SAT® Question Examples
Reading & Writing
Exercise 1 — Main idea / central claim
Text:
Urban trees can cool neighborhoods through shade and transpiration, reducing energy use and heat-related illness. But in drought-prone regions, planting water-hungry species can strain supplies and even raise local temperatures when trees die off. Effective urban forestry, therefore, depends less on planting as many trees as possible and more on selecting species suited to local conditions.
Question: Which choice best expresses the central idea of the passage?
A) Trees are the most cost-effective solution to urban heat.
B) Tree planting helps only when species are matched to local conditions.
C) Drought makes urban tree programs unworkable.
D) Transpiration is more important than shade in cooling cities.
Exercise 1 — Main idea / central claim
Explanation:
B is correct because the passage explicitly concludes that urban forestry is effective when species are chosen for local conditions, not merely planted in large numbers.
A is incorrect because the passage does not make a cost-effectiveness claim or compare trees to other solutions.
C is incorrect because the passage does not say tree programs are impossible in drought; it recommends appropriate species selection.
D is incorrect because it elevates one mechanism (transpiration) over another; the passage's main point is species selection, not a mechanism comparison.
Exercise 2 — Vocabulary in context
Sentence:
Because the conference aimed to foster temperate discussion on a polarizing topic, the moderator set clear rules for turn-taking and evidence.
Question: As used in the sentence, temperate most nearly means
A) seasonal
B) moderate
C) warm
D) friendly
Exercise 2 — Vocabulary in context
Explanation:
B is correct because “temperate” here modifies discussion, meaning moderated or restrained, which fits the context of rules that regulate tone and evidence.
A is incorrect: “seasonal” is a climatic sense that doesn't apply to a discussion.
C is incorrect: “warm” refers to temperature or affectionate tone, which is not as precise as “moderate.”
D is incorrect: “friendly” suggests amiable, but the sentence stresses regulated moderation, not friendliness.
Exercise 3 — Sentence correction (comma splice and clarity)
Original:
Archaeologists recently analyzed residues on pottery from a coastal site. The analysis revealed traces of ancient olive oil, it suggests trade networks were more extensive than previously thought.
Question: Which choice best replaces the underlined portion to create the most logically and grammatically correct sentence?
A) it suggests
B) ; it suggests
C), which suggests
D), suggesting that
Exercise 3 — Sentence correction (comma splice and clarity)
Explanation:
D is correct because “, suggesting that …” creates a participial phrase that links the result to the inference smoothly and eliminates the comma splice.
A is incorrect because it leaves a comma splice (two independent clauses joined by a comma).
B is incorrect because although the semicolon fixes the splice, “it” is ambiguous (olive oil or the analysis?).
C is incorrect because “which” would most naturally refer to the closest noun (olive oil), not the analysis, creating a referential ambiguity.
Exercise 4 — Logical transition
Sentence with blank:
Economists expected a steep decline in consumer spending following the fuel-price spike. _____, retail sales rose by 2.4 percent in the following quarter.
Question: Which choice most logically completes the sentence?
A) Nevertheless
B) Consequently
C) Similarly
D) Meanwhile
Explanation:
A is correct because “Nevertheless” signals a contrast between the expected decline and the current increase.
B is incorrect because “Consequently” implies causation rather than contradiction.
C is incorrect because “Similarly” indicates similarity, not contrast.
D is incorrect because “Meanwhile” indicates simultaneity and does not capture the logical opposition.
Exercise 5 — Dangling modifier / clarity and voice
Original:
After reviewing the dataset, the outliers were removed by the research team.
Question: Which choice best improves the sentence to eliminate ambiguity and strengthen the style?
A) the outliers were removed by the research team
B) the research team removed the outliers
C) the outliers were removed
D) the research team, after reviewing the dataset, the outliers were removed
Explanation:
B is correct because it aligns the introductory modifier (“After reviewing the dataset”) with the actual agent (“the research team”) and uses clear active voice.
A is incorrect because in passive voice the grammatical subject (“the outliers”) illogically appears to have done the reviewing (a dangling modifier).
C is incorrect because it omits the agent who acted, reducing clarity and leaving the same modifier problem.
D is incorrect because it is ungrammatical (sentence structure breaks) and still awkwardly places the modifier.
Math
Exercise 1 — Discriminant / parameter (SPR)
The quadratic x² − (k + 2)x + (k + 5) = 0 has exactly one real solution. What is the positive value of k?
Explanation:
For one real solution, the discriminant is 0: (k + 2)² − 4(k + 5) = k² − 16 = 0 ⇒ |k| = 4 ⇒ k = 4 (positive).
Exercise 2 — Rational function & asymptotes (multiple choice)
Let f(x) = (a·x + b) ÷ (x − 3). The graph has a vertical asymptote x = 3 and a horizontal asymptote y = 4. If f(5) = 3, what is a + b?
A) −14
B) −10
C) −6
D) 2
Explanation:
Divide: (a·x + b) ÷ (x − 3) = a + (3a + b) ÷ (x − 3).
Horizontal asymptote ⇒ a = 4.
Then f(5) = 4 + (12 + b) ÷ 2 = 3 ⇒ (12 + b) ÷ 2 = −1 ⇒ b = −14.
So a + b = 4 + (−14) = −10.
Exercise 3 — Exponential growth / least n (multiple choice)
A culture starts with 500 cells and grows by 20% each period. After n periods: N = 500·(1.2)ⁿ. What is the least integer n such that N ≥ 2000?
A) 6
B) 7
C) 8
D) 9
Explanation:
Need (1.2)ⁿ ≥ 4.
Compute: 1.2⁵ ≈ 2.488, 1.2⁶ ≈ 2.986, 1.2⁷ ≈ 3.583, 1.2⁸ ≈ 4.299 ≥ 4 ⇒ n = 8.
Exercise 4 — Tangent line to a circle (SPR)
The circle (x − 4)² + (y + 1)² = 25. A line through (1, 3) is tangent to the circle. Find the slope m of the line (give a reduced fraction).
Explanation:
Line: y = m·x + (3 − m).
Standard form: m x − y + (3 − m) = 0.
Distance from center (4, −1) to the line equals radius 5:
|3m + 4| ÷ √(m² + 1) = 5 ⇒ (3m + 4)² = 25(m² + 1) ⇒ 16m² − 24m + 9 = 0 ⇒ (4m − 3)² = 0 ⇒ m = 3/4.
Exercise 5 — Absolute value equation / sum of roots (SPR)
Solve |2x − 3| + |x − 5| = 10. What is the sum of all real solutions? (Express as a reduced fraction.)
Explanation:
Break at x = 1.5 and x = 5.
• x ≥ 5: (2x − 3) + (x − 5) = 10 ⇒ 3x − 8 = 10 ⇒ x = 6 (valid).
• 1.5 ≤ x < 5: (2x − 3) + (5 − x) = 10 ⇒ x + 2 = 10 ⇒ x = 8 (not in interval).
• x < 1.5: (3 − 2x) + (5 − x) = 10 ⇒ 8 − 3x = 10 ⇒ x = −2/3 (valid).
Sum = 6 + (−2/3) = 16/3.
