x = 5. Subtract 7 from both sides to get 3x = 15, then divide by 3.
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Practice questions
36 free SAT and ACT practice questions, with full explanations
Real questions across every major section. Every one shows the reasoning, not just the answer.
Jump to a section: SAT Reading & Writing · SAT Math · ACT English · ACT Math · ACT Reading · ACT Science. Every question below includes the reasoning behind the answer, the same explanation-first format used throughout Ember's full question bank.
SAT Reading and Writing
1 · Words in Context
The town council's decision to renovate the old mill was met with ______ support, as nearly every resident who attended the meeting voiced approval. Which word best fits the blank?
A reluctant
B overwhelming
C minimal
D divided
Reasoning
"Nearly every resident" voiced approval, which signals broad, strong support rather than reluctance, scarcity, or a split opinion.
2 · Standard English Conventions
"Marine biologists studying coral bleaching have found that reefs closer to shipping lanes recover more slowly, however this pattern does not hold in every region they've studied."
Which revision best fixes the punctuation error?
A lanes recover more slowly, however, this pattern
B lanes recover more slowly; however, this pattern
C lanes recover more slowly however this pattern
D lanes recover more slowly. however, this pattern
Reasoning
Two independent clauses joined by "however" need a semicolon before it and a comma after it. A comma alone creates a run-on.
3 · Expression of Ideas
A student is writing an essay about urban beekeeping and wants to add a sentence that supports the claim that city bees can outperform rural bees. Which choice best accomplishes this?
A Beekeeping requires specialized equipment and training.
B Urban gardens often bloom in overlapping waves throughout the year, giving city bees a longer, more varied food supply than rural bees dependent on a single crop's bloom.
C Many cities have passed ordinances regulating where hives can be placed.
D Rural beekeepers often manage larger numbers of hives than urban beekeepers do.
Reasoning
It directly supports the claim with a specific reason city bees would outperform rural ones. The others are true statements about beekeeping but don't support this particular claim.
4 · Expression of Ideas
Which choice completes the text with the most logical transition? "The bridge was closed for repairs for six months. ______, traffic on the surrounding streets increased noticeably."
A Similarly
B As a result
C In contrast
D For example
Reasoning
The second sentence describes a consequence of the first, so a cause-and-effect transition is needed.
5 · Words in Context
In context, which choice provides the most precise word? "The committee's ______ approach to budgeting left almost no room for unexpected expenses."
A careful
B rigid
C generous
D casual
Reasoning
"Rigid" specifically explains why there was no room for unexpected costs, more precisely than "careful," which could still allow flexibility.
6 · Standard English Conventions
Identify the error, if any: "Each of the students were required to submit their project by Friday."
A Each / were
B required / submit
C their / project
D No error
Reasoning
"Each" is singular and needs a singular verb: "Each of the students was required."
7 · Expression of Ideas
Which choice most effectively combines the two sentences? "The museum added a new wing in 2019. The wing houses a collection of modern sculpture."
A The museum added a new wing in 2019, and the wing houses a collection of modern sculpture.
B The museum's new wing, added in 2019, houses a collection of modern sculpture.
C In 2019 the museum added a new wing, it houses a collection of modern sculpture.
D The museum added a new wing, which was in 2019, that houses modern sculpture.
Reasoning
It's the most concise, grammatically clean combination without a comma splice or awkward phrasing.
8 · Information and Ideas
Based on the passage's argument that community gardens increase neighborhood social ties, which finding would most strengthen the author's claim?
A A survey showing gardeners in a study reported significantly more contact with neighbors than non-gardeners in the same area.
B A survey showing most gardeners grow vegetables rather than flowers.
C A report on the average size of community garden plots.
D A history of when the first community gardens were founded.
Reasoning
It directly measures the claimed outcome, increased social ties, with comparative data.
SAT Math
9 · Algebra
If 3x + 7 = 22, what is the value of x?
Show answer
10 · Algebra
A line passes through the points (2, 5) and (6, 13). What is the slope of the line?
Show answer
2. Slope equals the change in y divided by the change in x: (13 minus 5) divided by (6 minus 2) equals 8 divided by 4, which is 2.
11 · Algebra
A rectangular garden has a length that is 3 feet more than twice its width. If the width is w, which expression represents the perimeter of the garden?
A 2w + 3
B 4w + 3
C 6w + 6
D 6w + 3
Reasoning
Length equals 2w + 3. Perimeter equals 2(length) + 2(width), which is 2(2w + 3) + 2w, giving 4w + 6 + 2w, which simplifies to 6w + 6.
12 · Advanced Math
The function f(x) = 2x² − 8 has how many real zeros?
Show answer
2. Setting 2x² − 8 = 0 gives x² = 4, so x = 2 or x = −2, two real solutions.
13 · Problem-Solving and Data Analysis
A store marks up an item's wholesale cost by 40% to set the retail price. If the retail price is $84, what was the wholesale cost?
Show answer
$60. Retail equals wholesale times 1.4, so wholesale equals 84 divided by 1.4, which is 60.
14 · Geometry and Trigonometry
In a right triangle, one leg measures 9 and the hypotenuse measures 15. What is the length of the other leg?
Show answer
12. Using the Pythagorean theorem, 9² + b² = 15², so 81 + b² = 225, b² = 144, and b = 12. This is a scaled-up 3-4-5 triangle.
15 · Problem-Solving and Data Analysis
If the average (arithmetic mean) of five numbers is 18, and four of the numbers are 12, 15, 20, and 22, what is the fifth number?
Show answer
21. The sum of all five numbers is 18 times 5, which is 90. The sum of the four known numbers is 69. The fifth number is 90 minus 69, which is 21.
16 · Algebra
A system of equations is given: y = 3x − 4 and y = −x + 8. What is the x-coordinate of the solution?
Show answer
3. Set the two expressions for y equal: 3x − 4 = −x + 8. Adding x to both sides gives 4x − 4 = 8, then 4x = 12, so x = 3.
ACT English
17 · Sentence Structure
"The committee, after reviewing dozens of applications carefully considered only the top five candidates for interviews." Which punctuation correctly fixes this sentence?
A No change
B applications, carefully considered
C applications carefully, considered
D applications; carefully considered
Reasoning
A comma is needed after the introductory phrase "after reviewing dozens of applications" before the main clause begins.
18 · Knowledge of Language
Which choice is most concise while keeping the same meaning? "Due to the fact that the weather was extremely cold, the game was postponed."
A No change
B Because the weather was extremely cold,
C In light of the fact that it was cold weather,
D On account of the weather being cold in nature,
Reasoning
It says the same thing with far fewer words, matching the ACT's general preference for concise phrasing.
19 · Conventions of Standard English
"Neither the coach nor the players was aware of the schedule change." Which is the correct verb form?
A was
B were
C is
D are
Reasoning
With "neither/nor," the verb agrees with the closer subject, which is "players," a plural noun, so "were" is correct.
20 · Knowledge of Language
Which choice best maintains the passage's formal tone? "The research findings were, honestly, kind of a big deal for the field."
A No change
B pretty significant
C considered highly significant
D a huge deal, no joke
Reasoning
It conveys the same idea in language consistent with an academic or formal register, unlike the casual phrasing in the other options.
21 · Conventions of Standard English
"Its important to double check your work before submitting the exam." What is the correct fix?
A No change
B It's important
C Its' important
D Its important,
Reasoning
"It's" is the contraction for "it is," which is needed here. "Its" is the possessive form and doesn't fit this sentence.
22 · Production of Writing
Which sentence, if inserted here, would best introduce a paragraph about the economic impact of a new highway?
A The highway was completed after several delays.
B Local businesses reported a 20 percent increase in customer traffic within the first year after the highway opened.
C The highway spans twelve miles between two counties.
D Construction crews worked in three shifts to meet the deadline.
Reasoning
It directly introduces the topic of economic impact with a concrete figure, setting up the paragraph's focus.
ACT Math
23 · Pre-Algebra
What is the value of 5² − 3(4 − 1)?
Show answer
16. Following order of operations: 4 − 1 = 3, then 3 times 3 = 9, then 25 − 9 = 16.
24 · Pre-Algebra
A recipe calls for 2 cups of flour to make 24 cookies. How many cups of flour are needed to make 60 cookies, assuming the ratio stays constant?
Show answer
5 cups. Set up a proportion: 2/24 = x/60. Cross-multiplying gives 24x = 120, so x = 5.
25 · Plane Geometry
What is the area of a circle with a diameter of 10?
Show answer
25π. Radius is half the diameter, so r = 5. Area equals πr², which is 25π.
26 · Intermediate Algebra
If f(x) = x² + 3x − 4, what is f(2)?
Show answer
6. Plug in 2: (2)² + 3(2) − 4 equals 4 + 6 − 4, which is 6.
27 · Pre-Algebra
A jar contains only red and blue marbles in a ratio of 3 to 5. If there are 40 marbles total, how many are red?
Show answer
15. The ratio parts total 8 (3 + 5). Each part represents 40 divided by 8, which is 5 marbles. Red marbles are 3 parts, so 3 times 5 equals 15.
28 · Intermediate Algebra
What is the solution set for the inequality 2x − 5 > 9?
Show answer
x > 7. Add 5 to both sides to get 2x > 14, then divide by 2.
ACT Reading
An original passage, with four questions built around it.
Passage · Reading: Social Science
For most of the twentieth century, lighthouse keepers lived isolated lives, tending the light and logging weather conditions in near-total solitude for weeks at a time. Automation changed that role permanently. By the 1990s, most lighthouses in the United States operated without a resident keeper, their lamps and foghorns controlled remotely. Some historians argue this shift, while improving efficiency and reducing risk to human life, quietly erased a distinct way of life that had shaped coastal communities for generations. Former keepers describe the job less as isolating and more as a form of stewardship, a daily relationship with a specific stretch of coastline that no remote sensor can replicate.
29
According to the passage, what changed lighthouse keeping most significantly in the twentieth century?
A A decline in shipping traffic
B The automation of lighthouse operations
C New laws restricting who could become a keeper
D A shortage of qualified applicants
Reasoning
The passage states automation changed the role permanently and that most lighthouses stopped having resident keepers by the 1990s.
30
The phrase "a form of stewardship" in the passage most likely suggests that former keepers viewed their work as:
A A tedious obligation they were eager to leave behind
B A caretaking relationship with the coastline rather than just a job
C A dangerous task best left to machines
D A temporary position before better-paying work
Reasoning
The passage contrasts "stewardship" with isolation, describing it as "a daily relationship with a specific stretch of coastline," which frames the work as caretaking rather than a burden.
31
Which statement best captures the passage's overall tone toward automation?
A Fully celebratory, with no reservations
B Acknowledging its benefits while noting something meaningful was lost
C Strongly opposed to any technological change
D Neutral and purely factual, with no perspective offered
Reasoning
The passage explicitly credits automation with improving efficiency and safety, but also says it "quietly erased a distinct way of life," showing a mixed, reflective tone.
32
Based on the passage, a resident keeper's daily responsibilities most likely included:
A Repairing ships damaged at sea
B Logging weather conditions and tending the light
C Training new sailors in navigation
D Managing shipping schedules for nearby ports
Reasoning
The passage directly states keepers spent their time "tending the light and logging weather conditions."
ACT Science
A data set, with four questions built around it.
Setup
A student measured how quickly a sugar cube dissolved in water at four different temperatures. Each trial used the same size cube and the same amount of water, stirred at the same rate.
| Water temperature (°C) | Time to fully dissolve (seconds) |
|---|---|
| 10 | 210 |
| 25 | 140 |
| 40 | 95 |
| 55 | 60 |
33
Based on the data, what is the general relationship between water temperature and dissolving time?
A As temperature increases, dissolving time increases
B As temperature increases, dissolving time decreases
C Dissolving time stays constant regardless of temperature
D There is no clear pattern in the data
Reasoning
Each increase in temperature corresponds to a shorter dissolving time across all four trials.
34
If the trend in the data continued, which of the following is the most reasonable estimate for the dissolving time at 70°C?
A 90 seconds
B 60 seconds
C 40 seconds
D 210 seconds
Reasoning
The gap between each temperature step is shrinking but continues to decrease (210 to 140 to 95 to 60), so a further decrease to somewhere around 35 to 45 seconds is the most reasonable extrapolation among the choices given.
35
Which variable in this experiment was deliberately held constant across all trials?
A Water temperature
B Time to dissolve
C Amount of water and cube size
D Stirring speed only
Reasoning
The setup states the same size cube and same amount of water were used in every trial, along with the same stirring rate, but temperature was the variable being changed.
36
A second student proposes that stirring speed, not temperature, was the main factor in how fast the sugar dissolved. Does the data support this claim?
A Yes, because stirring speed was never recorded
B No, because stirring speed was held constant across all trials, so it cannot explain the differences observed
C Yes, because faster stirring always dissolves sugar faster
D No, because temperature was not actually measured accurately
Reasoning
Since stirring speed was the same in every trial, it cannot account for the differences in dissolving time between trials. Only the variable that changed, temperature, can explain the pattern.
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