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CAASPP practice questions

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Question 1Smarter Balanced Summative Assessments for ELA

A student is writing a Smarter Balanced explanatory essay and needs a precise academic verb to introduce evidence from a source. Which word best fits a formal, evidence-based sentence?

  1. demonstrates Correct answer.
  2. goes
  3. puts
  4. shows

Explanation

Academic explanatory writing favors precise verbs that name what evidence does, such as demonstrates, illustrates, or reveals. Demonstrates signals a reasoned claim supported by evidence, matching the Smarter Balanced emphasis on citing sources to explain ideas.

Question 2Smarter Balanced Summative Assessments for ELA

In a Smarter Balanced performance task, a student must integrate a direct quotation from a source into an argument. Which choice correctly uses quotation marks and attribution?

  1. The author states, "Urban gardens reduce heat and cites city temperature data.
  2. The author states, "Urban gardens reduce heat," and cites city temperature data. Correct answer.
  3. The author states "Urban gardens reduce heat, and cites city temperature data."
  4. The author states that "Urban gardens reduce heat and cites city temperature data."

Explanation

A direct quotation must be enclosed in quotation marks and set off from the attribution with a comma. The closing quotation mark must come directly after the quoted words, before the sentence continues.

Question 3Smarter Balanced Summative Assessments for ELA

A student reads two Smarter Balanced sources on school start times and must write an argument. Which sentence states a defensible claim rather than a summary?

  1. Later start times should be adopted because teen sleep research links early bells to lower attendance. Correct answer.
  2. Many schools start before 8:00 a.m., and some researchers study teen sleep.
  3. This essay will discuss school start times and the research about them.
  4. Teen sleep is a topic that many people find interesting to discuss.

Explanation

A defensible claim takes a position and gives a reason that can be supported with evidence. Option 0 asserts a recommendation and ties it to attendance data, which is arguable and evidence-based.

Question 4Smarter Balanced Summative Assessments for ELA

Which sentence uses a colon correctly to introduce a list within a Smarter Balanced informative essay?

  1. The plan includes: three steps surveying, planting, and monitoring.
  2. The plan includes three steps; surveying, planting, and monitoring.
  3. The plan includes three steps, surveying: planting, and monitoring.
  4. The plan includes three steps: surveying, planting, and monitoring. Correct answer.

Explanation

A colon follows a complete independent clause and introduces the list that explains it. The clause before the colon must stand alone, which it does in option 0.

Question 5Smarter Balanced Summative Assessments for ELA

A student writing a Smarter Balanced literary analysis wants to describe how an author's word choice creates mood. Which term names the author's choice of words?

  1. diction Correct answer.
  2. setting
  3. plot
  4. theme

Explanation

Diction refers to an author's choice of words and phrasing, which shapes tone and mood. Literary analysis in Smarter Balanced tasks often asks students to connect word choice to effect.

Question 6Smarter Balanced Summative Assessments for ELA

Which sentence from a Smarter Balanced research summary uses the subjunctive mood correctly?

  1. The committee recommends that the district will adopts a later start time.
  2. The committee recommends that the district adopting a later start time.
  3. The committee recommends that the district adopt a later start time. Correct answer.
  4. The committee recommends that the district adopts a later start time.

Explanation

After verbs of recommendation such as recommend or suggest, formal English uses the subjunctive, which takes the base form adopt regardless of subject. This is the standard construction in academic writing.

Question 7Smarter Balanced Summative Assessments for ELA

A Smarter Balanced listening task asks a student to summarize a speaker's main point. Which summary best reflects the purpose of a summary?

  1. It gives the student's opinion about whether the speaker is convincing.
  2. It restates the central idea and key supporting points briefly in the student's own words. Correct answer.
  3. It repeats the speaker's sentences word for word to preserve accuracy.
  4. It lists every detail the speaker mentioned in the order given.

Explanation

A summary condenses a source to its central idea and essential support using the reader's own phrasing. Copying, evaluating, or listing every detail does not meet that purpose.

Question 8Smarter Balanced Summative Assessments for ELA

In a Smarter Balanced argument essay, which transition most clearly signals a contrast between two pieces of evidence?

  1. Therefore
  2. For instance
  3. Similarly
  4. However Correct answer.

Explanation

However signals contrast, showing that the next point opposes or qualifies the previous one. The other choices signal cause, similarity, or example rather than contrast.

Question 9Smarter Balanced Summative Assessments for ELA

A student evaluating a source for a Smarter Balanced research task finds a website with no author, no date, and no citations. Which conclusion is most reasonable?

  1. The source's reliability is questionable because it lacks verifiable authorship and evidence. Correct answer.
  2. The source is reliable because it uses an informal tone.
  3. The source is reliable because it has no author to bias it.
  4. The source is reliable because it appears on the internet.

Explanation

Reliability depends on verifiable authorship, currency, and supporting evidence. A source missing all of these signals cannot be confidently trusted and should be corroborated.

Question 10Smarter Balanced Summative Assessments for ELA

A student must use a source's data in an argument about recycling. Which use of the data best reflects accurate integration?

  1. The student mentions the figure but attributes it to a different study.
  2. The student copies the figure into the essay without saying where it came from.
  3. The student cites the figure, names the source, and explains how it supports the claim. Correct answer.
  4. The student changes the figure slightly to make the argument stronger.

Explanation

Accurate integration requires citing the source and connecting the evidence to the claim through explanation. Misattributing or altering data violates accuracy and academic honesty.

Question 11Smarter Balanced Summative Assessments for ELA

Read this sentence: 'The researcher, who studied sleep for a decade, argues that later bells improve attendance.' Which function does the clause 'who studied sleep for a decade' serve?

  1. It is an independent clause that could stand alone as a sentence.
  2. It is a restrictive clause essential to identifying which researcher is meant.
  3. It is an appositive renaming the noun sleep.
  4. It is a nonrestrictive relative clause adding extra information about the researcher. Correct answer.

Explanation

The clause is set off by commas and adds supplementary detail about an already-identified researcher, making it nonrestrictive. Removing it would not change which researcher is meant.

Question 12Smarter Balanced Summative Assessments for ELA

A student is analyzing how an author builds an argument in a Smarter Balanced source. The author presents a counterargument and then rebuts it. What is the main purpose of this move?

  1. To confuse readers about which side the author supports.
  2. To strengthen credibility by addressing objections and showing why the claim still holds. Correct answer.
  3. To introduce a second unrelated topic into the essay.
  4. To avoid taking any position on the issue.

Explanation

Addressing a counterargument and rebutting it demonstrates that the author has considered opposing views, which strengthens the argument's credibility. It also clarifies why the original claim remains valid.

Question 13Smarter Balanced Summative Assessments for ELA

A Smarter Balanced narrative task asks students to develop a character through indirect characterization. Which technique best accomplishes this?

  1. Describing the setting in detail without mentioning the character.
  2. Listing the character's age, height, and hometown.
  3. Stating directly that the character is generous and kind.
  4. Showing the character's choices and reactions during a conflict. Correct answer.

Explanation

Indirect characterization reveals personality through actions, dialogue, thoughts, and reactions rather than direct statements. Choices during conflict show character traits implicitly.

Question 14Smarter Balanced Summative Assessments for ELA

Which revision best improves sentence variety in this Smarter Balanced essay excerpt: 'The city planted trees. The city added benches. The city built paths.'

  1. The city planted trees. The city added benches. The city built paths.
  2. The city planted trees, the city added benches, the city built paths.
  3. The city planted trees, added benches, and built paths. Correct answer.
  4. The city planted trees and the city added benches and the city built paths.

Explanation

Combining short repetitive sentences into a parallel series improves flow and sentence variety. The revised sentence uses parallel verbs joined correctly.

Question 15Smarter Balanced Summative Assessments for ELA

A student must determine an author's point of view in an informational Smarter Balanced source. Which evidence most directly reveals the author's attitude toward the topic?

  1. The publication date printed at the top of the page
  2. The number of paragraphs in the article
  3. The presence of a table of contents
  4. Evaluative language such as 'promising' and 'urgently needed' Correct answer.

Explanation

An author's attitude is revealed through evaluative and connotative word choices that signal approval, concern, or urgency. Structural features like dates and headings do not convey stance.

Question 16Smarter Balanced Summative Assessments for ELA

Which sentence correctly uses a semicolon in a Smarter Balanced analytical paragraph?

  1. The data were inconclusive; calling for a larger sample.
  2. The data were inconclusive; because a larger sample was needed.
  3. The data were inconclusive; and the researchers called for a larger sample.
  4. The data were inconclusive; the researchers called for a larger sample. Correct answer.

Explanation

A semicolon may join two closely related independent clauses without a conjunction. Each side of the semicolon in option 0 can stand alone as a sentence.

Question 17Smarter Balanced Summative Assessments for ELA

A student compares two Smarter Balanced sources that reach opposite conclusions about homework. Which approach best demonstrates analysis rather than summary?

  1. Reporting only the source that agrees with the student's view
  2. Listing each source's main idea one after the other
  3. Explaining how each source's evidence and assumptions lead to its different conclusion Correct answer.
  4. Choosing the longer source as the more accurate one

Explanation

Analysis examines how evidence, reasoning, and assumptions produce different conclusions. Merely listing ideas or selecting by length or preference is summary or bias, not analysis.

Question 18Smarter Balanced Summative Assessments for ELA

Which sentence maintains formal academic register appropriate for a Smarter Balanced explanatory essay?

  1. The evidence suggests that urban trees lower surface temperatures. Correct answer.
  2. Everybody knows trees make cities way cooler.
  3. The evidence totally proves trees are super cool for cities.
  4. Trees are like, really helpful for keeping cities cool.

Explanation

Formal academic register uses precise vocabulary, hedged claims, and standard grammar. The other options rely on slang, filler words, or overgeneralization unsuitable for explanatory writing.

Question 19Smarter Balanced Summative Assessments for ELA

A student paraphrases a source in a Smarter Balanced research task. Which practice best avoids plagiarism?

  1. Using the idea without citation because it was reworded.
  2. Changing a few words while keeping the original sentence structure, with no citation.
  3. Copying the sentence exactly but adding quotation marks only around one phrase.
  4. Restating the idea in original wording and citing the source. Correct answer.

Explanation

Proper paraphrase requires both original phrasing and attribution to the source. Minor word swaps or uncited reuse of ideas still constitute plagiarism.

Question 20Smarter Balanced Summative Assessments for ELA

An author writes: 'The new policy is a patch on a bursting dam.' Which analysis best explains the effect of this figurative language?

  1. The personification implies the policy can make decisions.
  2. The hyperbole shows the policy is popular with the public.
  3. The metaphor suggests the policy offers only a small, temporary fix for a much larger problem. Correct answer.
  4. The simile compares the policy to a construction project that will succeed.

Explanation

The metaphor compares a small repair to a failing structure, implying the fix is inadequate for the scale of the problem. Recognizing the comparison's implication is the analytical step.

Question 21Smarter Balanced Summative Assessments for ELA

A student's Smarter Balanced argument includes this sentence: 'Social media harms teenagers.' Which revision makes the claim more precise and defensible?

  1. Social media should be banned because it is harmful.
  2. Excessive late-night social media use is associated with reduced sleep among teenagers. Correct answer.
  3. Social media is bad for everyone in many different ways.
  4. Teenagers use social media and it affects them.

Explanation

A precise claim narrows the scope, specifies the population, and uses measured language that evidence can support. Broad or absolute statements are harder to defend.

Question 22Smarter Balanced Summative Assessments for ELA

In a Smarter Balanced research task, a student finds a study funded by an industry group that reaches conclusions favorable to that industry. Which evaluation is most appropriate?

  1. Accept the study because published research is always objective.
  2. Reject the study outright because funding always invalidates results.
  3. Consider the funding as a possible bias and seek independent corroboration. Correct answer.
  4. Ignore the funding because it does not affect how readers judge the source.

Explanation

Funding is relevant context that may indicate bias, but it does not automatically invalidate findings. Careful readers weigh it alongside methodology and independent corroboration.

Question 23Smarter Balanced Summative Assessments for ELA

A student writes: 'The author argues that recess improves focus; moreover, she claims it builds social skills; consequently, her case is persuasive.' Which analysis of the sentence's logic is most accurate?

  1. The word moreover signals a contrast between the two claims.
  2. The transitions correctly show that the conclusion follows necessarily from the claims.
  3. The transitions stack claims and a conclusion without explaining the reasoning connecting them. Correct answer.
  4. The semicolons should be replaced by commas to join independent clauses.

Explanation

The sentence lists claims and jumps to a conclusion without showing why the evidence supports it. Strong analysis requires explaining the reasoning, not just linking statements with transitions.

Question 24Smarter Balanced Summative Assessments for ELA

Which sentence uses a restrictive clause correctly to narrow meaning in a research claim?

  1. Students, who sleep fewer than six hours, report more absences.
  2. Students, who sleep fewer than six hours report more absences.
  3. Students who sleep fewer than six hours report more absences. Correct answer.
  4. Students who sleep fewer than six hours, report more absences.

Explanation

A restrictive clause identifies a subset of students and should not be set off by commas. Adding commas would imply all students sleep fewer than six hours, changing the claim.

Question 25Smarter Balanced Summative Assessments for ELA

A student must synthesize three Smarter Balanced sources on water conservation, two agreeing and one dissenting. Which synthesis best reflects the evidence?

  1. The weight of evidence supports conservation, though one source raises limitations worth addressing. Correct answer.
  2. The dissenting source should be omitted to keep the essay consistent.
  3. All sources agree that conservation works, so no limitations exist.
  4. Because one source disagrees, the topic cannot be resolved at all.

Explanation

Synthesis weighs the body of evidence while acknowledging credible dissent and limitations. Omitting disagreement or declaring the topic unresolvable misrepresents the sources.

Question 26Smarter Balanced Summative Assessments for ELA

A student is drafting a Smarter Balanced explanatory essay and wants to combine these two sentences into one that clearly shows cause and effect: 'The city added bike lanes. Traffic injuries fell sharply.' Which revision best expresses the causal relationship?

  1. The city added bike lanes, so traffic injuries fell sharply, however.
  2. The city added bike lanes, and traffic injuries fell sharply.
  3. The city added bike lanes; traffic injuries fell sharply.
  4. Because the city added bike lanes, traffic injuries fell sharply. Correct answer.

Explanation

A causal relationship is signaled by a subordinating conjunction such as 'because,' which makes one clause the reason for the other and removes any ambiguity about which event caused which. Coordination with 'and' or a semicolon only places the events side by side, leaving the logic unstated.

Question 27Smarter Balanced Summative Assessments for ELA

A Smarter Balanced performance task asks a student to introduce a quotation from a source about urban farming into an argument essay. Which sentence introduces the quotation most effectively by providing context before the quoted words?

  1. "Urban farms reduce food miles significantly," the report states.
  2. Urban farms reduce food miles significantly, according to a report.
  3. In a 2022 study of city agriculture, researcher Lena Ortiz reports that "urban farms reduce food miles significantly." Correct answer.
  4. The report states that "urban farms reduce food miles significantly."

Explanation

Effective integration names the source and supplies context, such as the author and the study setting, before the quoted material so readers understand who is speaking and why it matters. Options that drop the quotation into the sentence without attribution or context leave the evidence unsupported.

Question 28Smarter Balanced Summative Assessments for ELA

A student reading a Smarter Balanced informational source notices the author repeatedly uses the phrase 'concerned parents' when describing people who oppose a school policy. Which analysis best explains the rhetorical effect of this word choice?

  1. The phrase loads the description with a sympathetic emotion, subtly framing opponents as caring and reasonable. Correct answer.
  2. The phrase signals that the author is presenting a direct quotation from a named source.
  3. The phrase is a factual statistic that strengthens the author's use of quantitative evidence.
  4. The phrase is a neutral descriptor that simply identifies the people involved in the debate.

Explanation

Word choice can carry evaluative connotations; calling opponents 'concerned parents' invites sympathy and frames their position as motivated by care, which shapes how readers judge the debate. Recognizing this loaded language is central to analyzing how an author's diction influences tone and argument.

Question 29Smarter Balanced Summative Assessments for ELA

A student is revising a Smarter Balanced argument essay and finds this sentence: 'The district should fund arts programs, sports teams receive more money than they need.' Which revision best corrects the sentence while preserving its meaning?

  1. The district should fund arts programs, sports teams receive more money than they need.
  2. The district should fund arts programs, and sports teams receive more money than they need.
  3. The district should fund arts programs because sports teams receive more money than they need.
  4. The district should fund arts programs; sports teams receive more money than they need. Correct answer.

Explanation

The original joins two independent clauses with only a comma, creating a comma splice. A semicolon correctly separates the two complete clauses while preserving the contrast the writer intends, and it keeps the sentence as one concise unit.

Question 30Smarter Balanced Summative Assessments for Mathematics

A student graphs the linear function y = -2x + 5 on a coordinate plane. What is the slope of the graph?

  1. 2
  2. 5
  3. -5
  4. -2 Correct answer.

Explanation

In slope-intercept form y = mx + b, the coefficient m is the slope and b is the y-intercept. Here m = -2, so the line falls 2 units for every 1 unit it moves right. The value 5 is the y-intercept, not the slope.

Question 31Smarter Balanced Summative Assessments for Mathematics

A bag contains 4 red, 6 blue, and 10 green marbles. One marble is drawn at random. What is the probability that it is blue?

  1. 6/20
  2. 6/16
  3. 1/6
  4. 3/10 Correct answer.

Explanation

The total number of marbles is 4 + 6 + 10 = 20, and 6 of them are blue. The probability is 6/20, which simplifies to 3/10. Simplifying the fraction is required to match the reduced form.

Question 32Smarter Balanced Summative Assessments for Mathematics

Which expression is equivalent to (3x^2)(4x^5)?

  1. 7x^7
  2. 12x^7 Correct answer.
  3. 12x^10
  4. 12x^3

Explanation

When multiplying powers with the same base, multiply the coefficients and add the exponents: 3 times 4 is 12, and x^2 times x^5 is x^(2+5) = x^7. The result is 12x^7.

Question 33Smarter Balanced Summative Assessments for Mathematics

A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

  1. √21
  2. 15 Correct answer.
  3. 3
  4. 21

Explanation

The Pythagorean theorem gives hypotenuse squared equals 9 squared plus 12 squared, which is 81 + 144 = 225. The square root of 225 is 15, a 3-4-5 triangle scaled by 3.

Question 34Smarter Balanced Summative Assessments for Mathematics

Which value is the greatest common factor of 36 and 60?

  1. 6
  2. 12 Correct answer.
  3. 180
  4. 4

Explanation

Factor 36 = 2^2 · 3^2 and 60 = 2^2 · 3 · 5. The GCF takes the lowest power of each shared prime: 2^2 · 3 = 12.

Question 35Smarter Balanced Summative Assessments for Mathematics

The mean of five test scores is 78. Four of the scores are 70, 82, 75, and 80. What is the fifth score?

  1. 85
  2. 90
  3. 83 Correct answer.
  4. 78

Explanation

A mean of 78 across five scores means the total is 78 × 5 = 390. The four known scores sum to 307, so the fifth score is 390 − 307 = 83.

Question 36Smarter Balanced Summative Assessments for Mathematics

A function is defined as f(x) = 2x + 3. What is f(4)?

  1. 14
  2. 11 Correct answer.
  3. 7
  4. 8

Explanation

Substitute x = 4 into the rule: 2(4) + 3 = 8 + 3 = 11. Function notation means replace every x with the input value.

Question 37Smarter Balanced Summative Assessments for Mathematics

A square has a side length of 5 centimeters. What is the area of the square?

  1. 50 square centimeters
  2. 10 square centimeters
  3. 25 square centimeters Correct answer.
  4. 20 square centimeters

Explanation

The area of a square is side length squared, so 5 × 5 = 25 square centimeters. Perimeter would be 4 × 5 = 20 centimeters.

Question 38Smarter Balanced Summative Assessments for Mathematics

A store sells notebooks for $3 each and pens for $1.50 each. A student buys n notebooks and p pens. Which expression represents the total cost in dollars?

  1. 3n + 1.5np
  2. 4.5(n + p)
  3. 3p + 1.5n
  4. 3n + 1.5p Correct answer.

Explanation

Each notebook costs $3, so n notebooks cost 3n dollars, and p pens cost 1.5p dollars. The total is the sum 3n + 1.5p.

Question 39Smarter Balanced Summative Assessments for Mathematics

Solve the inequality 3x - 7 < 8 for x.

  1. x < 5 Correct answer.
  2. x > 5
  3. x < 1
  4. x < 15

Explanation

Add 7 to both sides to get 3x < 15, then divide by the positive 3 to get x < 5. Dividing by a positive number does not flip the inequality sign.

Question 40Smarter Balanced Summative Assessments for Mathematics

A line passes through the points (2, 3) and (6, 11). What is the slope of the line?

  1. 1/2
  2. 4
  3. 2 Correct answer.
  4. 8

Explanation

Slope equals the change in y divided by the change in x: (11 - 3)/(6 - 2) = 8/4 = 2. The line rises 2 units for every 1 unit it moves right.

Question 41Smarter Balanced Summative Assessments for Mathematics

A cylinder has a radius of 3 inches and a height of 10 inches. Using π ≈ 3.14, what is the volume of the cylinder?

  1. 188.4 cubic inches
  2. 282.6 cubic inches Correct answer.
  3. 94.2 cubic inches
  4. 30 cubic inches

Explanation

The volume of a cylinder is πr^2h. Computing 3.14 × 9 × 10 gives 282.6 cubic inches.

Question 42Smarter Balanced Summative Assessments for Mathematics

Which equation represents a line parallel to y = 4x - 1 that passes through the point (0, 3)?

  1. y = 4x + 3 Correct answer.
  2. y = (1/4)x + 3
  3. y = 4x - 3
  4. y = -4x + 3

Explanation

Parallel lines share the same slope, so the new line has slope 4. With y-intercept 3, the equation is y = 4x + 3.

Question 43Smarter Balanced Summative Assessments for Mathematics

A system of equations is given: x + y = 10 and x - y = 4. What is the value of x?

  1. 3
  2. 14
  3. 7 Correct answer.
  4. 6

Explanation

Adding the two equations eliminates y: 2x = 14, so x = 7. Substituting back gives y = 3, which satisfies both equations.

Question 44Smarter Balanced Summative Assessments for Mathematics

A quadratic function is f(x) = x^2 - 6x + 8. What are the zeros of the function?

  1. x = 2 and x = 4 Correct answer.
  2. x = 3 and x = 3
  3. x = -2 and x = -4
  4. x = 1 and x = 8

Explanation

Factor x^2 - 6x + 8 as (x - 2)(x - 4). Setting each factor to zero gives x = 2 and x = 4.

Question 45Smarter Balanced Summative Assessments for Mathematics

A data set has a median of 20 and a mean of 26. Which statement best explains the difference between the mean and median?

  1. The data set contains no outliers.
  2. The mean is pulled upward by unusually high values in the data set. Correct answer.
  3. The median is always greater than the mean in any data set.
  4. The mean and median must be equal for symmetric data.

Explanation

When the mean exceeds the median, the distribution is skewed to the right because high values pull the mean upward. The median resists the influence of extreme values.

Question 46Smarter Balanced Summative Assessments for Mathematics

A triangle has angles measuring 40 degrees and 65 degrees. What is the measure of the third angle?

  1. 105 degrees
  2. 65 degrees
  3. 75 degrees Correct answer.
  4. 85 degrees

Explanation

The angles of a triangle sum to 180 degrees. Subtracting 40 + 65 = 105 from 180 leaves 75 degrees.

Question 47Smarter Balanced Summative Assessments for Mathematics

Simplify the expression (2x^2 + 3x - 5) - (x^2 - 4x + 2).

  1. x^2 + 7x - 7 Correct answer.
  2. 3x^2 - x - 3
  3. x^2 + 7x + 7
  4. x^2 - x - 3

Explanation

Distribute the subtraction: 2x^2 + 3x - 5 - x^2 + 4x - 2. Combining like terms gives x^2 + 7x - 7.

Question 48Smarter Balanced Summative Assessments for Mathematics

A spinner has 5 equal sections numbered 1 through 5. What is the probability of spinning an even number or a number greater than 3?

  1. 2/5
  2. 4/5 Correct answer.
  3. 1/5
  4. 3/5

Explanation

Even numbers are 2 and 4; numbers greater than 3 are 4 and 5. The union is {2, 4, 5}, which has 3 outcomes, so the probability is 3/5. The overlap 4 is counted once.

Question 49Smarter Balanced Summative Assessments for Mathematics

A rectangle is dilated by a scale factor of 3. How does the area of the image compare to the area of the original rectangle?

  1. The area is 6 times the original area.
  2. The area is unchanged.
  3. The area is 9 times the original area. Correct answer.
  4. The area is 3 times the original area.

Explanation

Under a dilation with scale factor k, lengths multiply by k but areas multiply by k^2. With k = 3, the area becomes 9 times larger.

Question 50Smarter Balanced Summative Assessments for Mathematics

The value of a car is modeled by V(t) = 24000(0.85)^t, where t is years since purchase. What does the 0.85 represent?

  1. The car loses 85% of its value each year.
  2. The car gains 85% of its value each year.
  3. The car retains 85% of its value each year. Correct answer.
  4. The car's value is 85 dollars per year.

Explanation

In exponential decay of the form a(b)^t, the base b is the decay factor. A base of 0.85 means 85% of the value remains each year, a 15% annual decrease.