for 39w hours of work can be found by setting up the proportion 39
p x
w w = .
This can be rewritten as 39pw xw = . Dividing both sides by w results in x p =39 .

Question 2:

Ans. Choice D is correct. It′s given that Juan rides his bike at an average rate of
5.7 minutes per mile. The number of minutes it will take Juan to ride x miles can
be determined by multiplying his average rate by the number of miles, x , which
yields 5.7x . Therefore, the function mx x ( )=5.7 models the number of minutes it
will take Juan to ride x miles.

 

Question 3:

Ans. Choice B is correct. Adding the second equation in the given system to the first
equation in the given system yields 3 3 12 6 x xy +- + = +- ( ) ( ), which is equivalent
to y =6.

 

Question 4:

Ans. Choice D is correct. In the given equation, s is the speed, in miles per hour, of a
certain car t seconds after it began to accelerate. Therefore, the speed of the
car, in miles per hour, 5 seconds after it began to accelerate can be found by
substituting 5 for t in the given equation, which yields s = + 40 3 5( ), or s =55.
Thus, the speed of the car 5 seconds after it began to accelerate is 55 miles per
hour.

 

Question 5:

Ans. Choice D is correct. By the Pythagorean theorem, if a right triangle has a
hypotenuse with length c and legs with lengths a and b, then 222 cab = + . In
the right triangle shown, the hypotenuse has length c and the legs have lengths
a and b. It’s given that a = 4 and b =5. Substituting 4 for a and 5 for b in the
Pythagorean theorem yields 2 22 c = + 4 5 . Taking the square root of both sides of
this equation yields 2 2 c =± + 4 5 . Since the length of a side of a triangle must be
positive, the value of c is 2 2 4 5 + .

 

Question 6:

Ans. The correct answer is 40. Subtracting 5 from both sides of the given equation
yields 4 160 x = . Dividing both sides of this equation by 4 yields x = 40.
Therefore, the solution to the given equation is 40.

 

Question 7:

Ans. The correct answer is 7. It’s given that the x-intercept of the graph shown is ( ) x,0 .
The graph passes through the point ( ) 7,0 . Therefore, the value of x is 7.

 

Question 8:

Ans. Choice B is correct. The y-intercept of the graph of a function in the xy-plane is
the point on the graph where x =0. It′s given that ( ) 1
10
fx x = -2. Substituting 0

for x in this equation yields ( ) ( ) 1
10
f 0 02 = – , or f( ) 0 2 =- . Since it′s given that
y fx = ( ), it follows that y =-2 when x =0. Therefore, the y-intercept of the
graph of y fx = ( ) in the xy-plane is ( ) 0, 2 – .

 

Question 9:

Ans. Choice D is correct. If the graph of y gx = ( ) is the result of shifting the graph
of y fx = ( ) down k units in the xy-plane, the function g can be defined by an
equation of the form gx fx k ( ) ( ) = – . It’s given that ( ) 3 fx x =7 and the graph of
y gx = ( ) is the result of shifting the graph of y fx = ( ) down 2 units. Substituting

 Question 10:

Ans. Choice A is correct. The solution to a system of equations is the ordered pair
( ) x y, that satisfies all equations in the system. It’s given by the first equation in
the system that x + =7 10. Substituting 10 for x +7 into the second equation
yields 2 10 = y, or y =100. The x-coordinate of the solution to the system
of equations can be found by subtracting 7 from both sides of the equation
x + =7 10, which yields x =3. Therefore, the ordered pair ( ) 3, 100 is a solution to
the given system of equations.

Get Trial Session Download Course Brochure

 

English Hardest Question 

 

Q1. For painter Jacob Lawrence, being _______ was an
important part of the artistic process. Because he
paid close attention to all the details of his Harlem
neighborhood, Lawrence’s artwork captured nuances
in the beauty and vitality of the Black experience
during the Harlem Renaissance and the
Great Migration.

Which choice completes the text with the most
logical and precise word or phrase?
A) skeptical
B) observant
C) critical
D) confident

Ans. Choice B is the best answer because it most logically completes the text’s
discussion of Jacob Lawrence’s artistic process. In this context, “observant”
means watchful and perceptive. The text emphasizes that the “close attention”
Lawrence paid to “all the details” of his neighborhood allowed him to reflect subtle
elements of “the beauty and vitality of the Black experience” in his artwork. This
context indicates that being observant of his surroundings was an important part
of Lawrence’s work as an artist.

Q2. Mônica Lopes-Ferreira and others at Brazil’s
Butantan Institute are studying the freshwater
stingray species Potamotrygon rex to determine
whether biological characteristics such as the rays’
age and sex have _______ effect on the toxicity of
their venom—that is, to see if differences in these
traits are associated with considerable variations in
venom potency.

Which choice completes the text with the most
logical and precise word or phrase?
A) a disconcerting
B) an acceptable
C) an imperceptible
D) a substantial

Ans. Choice D is the best answer because it most logically completes the text’s
discussion of the research that Lopes-Ferreira and her colleagues are conducting
on the stingray species Potamotrygon rex. As used in this context, “a substantial”
effect means an effect that is sizable or noteworthy. The text indicates that the
researchers are seeking to determine whether there are “considerable variations”
in the potency of stingray venom that are associated with variation in the
stingrays’ age and sex. This context suggests that the researchers want to find
out whether stingray age and sex have a substantial effect on venom toxicity.

Q3. Researchers have struggled to pinpoint specific
causes for hiccups, which happen when a
person’s diaphragm contracts _______ . However,
neuroscientist Kimberley Whitehead has found that
these uncontrollable contractions may play an
important role in helping infants regulate their
breathing.
 

Which choice completes the text with the most
logical and precise word or phrase?
A) involuntarily
B) beneficially
C) strenuously
D) smoothly

Ans. Choice A is the best answer because it most logically completes the text’s
discussion of diaphragm contractions and hiccups. In this context, “involuntarily”
means done without any control, or by reflex. The text explains that when a
person’s diaphragm repeatedly contracts and results in hiccups (which may be
beneficial for infants), those muscle contractions are “uncontrollable.” This context
indicates that the diaphragm contractions occur without the person’s control.

Q4. Critics have asserted that fine art and fashion rarely _______ in a world where artists create timeless
works for exhibition and designers periodically
produce new styles for the public to buy. Luiseño/
Shoshone-Bannock beadwork artist and designer
Jamie Okuma challenges this view: her work can be
seen in the Metropolitan Museum of Art and
purchased through her online boutique.

Which choice completes the text with the most
logical and precise word or phrase?
A) prevail
B) succumb
C) diverge
D) intersect

Ans. Choice D is the best answer because it most logically completes the text’s
discussion about the relationship between fine art and fashion. As used in this
context, “intersect” means to connect or overlap. The text indicates that Jamie
Okuma challenges the position held by critics because her work can be seen
at an art museum and can be bought by the public from her online boutique.
The text also presents the critics’ view as being influenced by a perception that
fine artists create works that are “timeless” and meant for exhibition, whereas
fashion designers periodically produce new styles that are meant for purchase.
This context suggests that the critics believe that fine art and fashion tend not to
overlap—in other words, that they rarely intersect.

Q5. Scholarly discussions of gender in Shakespeare's
comedies often celebrate the rebellion of the
playwright's characters against the rigid expectations
by Elizabethan society. Most of the
comedies end in marriage, with characters returning
to their socially dictated gender roles after previously
defying them, but there are some notable exceptions.
 

Which choice completes the text with the most
logical and precise word or phrase?
A) interjected
B) committed
C) illustrated
D) prescribed

Ans. Choice D is the best answer because it most logically completes the text’s
discussion of gender roles in Shakespeare’s comedies. As used in this context,
“prescribed” would mean laid down as rules. The text indicates that the characters
in the comedies often defy gender roles that are “socially dictated” (even if most
characters do return to those roles eventually) and that scholars have been
very interested in these acts of defiance. This context indicates that what the
characters are rebelling against are standards of behavior prescribed by the
society of the time.

Q6. In studying the use of external stimuli to reduce the
itching sensation caused by an allergic histamine
response, Louise Ward and colleagues found that
while harmless applications of vibration or warming
can provide a temporary distraction, such
stimuli actually offer less relief than a stimulus that
seems less benign, like a mild electric shock.
 

Which choice completes the text with the most
logical and precise word or phrase?
A) deceptive
B) innocuous
C) novel
D) impractical

Ans. Choice B is the best answer because it most logically completes the text’s
discussion of Ward and colleagues’ findings. As used in this context, “innocuous”
means mild or unharmful. The text describes the vibration and warming that Ward
and colleagues used to alleviate itching as “harmless applications” and goes on to
contrast these applications with another stimulus that actually offers more relief
even though it seems to be stronger and “less benign.” This context conveys the
idea that vibration and warming were innocuous stimuli.

Q7. The province of Xoconochco was situated on the
Pacific coast, hundreds of kilometers southeast of
Tenochtitlan, the capital of the Aztec Empire.
Because Xoconochco’s location within the empire
was so _______ , cacao and other trade goods
produced there could reach the capital only after a
long overland journey.
 

Which choice completes the text with the most
logical and precise word or phrase?
A) unobtrusive
B) concealed
C) approximate
D) peripheral

Choice D is the best answer because it most logically completes the text’s
discussion of the location of the province of Xoconochco within the Aztec Empire.
As used in this context, “peripheral” means situated toward the outer bounds
rather than the center. The text indicates that Xoconochco was located on a
coast, hundreds of kilometers away from the capital of the Aztec Empire. The
text also states that trade between the province and the capital required “a long
overland journey.” This context suggests that Xoconochco was situated toward
an edge of the empire’s territory rather than near its center.

Q8. The following text is from Charlotte Brontë's 1847
novel Jane Eyre. Jane works as a governess at
Thornfield Hall.
I went on with my day's business tranquilly; but
ever and anon vague suggestions kept wandering
across my brain of reasons why I should quit
Thornfield; and I kept involuntarily framing
advertisements and pondering conjectures about
new situations: these thoughts I did not think to
check; they might germinate and bear fruit if
they could.
 

Which choice best states the main purpose of the
text?
A) To convey a contrast between Jane's outward
calmness and internal restlessness
B) To emphasize Jane's loyalty to the people she
works for at Thornfield Hall
C) To demonstrate that Jane finds her situation
both challenging and deeply fulfilling
D) To describe Jane's determination to secure
employment outside of Thornfield Hall

Ans. Choice A is the best answer because it most accurately describes the main
purpose of the text, which is to show that while Jane calmly goes about her daily
tasks, she is experiencing internal agitation about possibly seeking a new job.
At the start of the text, Jane says, “I went on with my day’s business tranquilly,”
indicating that she is outwardly calm. This outward calmness is then contrasted
with her intense internal restlessness, as Jane says that thoughts of leaving her job
keep running through her mind, that she is “involuntarily framing advertisements”
(meaning that she can’t stop herself from thinking up potential listings for jobs),
and that she often wonders what new “situations” (or jobs) would be like.

Q9. Text 1
Most animals can regenerate some parts of their
bodies, such as skin. But when a three-banded
panther worm is cut into three pieces, each piece
grows into a new worm. Researchers are
investigating this feat partly to learn more about
humans’ comparatively limited abilities to
regenerate, and they’re making exciting progress. An
especially promising discovery is that both humans
and panther worms have a gene for early growth
response (EGR) linked to regeneration.

Text 2
When Mansi Srivastava and her team reported that
panther worms, like humans, possess a gene for EGR,
it caused excitement. However, as the team pointed
out, the gene likely functions very differently in
humans than it does in panther worms. Srivastava
has likened EGR to a switch that activates other
genes involved in regeneration in panther worms,
but how this switch operates in humans remains
unclear.

Based on the texts, what would the author of Text 2
most likely say about Text 1’s characterization of the
discovery involving EGR?
A) It is reasonable given that Srivastava and her
team have identified how EGR functions in both
humans and panther worms.
B) It is overly optimistic given additional
observations from Srivastava and her team.
C) It is unexpected given that Srivastava and her
team’s findings were generally met with
enthusiasm.
D) It is unfairly dismissive given the progress that
Srivastava and her team have reported.

Ans. Choice B is the best answer because it reflects how the author of Text 2
would most likely respond to Text 1 based on the information provided.

Text 1

discusses the discovery of a regeneration-linked gene, EGR, in both three-
banded panther worms (which are capable of full regeneration) and humans

(whohave relatively limited regeneration abilities). Text 1 characterizes this discovery
as “especially promising” and a sign of “exciting progress” in understanding
human regeneration. The author of Text 2, on the other hand, focuses on the
fact that the team that reported the EGR finding pointed out that while EGR’s
function in humans isn’t yet known, it’s likely very different from its function in
panther worms. Therefore, the author of Text 2 would most likely say that Text 1’s
enthusiasm about the EGR discovery is overly optimistic given Srivastava’s team’s
observations about EGR in humans.

Q10. The following text is adapted from William
Shakespeare’s 1609 poem “Sonnet 27.” The poem is
addressed to a close friend as if he were physically
present.
Weary with toil, I [hurry] to my bed,
The dear repose for limbs with travel tired;
But then begins a journey in my head
To work my mind, when body’s work’s expired:
For then my thoughts—from far where I abide—
[Begin] a zealous pilgrimage to thee,
And keep my drooping eyelids open wide,
What is the main idea of the text?
A) The speaker is asleep and dreaming about
traveling to see the friend.
B) The speaker is planning an upcoming trip to the
friend’s house.
C) The speaker is too fatigued to continue a
discussion with the friend.
D) The speaker is thinking about the friend instead
of immediately falling asleep.

Ans. Choice D is the best answer because it most accurately states the main idea of
the text. The speaker describes the experience of being “weary” and “tired” and
going to bed to seek “dear repose” (that is, sleep), but instead of sleeping, the
speaker is kept awake (“keep my drooping eyelids open wide”) by thoughts of a
friend (“my thoughts… [Begin] a zealous pilgrimage to thee”).

 

Useful SAT Links You Should Not Miss:

• SAT Exam Dates
• SAT Registration
• SAT Syllabus
• SAT Preparation
• SAT Practice Test
• SAT Documents Required
• SAT Articles / SAT Blogs
• Hall of Fame (SAT Achievers)
• SAT Score And SAT Result
• SAT 1 General Online
• How to Ace the SAT : 6 Expert Tips and Strategies
• Free SAT Preparation
• SAT Tutors

• Handful List of Extracurricular Activities
• What is Exactly Tested on SAT Reading Section?
• Tips for Parents: How to Prepare Child for SAT?
• How to Save Time on SAT Reading ?
• College Application Essay Format
• Easy Scholarships That Are Cakewalks
• SAT Score Conversion into Numerical and Letter Class Grades
• What is the SAT Waitlist? Should You Have Chances
• All SAT/ACT Registration Costs
• SAT Registration & SAT Tests Cancellation
• Is The SAT Really Hard?
• How to Submit Letters of Recommendation to a College?
• Guide to College Research
• SAT/ACT Scores Required for Athletes to Join Ivy League Schools
• Good SAT/ACT Scores for 10th Grade Students
• Good SAT Scores As Per 100 Schools
• How To Write a Diversity Essay for College?

View all SAT Articles Here

For More Details About SAT Preparation Online You Can Visit Here

SAT Coaching Centers:

• SAT Prep Course in Gurgaon
• SAT Prep Courses in Delhi
• SAT Prep Courses in Kerala
• SAT Prep Courses in Riyadh
• SAT Prep Courses in Oman
• SAT Prep Courses in Quatar
• SAT Prep Courses in Bahrain
• SAT Prep Courses in Kuwait
• SAT Prep Courses in Beijing (China)
• SAT Prep Courses in Dubai