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Digital SAT Mock Test - 1 - SAT MCQ


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30 Questions MCQ Test SAT Mock Test Series 2025 - Digital SAT Mock Test - 1

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Digital SAT Mock Test - 1 - Question 1

Which quotation from a scholarly article best supports the assertion of the historians mentioned in the text?

Detailed Solution for Digital SAT Mock Test - 1 - Question 1

Choice C is the best answer. The fact that Henry VIII commissioned a survey of church holdings just before enacting the Dissolution of the Monasteries suggests that he was interested in the potential profits from claiming their assets. This supports the historians’ assertion.
Choice A is incorrect. This choice describes a potential effect of the Dissolution of the Monasteries. The decrease in the proportion of monks in England isn’t relevant to the question of Henry VIII’s motivations. Choice B is incorrect. Details about how the monks were treated during the dissolution don’t address Henry VIII’s motivations for enacting the policy in the first place. That the monks could keep the content of their cells (their rooms) and sell off the timber they’d harvested has no impact on the value of the monasteries’ estates—their land holdings. Choice D is incorrect. This choice mentions one impact that the Dissolution of the Monasteries contributed to, two years after it happened. But it doesn’t help explain why Henry VIII might have wanted to enact the policy in the first place.

Digital SAT Mock Test - 1 - Question 2

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

Detailed Solution for Digital SAT Mock Test - 1 - Question 2

Choice 1 is the best answer. The claim is that when winds are stronger than forecasted, wind turbines can generate more energy than predicted. The supporting graph shows the additional amount (above the predicted amount) that the turbines generated under those conditions, with the West generating about 150 thousand additional MWh.
Choice 2 is incorrect. This choice doesn’t complete the example. The graph shows the additional amount of electricity that the wind turbines generated. The West bar is greater than 0, so the West generated more than the predicted amount.
Choice 3 is incorrect. This choice doesn’t complete the example. The graph shows the additional amount of electricity that the wind turbines generated. The West bar is greater than 0, so the West generated more than the predicted amount.
Choice 4 is incorrect. This choice misreads the graph. The graph shows us that the West (the bar on the left) generated about 150 thousand additional MWh.

Digital SAT Mock Test - 1 - Question 3

Which finding, if true, would most strongly support the team’s conclusion?

Detailed Solution for Digital SAT Mock Test - 1 - Question 3

Choice 1 is the best answer because it presents a finding that, if true, would most strongly support the team’s conclusion that cattle were likely raised closer to human settlements than sheep and goats were. The text explains that Vaiglova, Liu, and their colleagues analyzed the chemical composition of sheep, goat, and cattle bones from the Bronze Age in China in order to investigate the animals’ domestication, or their adaptation from a wild state to a state in which they existed in close connection with humans. According to the text, the team’s analysis showed that sheep and goats of the era fed largely on wild plants, whereas cattle fed on millet—importantly, a crop cultivated by humans. If analysis of the animal bones shows that the cattle’s diet also consisted of wheat, another crop cultivated by humans in China during the Bronze Age, the finding would support the team’s conclusion by offering additional evidence that cattle during this era fed on human-grown crops—and, by extension, that humans raised cattle relatively close to the settlements where they grew these crops, leaving goats and sheep to roam farther away in areas with wild vegetation, uncultivated by humans.

Choice 2 is incorrect because if it were true that sheep’s and goats’ diets consisted of small portions of millet, which the text states was a crop cultivated by humans, the finding would suggest that sheep and goats were raised relatively close to human settlements, weakening the team’s conclusion that cattle were likely raised closer to those settlements than sheep and goats were.

Choice 3 is incorrect because the finding that cattle generally require more food and nutrients than do sheep and goats wouldn’t support the team’s conclusion that cattle were likely raised closer to human settlements than sheep and goats were. Nothing in the text suggests that cattle were incapable of obtaining sufficient food and nutrients without access to human-grown crops. Hence, even if cattle’s diets are found to have different requirements than the diets of sheep and goats, the cattle could have met those requirements from food located far from human settlements.

Choice 4 is incorrect because if it were true that the diets of sheep, goats, and cattle varied based on what the farmers in each Bronze Age settlement could grow, the finding would weaken the team’s conclusion that cattle were likely raised closer to human settlements than sheep and goats were, suggesting instead that all three types of animals were raised close enough to human settlements to feed on those settlements’ crops.

Digital SAT Mock Test - 1 - Question 4

According to the text, why was Wang and his team’s discovery of the Terropterus xiushanensis fossil significant?

Detailed Solution for Digital SAT Mock Test - 1 - Question 4

Choice 4 is the best answer because it states why Wang and his team’s discovery of the Terropterus xiushanensis fossil was significant. The text explains that up until Wang and his team’s discovery, the only fossil evidence of mixopterids came from the paleocontinent of Laurussia. Wang and his team, however, identified fossil remains of a mixopterid species from the paleocontinent Gondwana. Therefore, the team’s discovery was significant because the fossil remains of a mixopterid species were outside of the paleocontinent Laurussia.

Choice 1 is incorrect. Although the text states that Wang and his team identified fossilized remains of a mixopterid species that lived more than 400 million years ago, it doesn’t indicate that mixopterid fossils previously found by scientists dated to a more recent period than that.
Choice 2 is incorrect. Although the text states that mixopterids are related to modern arachnids and horseshoe crabs, it doesn’t suggest that the fossil discovered by Wang and his team confirmed that this relationship is closer than scientists had previously thought.
Choice 3 is incorrect because the team’s fossil established the presence of mixopterids on Gondwana, not on Laurussia. Moreover, the text only discusses the fossil in relation to the geographical distribution of mixopterids, not in relation to their evolution.

Digital SAT Mock Test - 1 - Question 5

Which quotation from a scholarly article best supports the assertion of the historians mentioned in the text?

Detailed Solution for Digital SAT Mock Test - 1 - Question 5

Choice 3 is the best answer. The fact that Henry VIII commissioned a survey of church holdings just before enacting the Dissolution of the Monasteries suggests that he was interested in the potential profits from claiming their assets. This supports the historians’ assertion.

Choice 1 is incorrect. This choice describes a potential effect of the Dissolution of the Monasteries. The decrease in the proportion of monks in England isn’t relevant to the question of Henry VIII’s motivations.
Choice 2 is incorrect. Details about how the monks were treated during the dissolution don’t address Henry VIII’s motivations for enacting the policy in the first place. That the monks could keep the content of their cells (their rooms) and sell off the timber they’d harvested has no impact on the value of the monasteries’ estates—their land holdings.
Choice 4 is incorrect. This choice mentions one impact that the Dissolution of the Monasteries contributed to, two years after it happened. But it doesn’t help explain why Henry VIII might have wanted to enact the policy in the first place.

Digital SAT Mock Test - 1 - Question 6

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

Detailed Solution for Digital SAT Mock Test - 1 - Question 6
  • Choice C is the best answer. The convention being tested is the use of finite and nonfinite verb forms within a sentence. The nonfinite present participle “forcing” is correctly used to form a participial phrase that supplements the main clause “those...cover,” describing the effects on monkeys of the lack of food sources.
  • Choice A is incorrect because the finite present tense verb “forces” can’t be used in this way to supplement the main clause (“those...cover”).
  • Choice B is incorrect. While the nonfinite to-infinitive “to force” could be used to form a subordinate clause that supplements the main clause (“those...cover”), to-infinitives conventionally express purpose, and nothing in the sentence suggests that the food sources become unavailable for the purpose of forcing monkeys to hunt marine animals.
  • Choice D is incorrect because the finite past tense verb “forced” can’t be used in this way to supplement the main clause (“those...cover”).
Digital SAT Mock Test - 1 - Question 7

Which choice completes the text with the most logical transition?

Detailed Solution for Digital SAT Mock Test - 1 - Question 7
  • Choice A is the best answer. “Still” logically signals that the information about Sher-Gil in this sentence— that she longed to leave Paris and return to India— contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris in the previous sentences.
  • Choice B is incorrect because “therefore” illogically signals that the information about Sher-Gil in this sentence is a result or consequence of the descriptions in the previous sentences. Instead, this information contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris.
  • Choice C is incorrect because “indeed” illogically signals that the information about SherGil in this sentence offers additional emphasis in support of the descriptions in the previous sentences. Instead, this information contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris.
  • Choice D is incorrect because “furthermore” illogically signals that the information about Sher-Gil in this sentence offers additional support for or confirmation of the descriptions in the previous sentences. Instead, this information contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris.
Digital SAT Mock Test - 1 - Question 8

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

Detailed Solution for Digital SAT Mock Test - 1 - Question 8
  • Choice C is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the present tense verb “experiences” is consistent with the other present tense verbs (e.g., “connects” and “prepares”) used to describe the events in Truong’s novels. Furthermore, it’s conventional to use the present tense when discussing a literary work.
  • Choice A is incorrect because the past tense verb “experienced” isn’t consistent with the other present tense verbs used to describe the events in Truong’s novels.
  • Choice B is incorrect because the past perfect tense verb “had experienced” isn’t consistent with the other present tense verbs used to describe the events in Truong’s novels.
  • Choice D is incorrect because the future progressive tense verb “will be experiencing” isn’t consistent with the other present tense verbs used to describe the events in Truong’s novels.
Digital SAT Mock Test - 1 - Question 9

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

Detailed Solution for Digital SAT Mock Test - 1 - Question 9
  • Choice C is the best answer. The convention being tested is punctuation between a subject and a verb. When, as in this case, a subject (“her 2019 novel Gingerbread”) is immediately followed by a verb (“offers”), no punctuation is needed.
  • Choice A is incorrect because no punctuation is needed between the subject and the verb.
  • Choice B is incorrect because no punctuation is needed between the subject and the verb.
  • Choice D is incorrect because no punctuation is needed between the subject and the verb.
Digital SAT Mock Test - 1 - Question 10

The student wants to make a generalization about the kind of study conducted by Glickman, Brown, and Song. Which choice most effectively uses relevant information from the notes to accomplish this goal?

Detailed Solution for Digital SAT Mock Test - 1 - Question 10
  • Choice D is the best answer. The sentence uses information from the notes to make a generalization about the kind of study Glickman, Brown, and Song conducted. Specifically, the sentence indicates that the study was of a kind that used statistical methods to address questions of authorship within the field of music.
  • Choice A is incorrect because the sentence summarizes the methodology and findings of a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted.
  • Choice B is incorrect because the sentence mentions the data and conclusion of a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted.
  • Choice C is incorrect because the sentence focuses on a specific conclusion from a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted.
Digital SAT Mock Test - 1 - Question 11

Which finding from Washington and Mullainathan’s study, if true, would most directly weaken the claim made by people who favor the traditional view of voter behavior?

Detailed Solution for Digital SAT Mock Test - 1 - Question 11
  • Choice C is the best answer because it presents a finding that, if true, would weaken the claim made by people who favor the traditional view of voter behavior. According to the text, people who favor that view believe that voting in an election doesn’t change a voter’s attitude toward the candidates in that election. If Washington and Mullainathan found that two years after an election, attitudes toward the winning candidate were significantly more polarized among subjects who had voted than among subjects who had been too young to vote, that would suggest that the act of voting did have an effect on the voters’ attitudes toward the candidates, which would undermine the claim that voting doesn’t change voters’ attitudes.
  • Choice A is incorrect because a finding about links between subjects’ attitudes and general political orientation, regardless of age and ability to vote, wouldn’t address the presence or absence of changes in attitudes among those subjects who did actually vote. Therefore, the finding wouldn’t have any bearing on the claim that voting in an election doesn’t change a voter’s attitude toward the candidates in that election.
  • Choice B is incorrect because a finding that positive attitudes toward a winning candidate significantly increased in the two years after the election among subjects who had been too young to vote would involve only people who didn’t vote; therefore, the finding wouldn’t have any bearing on the claim that when people do vote, the act of voting doesn’t change their attitudes toward the candidates.
  • Choice D is incorrect because the finding that subjects in both groups were more likely to have negative attitudes than positive attitudes toward the winning candidate two years after an election would reflect all subjects’ attitudes at one particular time whether they voted or not, rather than the presence or absence of a change in voters’ attitudes after voting. Therefore, the finding would neither weaken nor strengthen the claim that voting in an election doesn’t change a voter’s attitude toward the candidates.
Digital SAT Mock Test - 1 - Question 12

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

Detailed Solution for Digital SAT Mock Test - 1 - Question 12
  • Choice A is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the simple past tense verb “suggested” properly indicates that Zufall offered her suggestion for the product’s name in the past. This verb tense is consistent with the previous sentence’s use of a simple past tense verb (“advised”) to describe Zufall’s advice to McVicker in the 1950s.
  • Choice B is incorrect because the present tense verb “suggests” doesn’t indicate that Zufall offered her suggestion in the past.
  • Choice C is incorrect because the past perfect verb “had suggested” isn’t consistent with the previous sentence’s use of the simple past tense verb “advised” to describe Zufall’s advice to McVicker.
  • Choice D is incorrect because the past progressive verb “was suggesting” isn’t consistent with the previous sentence’s use of the simple past tense verb “advised” to describe Zufall’s advice to McVicker.
Digital SAT Mock Test - 1 - Question 13

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

Detailed Solution for Digital SAT Mock Test - 1 - Question 13
  • Choice C is the best answer because it uses data from the graph to effectively complete the example of Eludoyin and his colleagues’ findings concerning female farmers in some regions of Ondo State, Nigeria. The graph presents values for the percentage of Ondo State small-scale farmers who are female, by type of crop and region. The graph shows that of the farmers mainly cultivating nonroot vegetables, approximately 57% in north Ondo and approximately 54% in south Ondo are female; in other words, most of those farmers are female, which exemplifies the idea that female farmers make up the majority (more than half) of the farmers cultivating specific types of crops in some regions.
  • Choice A is incorrect because it inaccurately cites data from the graph: the graph shows that in south Ondo, most of the farmers mainly cultivating non-root vegetables are women (approximately 54%), but that only about 35% (less than half) of the farmers mainly cultivating cereals are women.
  • Choice B is incorrect because it inaccurately cites data from the graph: the graph shows that more women in central Ondo mainly cultivate cereals than mainly cultivate root crops (approximately 36% and 20%, respectively). Additionally, it doesn’t effectively complete the example because the graph shows that female farmers don’t make up the majority (more than half) of the farmers for any type of crop in central Ondo.
  • Choice D is incorrect because it doesn’t effectively complete the example; it simply states that a relatively equal proportion of women across the three regions mainly cultivate cereals, which doesn’t address the value for that proportion and thus doesn’t show that a majority (more than half) of the farmers cultivating certain crops are female.
Digital SAT Mock Test - 1 - Question 14

A babysitter earns $8 an hour for babysitting 2 children and an additional $3 tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned?

Detailed Solution for Digital SAT Mock Test - 1 - Question 14

Choice A is the correct answer. Let x be the number of hours that the babysitter worked. Since the babysitter earns money at a rate of $8 per hour, she earned 8x dollars for the x hours worked. If the babysitter gets both children to bed on time, the babysitter earns an additional $3 tip. Therefore, the babysitter earned a total amount of 8x + 3 dollars.
Choice B is incorrect since the tip and the rate per hour have been interchanged in the expression. Choices C and D are incorrect since the number of children is not part of how the babysitter’s earnings are calculated.

Digital SAT Mock Test - 1 - Question 15

Which of the following is equivalent to 

Detailed Solution for Digital SAT Mock Test - 1 - Question 15

Choice C is the correct answer. Using the distributive property to expand the given expression gives 
Choices A, B, and D are incorrect. In each of these choices, at least one of the products in the expansion is not correct. For example 

Digital SAT Mock Test - 1 - Question 16

110x + y = 1,210
A coffee shop is running a promotion where a number of free coffee samples are given away each day. The equation above can be used to model the number of free coffee samples, y, that remain to be given away x days after the promotion began. What does it mean that (11, 0) is a solution to this equation?

Detailed Solution for Digital SAT Mock Test - 1 - Question 16

Choice C is the correct answer. Since x represents the number of days after the promotion began and y represents the remaining number of coffee samples, the fact that the ordered pair (11, 0) is a solution to the given equation means that it takes 11 days during the promotion until none of the samples are remaining.
Choice A is incorrect; if 11 samples were given away each day, then the coefficient of x in the equation would be 11. Therefore, this is not the correct interpretation of (11, 0) as a solution to the equation. Choice B is incorrect; the total number of free coffee samples given away during 11 days of the promotion was 1,210. But the number of customers who were in the store during those days need not be 1,210. Choice D is incorrect; according to the given equation, there were 1,210, not 11, samples available at the start of the promotion. 

Digital SAT Mock Test - 1 - Question 17

The formula d = rt is used to calculate the distance an object travels over a period of time, , at a constant rate, r. Based on this formula, what is the rate, r, in terms of d and t?

Detailed Solution for Digital SAT Mock Test - 1 - Question 17

Dividing each side of the equation d = rt by t results in an equation that expresses r in terms of the other variables: r = d/t
Choices B, C, and D are incorrect and may result from algebraic errors when rewriting the given equation.

Digital SAT Mock Test - 1 - Question 18

Giovanni wants to buy shirts that cost $19.40 each and sweaters that cost $24.80 each. An 8% sales tax will be applied to the entire purchase. If Giovanni buys 2 shirts, which equation relates the number of sweaters purchased, p, and the total cost in dollars, y?

Detailed Solution for Digital SAT Mock Test - 1 - Question 18

Digital SAT Mock Test - 1 - Question 19


If the equation above, where a is a constant, is true for all positive values of x and y, what is the value of a?

Detailed Solution for Digital SAT Mock Test - 1 - Question 19

Choice C is correct. After distributing the outside exponents to each expression within the parentheses by the rules of exponents, the left side of the equation can be rewritten as

Multiplying the expressions within the parentheses and applying the exponent rules yields which means the equation is true for all positive values of x and y. It follows that the corresponding exponents of x and y on both sides of the equation must be equal, which yields a = 5.
Choices A, B, and D are incorrect and may result from errors when applying the rules of exponents to the given expression.

Digital SAT Mock Test - 1 - Question 20

Question refer to the following information.
A high school developed a program called Propel, which offers extra guidance and support during the 9th-grade year. Before the school year began, 327 rising 9th graders were selected at random to participate in a study; 109 of those students were randomly assigned to enroll in the Propel program and the remaining students served as a control group. A summary of the year-end grade point averages (GPA) for the 327 9th-grade students who were chosen for the study is shown in the table below.

What is the difference, to the nearest whole percent, between the percentage of students enrolled in Propel who had a GPA of 3.0 or greater and the percentage of students not enrolled in Propel who had a GPA of 3.0 or greater?

Detailed Solution for Digital SAT Mock Test - 1 - Question 20

Choice D is correct. There are 61 students enrolled in Propel who had a GPA of 3.0 or greater and 48 students enrolled in Propel who had a GPA of less than 3.0, so there are a total of 61 + 48 = 109 students enrolled in Propel. The percentage of students enrolled in Propel who had a GPA of 3.0 or greater is or about 56%. There are 95 students who are not enrolled in Propel who had a GPA of 3.0 or greater and 123 students not enrolled in Propel who had a GPA of less than 3.0, so there are a total of 95 + 123 = 218 students who are not enrolled in Propel. The percentage of students not enrolled in Propel who had a GPA of 3.0 or greater isor about 44%. Therefore, the difference, to the nearest whole percent, between the percentage of students enrolled in Propel who had a GPA of 3.0 or greater and the percentage of students not enrolled in Propel who had a GPA of 3.0 or greater is 56% − 44% = 12%.
Choice A is incorrect. This answer choice is the result of finding the difference between the percentage of students in the study who both are enrolled in Propel and had a GPA of 3.0 or greater (61 ÷ 327 × 100% ≈ 18.7%) and the percentage of students in the study who both are enrolled in Propel and had a GPA less than 3.0 (48 ÷ 327 × 100% ≈ 14.7%). Choice B is incorrect. This answer choice is the result of finding the difference between the percentage of students in the study who both are not enrolled in Propel and had a GPA of 3.0 or greater. Choice C is incorrect. This answer choice may be the result of subtracting the number of students enrolled in Propel who had a GPA of 3.0 or greater from the number of students not enrolled in Propel who had a GPA of 3.0 or greater (95 – 61 = 34), then dividing the result by the total number of students in the study.

Digital SAT Mock Test - 1 - Question 21

A textile manufacturer receives two shipments of raw materials. Shipment A contains 30% polyester by weight, and shipment B contains 50% polyester by weight. Together, the two shipments contain 130 pounds of polyester. If x represents the total weight of the materials in shipment A and y represents the total weight of the materials shipment B, which equation models this relationship?

Detailed Solution for Digital SAT Mock Test - 1 - Question 21

If shipment A is 30% polyester and x represents the total weight of shipment A, then 0.3x represents the weight of polyester in shipment A. By the same reasoning, 0.5y represents the weight of polyester in shipment B. These two weights have a sum of 130, so 0.3x + 0.5y = 130. 

Digital SAT Mock Test - 1 - Question 22

Which of the following equations represents a line that is parallel to the line with the equation y = -2x + 4?

Detailed Solution for Digital SAT Mock Test - 1 - Question 22

Two lines that are parallel have the same slope. The linear equation in this question is in slope-intercept form, y = mx + b, and its slope, m, is -2. One way to see which choice also has a slope of —2 is to solve each equation for y:
A) y = -1/2x; slope = -1/2
B) y = 4x - 2; slope = 4
C) y = -2x + 3; slope = -2
D) y = 2x - 1; slope = 2

Digital SAT Mock Test - 1 - Question 23


The number of barrels of oil consumed by country X each year from 1991 to 1995 is shown in the graph above. If the total amount of oil consumed in those five years was 285,000 barrels, what is an appropriate label for the vertical axis of the graph?

Detailed Solution for Digital SAT Mock Test - 1 - Question 23

The bars correspond to values of 7, 9, 4.5, 3, and 5 on the vertical axis, for a total of 7 + 9 + 4.5 + 3 + 5 = 28.5. Since this sum corresponds a total of 285,000 barrels of oil, the unit on the vertical axis must be 285,000/28.5 = 10,000 barrels of oil.

Digital SAT Mock Test - 1 - Question 24

Question refer to the following information.

The bar graph above shows the total yield of five different crops on a particular farm in the years 2001 and 2002.
What is the percentage increase in the yield of corn from 2001 to 2002?

Detailed Solution for Digital SAT Mock Test - 1 - Question 24

According to the graph, in 2001, the yield of corn was 20 lbs, and, in 2002, it was 42.5 lbs,
for an increase of 42.5 - 20 = 22.5 lbs.
As a percent increase, this is 22.5/20 = 1.125 = 112.5%.

Digital SAT Mock Test - 1 - Question 25

what is the value of x?

Detailed Solution for Digital SAT Mock Test - 1 - Question 25


Multiply by 16 (the common denominator): 10x = -1
Divide by 10: x =

Digital SAT Mock Test - 1 - Question 26


The table above shows ordered pairs that satisfy the function f. Which of the following could define f?

Detailed Solution for Digital SAT Mock Test - 1 - Question 26

This question asks us to find the function that is satisfied by all four ordered pairs. Here, it is probably easiest to work by process of elimination, and cross off those choices that aren't satisfied by at least one of the ordered pairs. Let's consider the first ordered pair, (2, 1), and see which functions give an output of 1 for an input of 2:
(A) f(2) = 3(2)2 - 2 = 3(4) - 2 = 12 - 2 = 10 (No—eliminate.)
(B) f(2) = 3(2)2 - 4 = 3(4) - 4 = 12 - 4 = 8 (No—eliminate.)
(C) f(2) = 2(2)2 - 7 = 2(4) - 7 = 8 - 7 = 1 (Yes—don't eliminate.)
(D) f(2) = 2(2)2 = 2(4) = 8 (No—eliminate.)
So, it turns out we only have to test one ordered pair to get the right answer.

Digital SAT Mock Test - 1 - Question 27


Based on the ordered pairs in the table above, which of the following could express the relationship between the variables x and y?

Detailed Solution for Digital SAT Mock Test - 1 - Question 27

The first thing to notice about the ordered pairs is that as the value of x increases, the value of y decreases. More specifically, notice that the product of the two values in each ordered pair is always the same: (2)(10) = 20, (4)(5) = 20, and (10)(2) = 20. This is the hallmark of an inverse variation. The equation for this particular relationship is y = 20/x.

Digital SAT Mock Test - 1 - Question 28

Which of the following functions, when graphed in the xy-plane, will intersect the x-axis exactly 3 times?

Detailed Solution for Digital SAT Mock Test - 1 - Question 28

First, notice that the answer choices include the factors x2 - 1 and x2 + 1. The first of these is a difference of squares, so it can be factored further: x2 - 1 = (x + 1)(x - 1). However, x2 + 1 is a sum of squares, which cannot be factored over the real numbers. This enables us to express each function in completely factored form:
(A) f(x) = (x2 + 1) (x2 + 1) = (x2 + 1) (x2 + 1)
(B) f(x) = (x2 - 1) (x2 + 1) = (x + 1)(x - 1) (x2 + 1)
(C) f(x) = x2(x2 - 1) = x2(x + 1)(x - 1)
(D) f(x) = x2(x2 + 1) = x2(x2 + 1)
Now we can find all of the x-intercepts by setting each factor to 0 and (if possible) solving for x. Notice that if we do this for the factored form of each function, we see that (A) has no x-intercepts, (B) has intercepts at x = -1 and x = 1, (C) has intercepts at x = 0, x = -1, and x = 1, and (D) has an intercept at x = 0. Therefore, the function in choice (C) is the only one that has three x-intercepts.

Digital SAT Mock Test - 1 - Question 29

Mrs. Black has a bag of candy bars to hand out to the students in her class before they take their AP calculus BC exam. If she gives each student 3 candy bars, she will have 6 left over. In order to give each student 5 candy bars, she will need 50 more candy bars. How many students are in Mrs. Black's class?

Detailed Solution for Digital SAT Mock Test - 1 - Question 29

Begin by assuming that there are n students in Mrs. Black's class. If she gives out 3 candy bars to each student and has 6 left over, she must have 3n + 6 candy bars. If she needs 50 more candy bars in order to give each student 5 candy bars, she must have 5n - 50 candy bars. Since these two expressions both express the total number of candy bars, 3n + 6 = 5n - 50
Add 50 and subtract 3n: 56 = 2n
Divide by 2: 28 = n

*Answer can only contain numeric values
Digital SAT Mock Test - 1 - Question 30

When graphed in the xy-plane, the line y = mx - 4 intersects t he x-a x is at an angle of θ. If m > 0, 0° < θ < 90°, and cos θ = 3/√58, what is the value of m?


Detailed Solution for Digital SAT Mock Test - 1 - Question 30

The graph of the line y = mx - 4 has a slope of m and a y-intercept of -4. Since m > 0, this slope is positive. We are told that this line intersects the x-axis at an angle of θ, where cos θ = 3/√58. This gives us enough information to sketch a fairly detailed graph:

Notice that this information lets us construct a right triangle that includes θ, in which the adjacent side has length 3 and the hypotenuse has length √58 (remember cos θ = adjacent/hypotenuse). This triangle is particularly handy because it depicts the rise and the run for a portion of the line, which will enable us to find the slope. We simply have to find the rise with the
Pythagorean Theorem: 32 + rise2 = (√58)
Simplify: 9 + rise2 = 58
Subtract 9: rise2 = 49
Take square root: rise = 7
Therefore, the slope of the line is m = rise/run = 7/3 or 2.33

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