Mastering the Digital SAT Teacher Handout — eBook

Mastering the Digital SAT

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Answer Explanations Mastering the Digital SAT Student Handout

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The author wrote this content with the assistance of GPT-4, OpenAI’s large-scale language-generation model. The author has reviewed, edited, and revised all language in this work and takes ultimate responsibility for the content of this publication.

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Reading # Mini-Test 1

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 1

QUESTION 3

The Zhurong rover safely touched down on Mars in 2021. Chinese Academy of Science professor Xiaoguang Qin confirms that in spite of receiving various indications of a planet only capable of solid and gaseous water, Zhurong successfully __________ photos of the planet’s topography, sending evidence of liquid water to research teams in China.

Echolocation, a unique way of navigating by emitting sounds and interpreting their echoes, is usually simple to study in bats.

Since this ability exists but is less __________ in certain bird species, ornithologists often use experiments specifically created to demonstrate an individual bird’s’ proficiency in echolocation-based navigation.

Which choice completes the text with the most logical and precise word or phrase?

Which choice completes the text with the most logical and precise word or phrase?

A) obvious

A) covered

B) enthralling

B) captured

C) meaningful

C) trailed

D) advantageous

D) swapped

QUESTION 2 Studies performed by geologist Igor Fabrikant propose that dinosaur fossil evidence might not reliably __________ lethal asteroid theories. When scientists tested dinosaur remains, the fossils contained elevated iridium levels, but extensive volcanic activity would have left behind similar results; therefore, claims of an asteroid collision might now be under suspicion.

Which choice completes the text with the most logical and precise word or phrase?

A) support B) impact C) estimate D) imitate

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READING MINI TEST #1

1. The correct answer is B.

3. The correct answer is A. In certain bird species, echolocation ability is present but not as apparent as in bats. The word obvious highlights the contrast between the easily observable echolocation in bats and the less apparent echolocation abilities in birds.

Photos sent back to Earth for analysis would most logically be described as captured photos. This word indicates that the images were taken in one location and then viewed in another. It also implies that the rover collected valuable scientific information through these pictures, making captured the most suitable term.

Choice B is incorrect because enthralling, which means “captivating or fascinating,” does not fit with the passage’s focus on the visibility of echolocation in birds.

Choice A is incorrect because covered suggests a broad or comprehensive approach to documenting or reporting on a subject, which doesn’t precisely fit the specific act of taking photos.

Choice C is incorrect because meaningful suggests significance or importance, which does not directly address the contrast regarding the detectability or acknowledgment of echolocation abilities in birds compared to bats.

Choice C is incorrect because trailed implies following something or someone, which does not apply to the act of taking photos.

Choice D is incorrect because advantageous implies usefulness, which, while potentially applicable to echolocation, does not specifically address the relative difficulty of studying the trait in birds versus bats.

Choice D is incorrect because the word swapped suggests exchanging one thing for another, which is unrelated to the action of taking or sending photographs.

2. The correct answer is A. The sentence discusses the reliability of using dinosaur fossil evidence to validate or back up theories about a lethal asteroid being the cause of the dinosaurs’ extinction. In this context, support fits, as it means upholding or assisting a theory or idea.

Choice B is incorrect because impact refers to one thing affecting another but does not fit the context of providing evidence for or against a theory.

Choice C is incorrect because estimate is about making an approximate calculation or judgment about something, which is not applicable to the verification of theories through evidence.

Choice D is incorrect because imitate means to follow as a model or to copy something. This choice does not relate to the idea of providing evidence or backing for a theory.

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

READING MINI-TEST #1

QUESTION 4

QUESTION 5

The following text is adapted from Mark Twain’s 1869 travel book The Innocents Abroad. A young Twain is contemplating a pair of gloves that he is trying on and considering buying.

The following text is from the early twentieth century poem “At April” by Angelina Weld Grimké, a Black American writer.

Toss your gay heads,

A very handsome young lady in the store offered me a pair of blue gloves. I did not want blue, but she said they would look very pretty on a hand like mine. The remark touched me tenderly. I glanced furtively at my hand, and somehow it did seem rather a comely member. I tried a glove on my left and blushed a little. Manifestly the size was too small for me. But I felt gratified when she said:

Brown girl trees; Toss your gay lovely heads; Shake your brown slim bodies; Stretch your brown slim arms; Stretch your brown slim toes.

Who knows better than we, With the dark, dark bodies, What it means

“Oh, it is just right!” Yet I knew it was no such thing.

When April comes a-laughing and a-weeping Once again

I tugged at it diligently, but it was discouraging work. She said:

At our hearts?

Which choice best describes the overall structure of the text?

“Ah! I see you are accustomed to wearing kid gloves—but some gentlemen are so awkward about putting them on.”

A) The speaker describes the trees in her surroundings, then wonders how they make other people feel.

It was the last compliment I had expected.

I only understand putting on the buckskin article perfectly. I made another effort and tore the glove from the base of the thumb into the palm of the hand—and tried to hide the rent. She kept up her compliments, and I kept up my determination to deserve them or die.

B) The speaker addresses the trees as if they were humans, then identifies herself with them.

C) The speaker depicts the trees at a certain time of year, then imagines how they would look at another time of year.

Which choice best states the main purpose of the text?

D) The speaker portrays the trees as happy, then hopes they will live a long time.

A) To portray the contrast between what Twain thinks about the gloves and how he wishes to appear B) To describe Twain’s annoyance at the salesperson who is encouraging him to buy the gloves C) To highlight the unusually large size of Twain’s hands D) To clarify the differences between the kid gloves and the buckskin gloves Twain usually wears

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READING MINI TEST #1

4. The correct answer is A. In this excerpt, Mark Twain knows that the gloves are too small for him, but he is flattered by the saleswoman’s compliments. The contrast between Twain’s understanding of the situation and his desire to pretend he sees it differently is exactly what the answer choice describes.

Choice B is incorrect because the text focuses more on Twain’s internal conflict regarding the situation, rather than on annoyance at the salesperson.

Choice C is incorrect because the text does not ever suggest that Twain’s hands are unusually large, only that the gloves are too small for him.

Choice D is incorrect because the text does not aim to clarify the differences between kid gloves and buckskin gloves. Instead, it draws humor from the fact that the gloves do not fit Twain while he continues to act as if that is not the case.

5. The correct answer is B. In the early lines of the poem, the author personifies the trees, referring to them as brown girl trees and describing their movements in human terms, such as shake your brown slim bodies. Next, the author identifies herself with the trees, saying who knows better than we. This fits the pattern described in which the author addresses the trees as if they were humans and then identifies herself with them.

Choice A is incorrect because the speaker does not wonder about others’ feelings; she focuses on personifying the trees and identifying with them.

Choice C is incorrect because the author does not imagine the trees at different times of the year. Rather only one month is mentioned, implying only one season.

Choice D is incorrect because the text does not include a direct statement about a hope that the trees will live a long time.

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 6 Based on the texts, how would Benbow and Jiminez (Text 2) most likely react to the "traditional thinking" presented in Text 1?

Text 1 Traditional thinking suggests that human economic systems progressed through different phases, starting with simple bartering between individuals or small groups. The introduction of commodity money thousands of years ago drove further economic growth that generated the development of new financial practices: first with coinage, then banking, and most recently, cryptocurrency.

A) By admitting the significance of commodity money but stressing the higher importance of bartering B) By challenging the idea that economic systems have evolved through a straightforward series of steps or phases C) By recognizing that banking systems probably didn’t develop before the emergence of currency

Text 2 In a 2020 publication, economic historians Julie Benbow and Margarita Jiminez argue that human economic systems have always been complex, often hybridizing simple economic methods with advanced ones.

The historians call attention to evidence from 4,000 years ago of a banking system between farmers and vendors, sometimes even using sophisticated financial processes, like compound interest, while also employing traditional ones, like trading.

D) By questioning the assumption that bartering was among the first of ancient economic systems

STOP This is the end of this section. Wait for your instructor to tell you to move to the next section.

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READING MINI TEST #1

6. The correct answer is B. In text 2, Benbow and Jiminez argue that human economic systems have always been complex and multifaceted, incorporating both simple and advanced methods simultaneously.

This perspective directly challenges the traditional viewpoint that economic systems evolved in a straightforward sequence.

Choice A is incorrect because the contention in Text 2 is not about prioritizing the importance of bartering over commodity money; rather, they challenge the linear narrative of economic evolution.

Choice C is incorrect because the argument that banking systems probably didn’t develop before the emergence of currency directly contradicts Text 2’s assertion that traditional economic systems of trade existed alongside more complex financial systems.

Choice D is incorrect because it focuses on questioning the early existence of bartering, which is not the emphasis of Benbow and Jiminez’s argument in Text 2. They challenge the linear progression of economic systems, not the early emergence of bartering.

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Reading # Mini-Test 2

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 7

QUESTION 8

The following text is adapted from Howard Florian Smithwick’s 1911 novel Between the Brambles. Jessica, a young orphan, has been given a space of her own to make a garden.

The following text is from William Shakespeare’s early 17th-century “Sonnet 97.ˮ How like a winter hath my absence been From thee, the pleasure of the fleeting year!

The first morning she had dug and planned and worshipped shrubs and flowers until she was too tired to stand upright. After that, she laid on the grass. A sense of peace washed over her, and she smiled up at the blue sky and drank in the sounds of the hawthorn buds bursting and the robins and thrushes singing their morning chorus.

What freezings have I felt, what dark days seen!

What old December’s bareness everywhere!

And yet this time remov’d was summer's time, The teeming autumn, big with rich increase, Bearing the wanton burthen of the prime,

Which choice best states the main idea of the text?

Like widow’d wombs after their lords' decease:

A) Jessica retreats to the garden to avoid going to church.

Based on the text, in what way is the absence of a loved one like the winter?

B) Jessica is becoming annoyed with listening to all the birds in the garden.

A) It seems like it will last perpetually.

C) Jessica is cleaning up the garden to create a place to lay down.

B) It is difficult to get accustomed to.

D) Jessica feels quite content after she’s finished tending to the garden.

D) It is a necessary part of the cycle of time.

C) It feels unpleasant and dreary.

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READING MINI TEST #2

7. The correct answer is D. The text describes Jessica’s emotional fulfillment following her work, when she rests and observes nature. This is indicated by the fact that she smiles at the sky and enjoys the sounds of nature around her.

Choice A is incorrect because there is no mention of Jessica retreating to the garden to avoid going to church. Instead, the text focuses on her gardening activities and the peace she finds in nature afterward.

Choice B is incorrect because the text does not indicate that Jessica is annoyed by the birds.

Instead, it describes her enjoying the sounds of the robins and thrushes singing.

Choice C is incorrect because the text does not suggest that Jessica’s primary goal is to clean up the garden simply to create a place to lay down. While she does lay on the grass after working, the focus is on her enjoyment and fulfillment from being in nature.

8. The correct answer is C. This sonnet uses the metaphor of winter to describe the speaker’s feelings during a period of absence from a loved one. The sonnet conveys a sense of coldness, darkness, and barrenness associated with winter, which the answer choice characterizes as unpleasant and dreary.

Choice A is incorrect because the sonnet does not explicitly state that the absence feels like it will last forever. Instead, it focuses on the experience of the absence and the feelings it involves.

Choice B is incorrect because there is no indication that the sonnet is about the difficulty of adjusting to the absence. Instead, the emphasis is on the emotional experience of absence.

Choice D is incorrect because the sonnet does not suggest that absence is a necessary part of the cycle of time. While it mentions different seasons, the focus is on highlighting the negative aspects of absence.

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

READING MINI-TEST #2

QUESTION 9

QUESTION 10 U.S. States with the Greatest Number of Wind Turbines in 2022

The following text is adapted from Jack London’s 1905 novel White Fang. White Fang, an angry wolfdog from Yukon, Canada, has just met Weedon Scott.

White Fang snarled at the sound of his voice, but this time did not leap away from under the hand that was caressing his head and the back of his neck with long, soothing strokes.

It was the beginning of the end for White Fang—the ending of the old life and the reign of hate. A new and incomprehensibly fairer life was dawning. It required much thinking and endless patience on the part of Weedon Scott to accomplish this. And on the part of White Fang it required nothing less than a revolution.

Which choice best states the main idea of the text?

Wind turbines are structures for generating electric energy that attempts to diminish environmental damage by employing natural methods of energy collection and avoiding fossil fuels with toxic fumes. Wind turbines still only make up a small part of the total energy production in the United States, but they have been growing in popularity. According to the U.S. Department of Energy, in 2022 Texas had between 18,000 and 20,000 wind turbines and __________

A) White Fang has become weaker since meeting Weedon Scott.

B) White Fang does not trust humans and snarls whenever they touch him.

C) White Fang is sick and needs Weedon Scott’s help to get better.

D) White Fang is learning to trust humans because of Weedon Scott’s kindness.

Which choice most effectively uses data from the graph to complete the text?

A) Illinois had between 2,000 and 4,000 wind turbines.

B) California had fewer than 4,000 wind turbines.

C) Iowa and Oklahoma each had between 6,000 and 8,000 wind turbines.

D) Kansas had more than 6,000 wind turbines.

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READING MINI TEST #2

9. The correct answer is D. Despite initially responding with aggression, White Fang does not flee from Weedon Scott’s gentle touch, suggesting the beginning of a significant change in his life. The main idea is that White Fang is on the path to learning to trust humans, facilitated by Scott’s compassionate approach.

Choice A is incorrect because the text does not suggest that White Fang has become weaker. Instead, it indicates a change in his relationship with humans, and a move toward trust.

Choice B is incorrect because although White Fang initially snarls at Weedon Scott, the focus of the passage is on the change in his reaction due to Scott’s kindness, not on a continued mistrust of humans.

Choice C is incorrect because there is no indication that White Fang is sick or that his need for Weedon Scott’s help is medical in nature. The passage focuses on a behavioral transformation.

10. The correct answer is A. On the bar graph, Illinois is depicted as having a number of wind turbines that exceeds 2,000 but does not reach 4,000.

Choice B is incorrect because California is shown to have more than 4,000 wind turbines, not fewer than 4,000, as the answer choice states.

Choice C is incorrect because while Iowa does indeed fall between the 6,000 and 8,000 range, Oklahoma is shown to have fewer than 6,000 wind turbines.

Choice D is incorrect because Kansas is depicted as having fewer than 6,000 wind turbines, not more.

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 11

QUESTION 12 E�ects of Di�erent Light Colors on 3 Types E�ects of Di�erent Light ColorsBacteria on 3 Types of Photosynthetic of Photosynthetic Bacteria

Creative writing programs, like those of the United Kingdom’s Bath Spa University or the United States’ Spalding University, are places where aspiring writers can develop their skills in an academic setting: perhaps to write a novel, or to delve into a new style, or to seek the support of peers and professors. Whatever the motivation, creative writing programs normally include collaborative workshops among the writers.

Based on a recent string of discussions about a number of creative writing programs, a literary critic suggests that this can be problematic for writers who are attempting to develop their own voice.

Prefer blue light

Average size of bacteria exposed to blue light (in micrometers)

Average size of bacteria exposed to red light (in micrometers)

Purple bacteria

yes

7.3

2.1

Heliobacteria

no

6.2

5.8

Bacteria type Cyanobacteria

yes

8.5

4.2

Blue light affects various photosynthetic bacteria, boosting the size of certain types. A researcher created an experiment to investigate this phenomenon. The researcher selected three types of photosynthetic bacteria to use in the experiment, choosing two that prefer blue light (bacteria that benefit from exposure to blue light) and one type that prefers red light (a type that doesn’t benefit from exposure to blue light and could possibly be damaged by it). Then the researcher monitored a few samples of each type of bacteria under blue light and red light conditions. At the end of a week, the researcher measured the bacteria’s average size and astonishingly found that __________

Which quotation from the discussions best illustrates the literary critic’s claim?

A) “The first creative writing group I attended included several remarkably skilled writers, and we appreciated each other’s companionship, but because we had difficulty developing unique and authentic voices for our work, I left the writing group.”

B) “We write as a group, but that doesn’t suggest that each writer’s achievements are also the achievements of all involved. Most of the stories are predominantly the creation of the writer who originally presented the idea to us.”

Which choice most effectively uses data from the table to complete the statement?

A) heliobacteria exposed to blue light had a slightly greater average size than heliobacteria exposed to red light.

C) “Having written as a student in a creative writing program for three years, it’s at times difficult to remember how it was to write alone without the program’s encouragement. But that encouragement enables my authentic voice rather than stifles it.”

B) cyanobacteria exposed to blue light had a greater average size than heliobacteria exposed to blue light.

C) purple bacteria exposed to blue light had a much greater average size than purple bacteria exposed to red light.

D) cyanobacteria had the greatest average size of all three types of bacteria exposed to red light, while purple bacteria had the smallest.

D) “Once in a while a writer from outside the program will join us during a workshop, but all those workshops align with the overall scope of writing that the program is already pursuing.”

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READING MINI TEST #2

11. The correct answer is A. This quotation directly addresses the issue raised by the literary critic: the difficulty of developing a unique voice within a creative writing program. The writer acknowledges the group’s strengths but ultimately decides to leave because the collaborative setting was not helpful for finding a distinct voice.

Choice B is incorrect because it does not address the issue of developing a unique voice.

It simply states that group writing does not dilute individual achievement, implying that individuality is still maintained.

Choice C is incorrect because it offers a counterpoint to the critic’s claim, suggesting that the program’s encouragement has helped the development of an authentic voice.

Choice D is incorrect because it speaks to the conformity within the program’s scope of writing rather than the development of the writers’ own voices.

12. The correct answer is A. The data in the table shows that the average size of heliobacteria exposed to blue light (6.2 micrometers) was a slightly greater average size than heliobacteria exposed to red light (5.8 micrometers). This finding can be accurately described as astonishing because heliobacteria do not prefer blue light.

Choice B is incorrect because while it is true that cyanobacteria exposed to blue light (8.5 micrometers) had a greater average size than heliobacteria exposed to blue light (6.2 micrometers), this is not astonishing because cyanobacteria prefer blue light, while heliobacteria do not.

Choice C is incorrect because while it is true that purple bacteria exposed to blue light had a much greater average size than purple bacteria exposed to red light, this was not an astonishing finding because all three of the bacterium types grew larger under blue light than under red light.

Choice D is incorrect because according to the table, cyanobacteria exposed to red light (4.2 micrometers) do not have the greatest average size compared to heliobacteria exposed to red light (5.8 micrometers).

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

READING MINI-TEST #2

QUESTION 13 Vermeer’s Girl with the Pearl Earring, located among the paintings within the Rijksmuseum in the Netherlands, portrays a common woman wearing a pearl earring in the foreground. Some art historians have claimed that the earring is just a glass bauble, since pearls were known to have been associated with the aristocracy in 17th-century Europe, but Utrecht University art historian Lena Achterberg proposes that the earring might have been intended as a societal critique. The fact that this earring is portrayed on this woman, therefore, __________ Which choice most logically completes the text?

A) is not sufficient evidence that the earring is a glass bauble.

B) indicates that 17th-century earrings were often pearls.

C) excludes the possibility that the earring is a glass bauble.

D) would be an impossibility if the woman were not of the aristocracy.

STOP This is the end of this section. Wait for your instructor to tell you to move to the next section.

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READING MINI TEST #2

13. The correct answer is A. Lena Achterberg’s proposal that the earring in Vermeer’s painting represents a societal critique suggests that there may be more meaning behind the image than is immediately evident. The statement that the earring is on a common woman suggests an intentional choice by Vermeer that could be a critique of societal norms.

Choice B is incorrect because the text does not provide information on what 17th-century earrings were typically made of, nor does it suggest that pearls were commonly used.

Choice C is incorrect because Achterberg’s hypothesis about the earring serving as a societal critique does not exclude the possibility that the earring is made of glass; the material of the earring is independent of its symbolic meaning.

Choice D is incorrect because the suggestion that the painting might be a societal critique does not imply that it would be impossible for a non-aristocratic woman to wear a pearl earring; rather, it opens the possibility that Vermeer was challenging social norms through his art.

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Writing # Mini-Test 1

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 14

QUESTION 16

Music producers believe that over two-thirds of songs in films attributed to live actors or voice actors are actually sung by playback singers, expert vocalists who are reimbursed to sing an __________ but whose talents are never credited for their work.

After a deluge of symptoms in his early twenties, Stephen Hawking was informed that he would not survive long. Against all likelihood, Hawking didn’t merely survive, he __________ 1966 at the University of Cambridge in England, he received his PhD in both applied mathematics and theoretical physics and won high honors for his essays on general relativity, becoming a famous scholar by publishing countless influential works in the physics field.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) actor’s songs

Which choice completes the text so that it conforms to the conventions of Standard English?

B) actors song’s C) actors songs D) actor’s song’s

A) thrived—for 55 more years—in B) thrived—for 55 more years in C) thrived—for 55 more years, in D) thrived—for 55 more years. In

QUESTION 15

QUESTION 17

Like some other mammals, the domestic pig (Sus scrofa domesticus) has difficulty regulating its body temperature, so during times of hot weather, it __________ by wallowing in mud puddles, a practice that stops punishing heat from penetrating its skin.

In a great number of his humorous stories from the 1920s and 1930s, British American writer P.G. Wodehouse strived to reproduce the spirit of New York’s actorlined Manhattan Theater District through caricature, writing impressions of Americans to satirize their behavior. Curiously, the stories depicting the plays themselves __________ some of the most flattering stories in his works.

Which choice completes the text so that it conforms to the conventions of Standard English?

Which choice completes the text so that it conforms to the conventions of Standard English?

A) had cooled off B) cooled off C) would cool off

A) is

D) cools off

B) has been C) was D) are

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WRITING MINI-TEST 1

14. The correct answer is A.

16. The correct answer is D.

The blank in this sentence is preceded by the word an. In the context of the sentence, this tells us we’re looking for an answer choice that indicates the possession of songs by a singular actor. Choice A, actor’s songs, correctly completes the text because the word actor’s is in the possessive singular form.

This sentence describes Stephen Hawking’s achievements after being told he wouldn’t survive long. The proper way to structure the sentence is to use a period after 55 more years to conclude the sentence and then start a new sentence with In 1966 at the University of Cambridge in England. This allows for a clear separation of the main idea (that he thrived for 55 more years) and the additional context of where he achieved his accomplishments.

Choice B is incorrect because actors is plural and song’s has an apostrophe, indicating it’s in the possessive form, which is not necessary in this sentence.

Choice A is incorrect because using a hyphen instead of a period after 55 more years creates an awkward sentence structure and disrupts the flow of the sentence.

Choice C is incorrect because it lacks the possessive apostrophe needed to make the noun “actor” possessive.

Choice B is incorrect because it lacks punctuation to separate the two complete thoughts (independent clauses), leading to a run-on sentence.

Choice D is incorrect because it has a possessive apostrophe for both “actor” and “song,” which does not make sense in this context because the noun “song” should not be in possessive form in this sentence.

Choice C is incorrect because the comma after 55 more years incorrectly combines two complete thoughts (independent clauses) and creates a run-on sentence.

15. The correct answer is D. This sentence is in the present tense, and it’s describing a general action that pigs take to regulate their body temperature. Choice D, cools off, maintains the present tense to convey this behavior.

17. The correct answer is D. This sentence is written in the present tense and discusses the stories written by P.G. Wodehouse. The verb must agree in number with the subject stories. Therefore, the correct verb form is are (plural), because it agrees with the plural subject stories.

Choice A is incorrect because had cooled off is in the past perfect tense, which does not match the present tense of the rest of the sentence.

Choice A is incorrect because is is in singular form, so it does not agree with the plural subject stories.

Choice B is incorrect because cooled off is in the simple past tense, which does not match the present tense of the rest of the sentence.

Choice B is incorrect because has been is singular and does not agree with the plural subject.

Choice C is incorrect because would cool off is in the conditional tense, which is not appropriate for describing a general behavior of pigs in this context.

Choice C is incorrect because was is in singular form, so it does not agree with the tense of the sentence or with the plural subject.

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

WRITING MINI-TEST #1

QUESTION 18

QUESTION 19

Cherokee artist Sonia Donauwelle’s installation pieces appear in a variety of styles and arrangements. In 1933, Donauwelle shaped the walls of a mansion haphazardly to transform its 17-by-22-foot __________ in 1937, she altered the stone courtyard with a dozen papier-mâché statues and then chiseled them out of granite, constructing several life-sized whitegranite scenes.

Chinese national Tu Youyou is a researcher and chemist whose efforts have enabled millions across the globe to survive. Hailed in 2015 as one of the chief contributions to the pharmaceutical community in the last century, __________ led to the first widely available antidote against malaria.

Which choice completes the text so that it conforms to the conventions of Standard English?

Which choice completes the text so that it conforms to the conventions of Standard English?

A) Youyou discovered the lactone artemisinin in 1972; it B) in 1972 Youyou discovered the lactone artemisinin, which

A) foyer then, B) foyer;

C) Youyou’s 1972 discovery of the lactone artemisinin

C) foyer, D) foyer, then,

D) the lactone artemisinin was discovered

by Youyou in 1971 and

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WRITING MINI-TEST 1

18. The correct answer is B. This sentence discusses two different events in which Cherokee artist Sonia Donauwelle created installation pieces. To separate these two distinct ideas, a semicolon is needed.

Choice B includes a semicolon after the word foyer, providing the appropriate punctuation to seperate two independent clauses (complete thoughts).

Choices A and C are incorrect because they use a comma rather than a semicolon, which creates a run-on sentence. The best choice in this sentence is to clearly separate the two related ideas using a semicolon.

Choice D is incorrect because it uses a comma and the word then, which results in a run-on sentence that is difficult to read. A semicolon is needed in this sentence to clearly separate the two related ideas.

19. The correct answer is C. The question is asking for the option that correctly aligns with the modifying phrase at the beginning of the sentence. In other words, it’s asking who or what was hailed . . . as one of the chief contributions to the pharmaceutical community. Choice C states that (Youyou’s 1972 discovery of the lactone artimisinin) is what was hailed, making it the most logical match for the modifying phrase.

Choices A, B, and D are incorrect because their subjects (Youyou and the lactone artemisinin) are not in direct agreement with the modifying phrase.

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 20 The Land of the Leopard National Park in Russia and Kruger National Park in South Africa are two of the many wildlife sanctuaries around the world committed to protecting specific animal ________ conducting zoological studies; and providing information to visitors about animal preservation.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) species, both vulnerable and endangered, B) species, both vulnerable and endangered; C) species; both vulnerable and endangered, D) species both vulnerable and endangered

STOP This is the end of this section. Wait for your instructor to tell you to move to the next section.

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WRITING MINI-TEST 1

20. The correct answer is B. This sentence describes the three purposes of wildlife sanctuaries, which are to protect specific animal species, conduct zoological studies, and provide information to visitors about animal preservation. Because these three purposes are written in the form of a list, semicolons are needed to clearly separate each item in the list and avoid a run-on sentence (notice how a semicolon is included between the second a third purposes). Choice B includes a semicolon separating the first and second ideas, matching the structure of the rest of the sentence.

Choice A is incorrect because it uses a comma instead of a semicolon to separate the two independent ideas, which would create a runon sentence.

Choice C is incorrect because it uses a semicolon and a comma in the wrong order, which results in an unclear sentence and doesn’t conform to the conventions of Standard English.

Choice D is incorrect because it lacks the comma after species needed to conform to the conventions of Standard English. It also lacks the semicolon needed to separate the two independent ideas.

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Writing # Mini-Test 2

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 21

QUESTION 23

Historian Teresa Whata sits on the cultural board charged with selecting new locations for the Māori Historical Preservation Society, which oversees Mataatua and Kororipo Heritage Park. Whata doesn’t make these selections __________ all historical classifications must be sanctioned by a team of eleven other scholars from the disciplines of anthropology, sociology, literature, and Māori history.

J.D. Salinger was a seminal fiction writer from New York who published literary works widely throughout the mid-twentieth century.

The son of a Jewish father and an IrishScots mother, Salinger embraced his mixedethnicity heritage. For instance, he called himself a Lithuanian Jewish American. __________ he often integrated the motifs of traditional Jewish literature into his literary fiction works.

Which choice completes the text so that it conforms to the conventions of Standard English?

Which choice completes the text so that it conforms to the conventions of Standard English?

A) by herself, however;

A) Moreover,

B) by herself; however,

B) Really,

C) by herself, however,

C) Conversely,

D) by herself however

D) Nevertheless,

QUESTION 24

QUESTION 22

In 2020, anthropologist Gurman Singh and etymologist Sabine Neveux sampled a porridge made using a thousand-yearold recipe discovered on an Old English manuscript. When they ate the meal, known as hleahtor (laughter), they discovered that it had a powerful flavor and encouraged a feeling of happiness. _________ the scholars, aware that meals were often titled for the influence they have on someone, hypothesized that the porridge’s name, “laughter,” revealed its purpose: to inspire medieval individuals to have fun.

In June 1776, Virginia House Delegate Thomas Jefferson wrote the Declaration of Independence to pronounce independence from Great Britain. The document was not published immediately, but Jefferson was persistent. He collaborated with Benjamin Franklin and John Adams, two of the Founding Fathers of the United States, and they submitted the document to Congress that same month. __________ in August, the document reached Great Britain.

Which choice completes the text with the most logical transition?

Which choice completes the text with the most logical transition?

A) In contrast, B) Similarly,

A) Thus,

C) At last,

B) Instead,

D) Furthermore,

C) Regardless, D) Similarly,

24

30

WRITING MINI-TEST 2

21. The correct answer is A.

23. The correct answer is A.

This choice correctly uses a semicolon after however to split the two independent clauses (complete thoughts) in the sentence. The clause Whata doesn’t make these selections by herself contrasts the information in the first sentence that Whata sits on the cultural board. It’s a contrast because if she sits on the board, one might assume she makes the decisions, but the author is indicating that she doesn’t actually make the decisions by herself. Using a comma before however correctly signals that the clause Whata doesn’t make these selections by herself contrasts the previous information about Whata, and the semicolon afterward signals the start of a new, related independent clause.

The correct answer is moreover because it is used to introduce additional information or emphasize a claim. In the context of the passage, which discusses J.D. Salinger embracing his mixed-ethnicity heritage and incorporating elements of Jewish literature into his works, moreover effectively connects the final sentence that adds evidence to this thesis.

Choice B is incorrect because it uses a semicolon before however and a comma after it. In this case, since however is placed at the end of the clause, using a semicolon is not necessary, and only a comma before however is needed to separate the contrasting ideas.

Choice C is incorrect because conversely is used to introduce a statement or idea that contrasts or reverses a previous statement. The second part of the sentence does not contrast or reverse the first part; instead, it adds more information about Salinger’s connection to his heritage.

Choice B is incorrect because really can be used to affirm the veracity of a statement, but it doesn’t provide a clear connection between the two ideas presented in the final two sentences. The passage requires a transition that emphasizes the addition of supporting information.

Choice C is incorrect because it uses just a comma to connect the two independent clauses without the help of however. This mistake is called a comma splice, which occurs when a comma is used to join two independent clauses without a proper transition word or conjunction.

Choice D is incorrect because nevertheless is used to introduce a statement that contrasts with a previous statement or situation. In this case, the second part of the sentence does not contradict or contrast with the first part.

Choice D is incorrect because it doesn’t use any punctuation to connect the two independent clauses. This mistake is called a run-on sentence, which happens when two independent clauses are joined without proper punctuation or a transition word. Using a comma before however would correctly connect these contrasting ideas.

24. The correct answer is A. This choice emphasizes that the scholars’ hypothesis about the porridge’s purpose is based on their experience of its powerful flavor and mood-enhancing effects. Thus logically connects the scholars’ observations to their hypothesis, showing that it is a conclusion drawn from their experience.

Choice B is incorrect because instead implies a contrast or alternative to the previous statement, which doesn’t apply here, as there is no contrast between the two sentences.

22. The correct answer is C. The correct transition is at last because it implies a process has been completed. In the context of the passage, at last effectively signals the conclusion of this progression of events when the document reaches Great Britain.

Choice C is incorrect because regardless suggests that the following statement is true despite the previous one, which doesn’t fit the context, as the scholars’ hypothesis is derived from their experience.

Choice A is incorrect because in contrast suggests a contrast or opposition between ideas, which does not fit the context of the passage.

Choice D is incorrect because similarly implies a comparison or parallel between two things, which isn’t the focus of the transition in this passage.

Choice B is incorrect because similarly indicates a similarity or likeness between two ideas, which is not applicable to the passage’s focus on the timeline of events.

Choice D is incorrect because furthermore implies an addition or expansion of information, whereas the passage is describing a sequence of events in a chronological order.

31

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

WRITING MINI-TEST #2

QUESTION 25

QUESTION 26

While researching a topic, a student has taken the following notes:

While researching a topic, a student has taken the following notes:

· Finned marine vertebrates need oxygen

· Markuss Borisova is a Latvian American

· Whales and fish are finned marine

· He presented his piece Skyward Waltz in

· Whales are oxygen-breathing animals. · To acquire oxygen, whales need to

· Skyward Waltz contained a scene of paper

to be taken into the bloodstream, allowing the creatures to breathe.

sculptor who uses wind as his principal engine for artistic installations.

vertebrates.

2021.

characters hung from transparent wires.

· Whenever wind blew through the scene,

breathe in oxygen at the water’s surface into their lungs through a blowhole.

· Fish are a kind of oxygen-breathing animal

dancing characters activated.

· To acquire oxygen, fish need to breathe in oxygen but can do so underwater by filtering it through their gills.

The student wants to describe Skyward Waltz to an audience unfamiliar with Markuss Borisova.

Which choice most effectively uses relevant information from the notes to accomplish this goal?

The student wants to emphasize a difference between whales and fish. Which choice most effectively uses relevant information from the notes to accomplish this goal?

A) Borisova’s 2021 creation Skyward Waltz, which included a scene of paper characters hung from transparent wires, featured wind as its principal engine.

that have gills.

A) To live underwater, all finned marine vertebrates take in oxygen just as whales and fish do.

B) Whales and fish are finned marine vertebrates that, when underwater, need oxygen in their bloodstream to stay alive.

B) Latvian American wind artist Markuss Borisova presented Skyward Waltz in 2021.

C) The scene in Markuss Borisova’s Skyward Waltz was created by hanging paper characters from transparent wires.

D) In Skyward Waltz, a 2021 work by Latvian American artist Markuss Borisova, wind activated dancing paper characters as it blew through a scene Borisova had hung from transparent wires.

C) Whales are oxygen-breathing animals, and lungs are a kind of organ used for breathing.

D) To acquire oxygen while living underwater, whales need to come to the water’s surface, while fish do not.

25

32

WRITING MINI-TEST 2

25. The correct answer is D. The correct answer emphasizes a difference between whales and fish regarding how they obtain oxygen while underwater. Choice D explains that whales need to come to the water’s surface to breathe oxygen, unlike fish.

Choice A is incorrect because it highlights a similarity, not a difference, between whales and fish.

Choice B is incorrect because it doesn’t emphasize a difference between whales and fish; instead, it mentions a common need for oxygen in their bloodstream.

Choice C is incorrect because it only discusses whales and lungs, without providing contrasting information about fish, failing to emphasize a difference between the two.

26. The correct answer is D. The question asks us which choice uses information from the notes to explain Skyward Waltz to those unfamiliar with Markuss Borisova. Choice D uses the notes most effectively to provide a comprehensive description of Skyward Waltz. It includes the artist’s name, nationality, the year the piece was presented, and a detailed description of how the wind activated dancing paper characters in the scene.

Choice A is incorrect because it describes the artwork in less detail than in Choice D and does not mention the artist’s nationality.

Choice B is incorrect because it only provides the artist’s nationality and the year the piece was presented, without giving any description of the artwork itself.

Choice C is incorrect because it only describes the scene in Skyward Waltz, without mentioning the artist’s nationality or the year the piece was presented.

33

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 27 While researching a topic, a student has taken the following notes:

The student wants to present Smithwick’s findings to an audience unfamiliar with the Canterbury Cathedral. Which choice most effectively uses relevant information from the notes to accomplish this goal?

· England’s Canterbury Cathedral was erected in 597 A.D. to serve as a pilgrimage location for Catholics.

· It has been an Anglican church since the

A) Smithwick recorded Canterbury Cathedral’s stone exterior and then employed geometrical analysis software to study the videos.

sixteenth century.

· Geometrical analysis software is a

recent cyber architectural resource that examines the mathematics of 3D models of real structures.

B) Geometrical analysis software is a recent cyber architectural resource that Smithwick employed to investigate the mathematics of a 3D model of a real structure in a video.

· Architectural historian Herman Smithwick

employed geometrical analysis software to study the videos he had recorded of the Canterbury Cathedral’s stone exterior.

C) Employing a recent cyber architectural resource, Smithwick discovered thousands of previously unseen carving marks on the stone exterior of Canterbury Cathedral, an English church.

· Smithwick’s investigation discovered

thousands of previously unseen carving marks.

D) Built to serve as a pilgrimage location for Catholics before becoming an Anglican church, England’s Canterbury Cathedral hid thousands of carving marks in its stone exterior.

STOP This is the end of this section. Wait for your instructor to tell you to move to the next section.

26

34

WRITING MINI-TEST 1

27. The correct answer is C. The question asks us which choices uses information from the notes to present Smithwick’s findings to an audience unfamiliar with the Canterbury Cathedral. Choice C effectively introduces the audience to the Canterbury Cathedral by providing relevant information about its purpose (it was an English church). It also focuses on Smithwick’s use of the recent cyber architectural resource to study the cathedral and discover thousands of previously unseen carving marks on the stone exterior. This choice presents a clear and concise overview of Smithwick’s findings while providing context for an audience unfamiliar with the Canterbury Cathedral.

Choice A is incorrect because it only focuses on Smithwick’s process of recording the stone exterior and using geometrical analysis software, without providing context about the Canterbury Cathedral and its significance.

Choice B is incorrect because it does not directly mention the Canterbury Cathedral, making it difficult for an unfamiliar audience to understand the connection between the software and the cathedral.

Choice D is incorrect because it focuses more on the history of the Canterbury Cathedral and its original purpose, rather than emphasizing Smithwick’s findings and the use of geometrical analysis software.

35

Math # Mini-Test 1

37

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 1

QUESTION 3

A souvenir shop sold t-shirts on five weekdays.

The bar graph shows the number of t-shirts sold on each of the five days. How many t-shirts were sold on Wednesday?

5 more than 9 times a number x is equal to 95.

Which equation represents this situation?

A) (5)(9)x = 95 B) 9x = 95 + 5

t

C) 5x + 9 = 95 D) 9x + 5 = 95

A) 20 B) 28 C) 38 D) 40

QUESTION 2

QUESTION 4

What percentage of 500 is 125 ?

Alina’s student loan payment increases by a fixed amount each month. The function ƒ(m) = 200 + 15m expresses the total amount, in dollars, of Alina’s student loan payment after m months. What is the best interpretation of 15 in this context?

A)

25%

B)

50%

C) 125% D) 375%

A) With each month, Alina’s total student loan payment increases by $15.

B) Alina’s first student loan payment is $15.

C) After 1 month, Alina’s total student loan payment will be $15.

D) Alina will make a total of 15 student loan payments.

30

38

MATH MINI-TEST #1

1. The correct answer is B.

3. The correct answer is D.

To determine the number of t-shirts sold on Wednesday, we need to look at the bar corresponding to Wednesday on the bar graph.

The height of the bar represents the number of t-shirts sold, and the bar for Wednesday is at a height between 25 and 30. Comparing it to the answer choices, 28 (choice B) is the closest to the correct number of t-shirts sold.

The verbal statement 5 more than 9 times a number x is equal to 95 can be translated into an algebraic expression. 9 times a number x can be represented with the term 9x, and 5 more than means we must add 5 to this term.

Therefore, the equation that represents this situation is 9x + 5 = 95.

4. The correct answer is A.

2. The correct answer is A.

The function f(m) = 200 + 15m expresses the total amount of Alina’s student loan payment after m months. In this function, m has a coefficient of 15. This means that with each additional month, Alinaʼs payment will increase by $15.

To calculate what percentage 125 is of 500, you can use the formula: Percentage = (

Part ) • 100 Whole

Plugging in the numbers from the question: Percentage =

125 1 • 100 = ••=100 • 25% 500 4

39

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MATH MINI-TEST #1

QUESTION 5

QUESTION 7

Belle purchased 8 baskets that were all the same price. She used a gift card for $55 off the price of the whole purchase. After using the gift card, the total cost for the purchase was $41.

What was the original price, in dollars, for each basket?

Right triangles JKL and MNO are similar, where J corresponds to M. If the measure of angle K is 32o, what is the measure of angle M ?

A)

32o

B)

58o

C)

68o

D) 148o

QUESTION 6

For the linear function g, the table shows three values of x and their corresponding values of g(x). Which equation defines g(x) ?

A) g(x) = 4x + 31 B) g(x) = 31x + 35 C) g(x) = 39x + 31 D) g(x) = 35x + 39

STOP This is the end of this section. Wait for your instructor to tell you to move to the next section.

31

40

MATH MINI-TEST #1

5. The correct answer is 12.

7. The correct answer is B.

To find the original price of each basket, we first need to determine the total cost of the baskets before the gift card was applied. The remaining cost after the gift card was used is $41, and the value of the gift card is $55.

Therefore, the original total cost of the baskets is:

Since triangles JKL and MNO are similar and right triangles, their corresponding angles are equal. This means that angle J corresponds to angle M, angle K corresponds to angle N, and angle L corresponds to angle O (both of which are 90° because they are right angles).

We are given that angle K is 32°. This means that the corresponding angle N is also 32°.

Since the sum of angles in any triangle is 180°, we can find the measure of angle M in triangle MNO:

41 + 55 = 96 We’re told that Belle purchased 8 baskets, so we can find the cost per basket by dividing the original total cost, 96, by 8:

Angle M = 180° – (Angle N + Angle O)

96 = 12 8

Angle M = 180° – (32° + 90°) Angle M = 180°– 122°

6. The correct answer is A.

Angle M = 58°

To determine which equation defines g(x), we need to look at the rate of change of g(x) as x increases. The table shows us that when x increases by 1 (from 0 to 1 and from 1 to 2), g(x) increases by 4 (from 31 to 35 and from 35 to 39). This rate of change, 4, is the coefficient of x in the linear function. The value of g(x) when x = 0 (the y-intercept) is 31. Therefore, the equation that matches both the rate of change and the y-intercept is g(x) = 4x + 31.

41

Math # Mini-Test 2

43

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 8

QUESTION 9

The scatterplot shows the relationship between two variables, x and y.

What is an equation of the graph shown?

10 9

y

8 7 6 5 4 3 2 1

O

1 2 3 4 5 6 7 8 9 10

x

A) y = —3x — 6 B) y = x — 6

Which of the following equations is the most appropriate linear model for the data shown?

C) y = –x — 6 D) y = 3x — 6

A) y = 1.1 + 8.7x B) y = 1.1 — 8.7x C) y = 8.7 + 1.1x D) y = 8.7 — 1.1x

36

44

MATH MINI-TEST #2

8. The correct answer is D.

9. The correct answer is C.

To find the most appropriate linear model for the data shown in the scatterplot, we need to look at the general trend of the data points.

The scatterplot shows a downward trend, meaning that as x increases, y decreases. This indicates a negative slope. Looking over the answer choices, both choices A and C have positive slopes, so we can eliminate them.

To determine the equation of the line, we need to identify two key components from the graph: (1) the slope of the line and (2) the y-intercept, which is the point where the line crosses the y-axis. All our answer choices show a y-intercept of y = –6, so let’s determine the slope of the line to figure out which answer is correct.

Both choices B and D have negative slopes, so let’s examine their differences. Choice B has a y-intercept of 1.1, while choice D has a y-intercept of 8.7. Looking back at the graph, the scatterplot indicates a linear trend that crosses the y-axis between 8 and 9.

Additionally, the slope in choice D is –1.1. The points in the scatterplot decrease at a value that appears to be around 1 for each increase in x by 1. This makes choice D, y = 8.7 –1.1x, the most appropriate linear model for the data shown.

For the slope, we can pick two points on the line. For instance, the line passes through the points (0, –6) and (–6, 0). Using these two points, we can calculate the slope: ( y 2 – y1 ) ( x 2 – x1 ) (0 – (–6)) m= (–6 – 0) 6 m= –6 m = –1 m=

Therefore, the slope of the line is –1. Using the slope-intercept form of a line, y = mx + b, we can write the equation of the line as: y = –1x – 6, which simplifies to: y = –x – 6.

45

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MATH MINI-TEST #2 m =6 9 If m = 6 , what is the value of 9 ?

9 m 9 m

QUESTION 12

QUESTION 10

Square A has a side length of x inches. Square B has a perimeter that is 152 inches greater than the perimeter of square A. The function ƒgives the area of square B, in square inches. Which of the following defines ƒ ?

A) ƒ(x) = (x + 38)2 B) ƒ(x) = (x + 152)2 C) ƒ(x) = (152x + 38)2 D) ƒ(x) = (152x + 152)2

QUESTION 11

QUESTION 13

The ratio of a rectangle’s length to its width is 45 to 18. If the width of the rectangle increases by 5 units, how much should the length change to preserve the ratio?

24 b = 3 a + 15 8c

The given equation relates the distinct positive real numbers a, b, and c. Which equation correctly expresses a in terms of b and c ?

A) It should decrease by 12.5 units.

B) It should increase by 12.5 units.

A) a =

b – 15 c

B) a =

72 b – 15 24c

C) It should decrease by 5 units.

D) It should increase by 5 units.

C) a = ( b )2 – 15 c D) a = ( 72 b )2 – 15 24c

37

46

MATH MINI-TEST #2

10. The correct answer is

1 .

6

12. The correct answer is A. The perimeter of a square is equal to four times the length of one of its sides. If square A has a side length of x inches, then its perimeter is 4x inches.

9 To determine the value of , start by m m 9 identifying its relationship to . is the 9 m m reciprocal of , which means its numerator 9 and denominator are switched. We’re given m 6 that = 6, and another way to write 6 is .

9 1 m 9 Since is the reciprocal of , its value will 9 m 6 be the reciprocal of . Therefore, the value of 1 9 1 is . m 6

Square B has a perimeter that is 152 inches greater than the perimeter of square A. Therefore, the perimeter of square B is 4x + 152 inches.

Since each side of square B would be onefourth of its perimeter, we can find the length of one side of square B by dividing the perimeter by 4: Side length of square B =

11. The correct answer is B.

4 x 152 + 4 4 Side length of square B = x + 38 Side length of square B =

The ratio of the rectangle’s length to its width is 45 to 18. This can be simplified to a ratio of 5 to 2 (since both 45 and 18 are divisible by 9):

The area of a square is equal to the side length squared. Therefore, the function f that gives the area of square B in square inches is:

Length 5 = Width 2

f(x) = (x + 38)2

This means that for every 2 units that the width increases, the length must increase by 5 units to maintain the ratio. The question asks us what must happen to the length if the width increases by 5. Let x be equal to the number of units the length must increase by to maintain the ratio:

13. The correct answer is C. To determine which equation expresses a in terms of b and c, solve the given equation for a:

Length x = Width 5

24 b = 3 a + 15 8c

Then, set these two ratios equal to each other and solve for x:

24 b 1 1 • = 3 a + 15 • 8c 3 3

x 5 = 5 2

24 b = a + 15 24c

x 5 5( ) = 5( ) 5 2 x=

(4 x + 152) 4

b = a + 15 c

25 = 12.5 2

b ( )2 = a + 15 c b ( )2 – 15 = a c

47

Therefore, the equation that expresses a in b terms of b and c is a = ( )2 – 15 . c

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 14

QUESTION 15

Point A is the center of a circle. The measure of arc EM on this circle is 110o.

The expression 886 6226 6xx4242 ו×5 5335 5xx is equivalent to cxd, where c and d are positive constants and x > 1.

What is the measure, in degrees, of its associated angle EAM ?

What is the value of C + d ?

STOP This is the end of this section. Wait for your instructor to tell you to move to the next section.

38

48

MATH MINI-TEST #2

276 , or 55.2.

5 To find the value of c + d, start by simplifying

14. The correct answer is 110.

15. The correct answer is

Central angles and their corresponding arc measures are always equal in a circle.

Therefore, if the measure of arc EM is 110 degrees, then the measure of angle EAM is also 110 degrees.

the given expression: 8 6 26 x 42 • 5 35 x .

Each of these two irrational terms can be translated into rational forms by moving the root index into the denominator of the exponents inside the radicals and then removing the radical signs: 6 ( )

(

42

)

5 ( )

1 ( )

8 6 26 x 42 • 5 35 x = 8(2 6 x 6 ) • (3 5 x 5 ) Next, simplify this expression: 1 ( )

8(21 x 7 ) • (31 x 5 ) 1 ( )

8(2 x 7 ) • (3 x 5 ) 48x

1 (7+ ) 5

(

35 1 + )

48x 5 5 (

36

48x 5

)

Then, set this equal to the given equivalent expression cxd to determine the values of c and d: (

36

cx d = 48 x 5

)

In this equivalent expression, c = 48 and 36 d= .

5 The question asks us to find the value of c + d, so add these two terms together: 48 +

49

36 48(5) 36 240 36 276 + = = + = 5 5 5 5 5 5

Math # Mini-Test 3

51

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 16

QUESTION 18 y = –x2 + 4x – 3

A right triangle has sides of length 2 2 , 5 2 ,

y = –2x + a

and 58 units. What is the area of the triangle, in

In the given system of equations, a is a constant. The graphs of the equations in the given system intersect at exactly one point, (x, y), in the xy-plane. What is the value of x ?

square units?

A) 7 2 + 58

A) –6

B) 10

B) –3

C) 20 58 D) 20

C)

3

D)

6

QUESTION 17

QUESTION 19

The expression 5x2 + bx – 48, where b is a constant, can be rewritten as (mx + p)(x + q), where m, p, and q are integer constants. Which of the following must be an integer?

An isosceles right triangle has a hypotenuse of length 74 centimeters. What is the perimeter, in centimeters, of this triangle?

A)

A) 37 2

b m

B) 74 2

B) b p

C) 74 + 74 2

C) 48 m

D) 74 + 148 2

D) 48 p

42

52

MATH MINI-TEST #3

16. The correct answer is B.

17. The correct answer is D.

To find the area of a triangle, we use the formula: A=

The expression given is a quadratic expression in standard form:

1 •b•h 2

5x2 + bx – 48 which can be factored into the form:

In a right triangle, the two sides that are not the hypotenuse, or longest side, are the base and the height. 58 is the longest side, so we know 2 2 and 5 2 are the base and height.

Plug these into the formula for the area of a triangle:

(mx + p)(x + q) Since 5 is a prime number and can’t be factored into integers, m must be 5. This gives us: (5x + p)(x + q)

1 •2 2 •5 2 2 To solve, we can picture this equation as a long multiplication problem where each number we need to multiply is separate.

A=

A=

Notice that p and q, multiplied together, must give us –48. Keep that in mind as we review the answer choices.

Answer choices A and B involve the variable b. The problem states that b is a constant, but does not provide enough information to determine the value of b with certainty. This makes it impossible to be certain that choice A or choice B must be an integer, so these answer choices can be eliminated.

1 •2• 2 •5• 2 2

Next, we can rearrange the values to get 2 next to the other 2 : 1 •2•5• 2 • 2 2 Since 2 • equation:

For choice C, we know that the value of m is 5, 48 but doesn’t produce an integer. So, choice 5 C can also be eliminated.

2 is 2, we can simplify our

1 •2•5•2 2 Finally, multiply all of the values to solve for A:

On the other hand, variable p has to be a factor

A=

of –48. Multiple values are possible for p. For example, p could equal –2 and q could equal

1 A = •2•5•2 2 A = 10

24. Or, p could equal 3 and q could equal –16.

But in any case, the fact that p is a factor of 48 –48 ensures that will be an integer, making p choice D correct.

53

MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MASTERING THE DIGITAL SAT®

QUESTION 16

QUESTION 18 y = –x2 + 4x – 3

A right triangle has sides of length 2 2 , 5 2 ,

y = –2x + a

and 58 units. What is the area of the triangle, in

In the given system of equations, a is a constant. The graphs of the equations in the given system intersect at exactly one point, (x, y), in the xy-plane. What is the value of x ?

square units?

A) 7 2 + 58

A) –6

B) 10

B) –3

C) 20 58 D) 20

C)

3

D)

6

QUESTION 17

QUESTION 19

The expression 5x2 + bx – 48, where b is a constant, can be rewritten as (mx + p)(x + q), where m, p, and q are integer constants. Which of the following must be an integer?

An isosceles right triangle has a hypotenuse of length 74 centimeters. What is the perimeter, in centimeters, of this triangle?

A)

A) 37 2

b m

B) 74 2

B) b p

C) 74 + 74 2

C) 48 m

D) 74 + 148 2

D) 48 p

42

54

MATH MINI-TEST #3

18. The correct answer is C.

19. The correct answer is C.

The simplest method for solving this problem is using the Desmos graphing calculator. Because the system only has one solution, its graphs will have one and only one point of intersection.

An isosceles right triangle includes a right angle and has two sides that are the same length. Since the hypotenuse is the longest side in a right triangle, the other two sides will be the same length.

Start by entering the first equation into Desmos as y = –x2 + 4x – 3. Next, enter the beginning of the second equation as y = –2x + a, but don’t type in the letter a. Instead, try different values for a in the second equation to figure out which value produces a line that is tangent to the parabola (meaning it intersects at one and only one point). Judging by the slope of the line, you can tell that the tangent point will have to be somewhere to the right of the vertex. Keep trying points until you get a = 6, which will produce a line that is tangent to the parabola.

Finally, determine the x-value at this point of intersection: 3 (choice C).

hypotenuse

a

b The standard formula for the side lengths of a right triangle is a2 + b2 = c2, where c is the hypotenuse. In this case, sides a and b are the same length, so both can be labeled a. In addition, the problem tells us that the hypotenuse is 74.

We can also solve this algebraically, though it requires more time and calculations. Given the system of equations: y = –x2 + 4x – 3 y = –2x + a

a Here, a + b = c can be rewritten as: a2 + a2 = 742. Solving for a will provide the unknown side length.

2

–x + 4x – 3 = –2x + a 2

Rearrange the equation to bring all terms to one side: x2 – 2x + 3 + a = 0

2

2

From there, combine terms and use a calculator to get: 2a2 = 5,476.

This is a quadratic equation in the standard form y = ax2 + bx + c. To find the roots of this equation, one would typically use the quadratic formula:

Divide both sides by 2 to produce: a2 = 2,738.

Taking the square root of both sides of this equation will give us the value of a. Use a calculator to determine: a ≈ 52.33.

–b ± b2 – 4 ac x= 2a However, in this case, since we know there is exactly one point of intersection, the discriminant (the part under the square root in the quadratic formula) must be zero. This gives us: b2 − 4ac = 0.

52.33

For our quadratic x2 – 6x – (–3 – a), a = –1, b = 6, and c = (–3 – a). Plugging these into the above equation and solving for a gives:

74

52.33

(6)2 − 4(−1)(–3 – a) = 0 36 – (–4)(−3 − a) = 0 36 – (12 + 4a) = 0 36 – 12 − 4a = 0 24 = 4a a=6 Therefore, the second equation in the system is y = –2x + 6. Now that we have two full equations, we can plot them using Desmos to find their solution.

Plug the equations into Desmos and determine the point where they intersect: (3, 0). The question asks for the value of x, which is 3, making the correct answer choice C.

74

a

Since the graphs of the equations intersect at exactly one point, this means that there is one solution to the system of equations, which occurs when both equations are equal to each other. To find the value of x, set the two equations equal to each other:

Add up the three sides: 74 + 52.33 + 52.33 = 178.66 Since the answer choices are written in a form using the square root, use a calculator to determine the value of each.

Trying this with answer choice C shows us that 74 + 74 2 = 178.65. The rounding explains the difference of 0.01 between the answers, and choice C is correct.

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MASTERING THE DIGITAL SAT: STUDENT HANDOUT

MATH MINI-TEST #3

QUESTION 20

QUESTION 22

In the xy-plane, a parabola has vertex (6, –12) and intersects the x-axis at two points. If the equation of the parabola is written in the form y = ax2 + bx + c, where a, b, and c are constants, which of the following could be the value of a+b+c?

The function ƒ(x) = 314(1.018)x models the worth, in dollars, of a family heirloom at the end of each year from 1967 through 1988, where x is the number of years after 1967. In this context, which of the following is the most accurate explanation of “ƒ(6) is approximately equal to 349”?

A) –23

A) The worth of the heirloom is evaluated to be approximately 6 dollars greater in 1973 than in 1967.

B) –18 C) –12 D) –10

B) The worth of the heirloom is evaluated to be approximately 349 dollars in 1973.

C) The worth, in dollars, of the heirloom is evaluated to be approximately 6 times greater in 1973 than in 1967.

QUESTION 21

D) The worth of the heirloom is evaluated to increase by approximately 349 dollars every 6 years between 1967 and 1973.

Function g is defined by g(x) = –ax + b, where a and b are constants. In the xy-plane, the graph 109 109 (0,– at) (0,– ). of y = g(x) – 13 has a y-intercept 9 9 68 The product of a and b is 68 .

9 9 What is the value of a ?

STOP This is the end of this section. Wait for your instructor to tell you to move to the next section.

43

56

MATH MINI-TEST #3

–109 + 13 = –1 + b 9 –109 + 14 = b 9 –109 126 + =b 9 9

20. The correct answer is D. The parabola’s vertex at (6, –12) is below the x-axis. Since it intersects the x-axis at two points, it must open upward.

In the form y = ax2 + bx + c, the variable c represents the parabola’s y-intercept. Since the y-value of the vertex is –12 and the parabola opens upward, the y-intercept must be greater than –12.

17 =b 9 The problem also tells us the product of a and 68 b is . Plug the value we found for b into this 9 equation:

Since a and b are presented in y = ax2 + bx + c without negative signs, they represent positive values. Therefore, the value of a + b + c will be greater than c.

17 68 )= 9 9 68 a= 17 a=4

a(

Since c must be greater than –12, a + b + c must also be greater than –12. Of the available answer choices, only answer choice D, –10, is greater than –12.

22. The correct answer is B.

21. The correct answer is 4.

The function f(x) = 314(1.018)x models the value of a family heirloom over time, with x representing the number of years since 1967.

The expression f(6) represents the value of the heirloom 6 years after 1967, which is the year 1973. Choice B is correct because it describes the total value of the heirloom in 1973 and because 314(1.018)x ≈ 349 dollars.

The problem says the function g is defined by g(x) = – ax + b and that the graph of y = g(x) – 13 has a y-intercept at (0,–

109 ) . Since 9

109 ) represents a point on 68the graph, we 9 9 and plug in can 68 combine these two equations (0,–

Choice A is incorrect because it states that the worth of the heirloom is 6 dollars greater in 1973 than in 1967. But 6, the value of x, has to do with the number of years that have passed since 1967, not the dollar-value of the heirloom.

9 values for x and y: the First, rearrange the second equation to solve for g(x): y = g(x) – 13

Choice C is incorrect because it says that the worth of the heirloom is 6 times greater than in a prior year. However, 6, the value of x, has to do with the number of years that have passed since 1967, not the heirloom’s dollar value.

g(x) = y + 13 Then, set the first equation equal to this value for g(x): g(x) = –ax + b

Choice D is incorrect because the function does not directly provide information about the increase in the value of the heirloom. Rather, it provides the total value.

y + 13 = –ax + b Then, plug in the values for x and y given in the y-intercept: y + 13 = –ax + b –109 109 – + 13 = –a0 + b 9 Since a0 = 1, we can replace that term with 1 (don’t forget to keep the minus sign) and solve for b: 57