Free The Digital SAT Mastery: Preparation & Practice Study Resources

To answer a point of agreement question, look for an idea or fact that is supported by both texts. Text 1 states that the suburb's population "is currently $12,000." Text 2 states that the demographer "agrees with the city planner that the current population is $12,000." Therefore, both authors agree on this starting value. Choice A is only supported by Text 1. Choices B and D are only supported by Text 2. Answer: C

The input variable $t$ represents the number of years after the year 2010. Therefore, $t = 8$ corresponds to the year $2010 + 8 = 2018$, and$t = 5$corresponds to the year $2010 + 5 = 2015$.

The output $P(t)$ represents the population of the city at year $t$. Thus, $P(8)$ is the population in 2018, and $P(5)$ is the population in 2015.

The expression $P(8) - P(5)$ represents the difference between the population in 2018 and the population in 2015. The equation P(8) - P(5) = 12,000 indicates that the population in 2018 minus the population in 2015 equals $12,000. This means the population was $12,000 greater in 2018 than it was in 2015.

• Option A incorrectly assumes the expression represents only the population at $t = 8$.
• Option B incorrectly interprets the total difference as an annual rate of change.
• Option D incorrectly subtracts the inputs ($8 - 5 = 3$) and evaluates the change from the initial year (2010 to 2013).

Answer: C

To simplify the radical expression $\sqrt[3]{16x^7y^{12}}$, break down the radicand into perfect cubes and remaining factors:

1. Constant 16: The largest perfect cube factor of 16 is 8 (since $2^3 = 8$). Rewrite 16 as $$8 \cdot 2$. The cube root of 8 is 2, so \sqrt[3]{16} = 2\sqrt[3]{2}$.
2. Variable $x^7$: Divide the exponent 7 by the root index 3. The quotient is 2 with a remainder of 1. This means $x^7 = (x^2)$^3 \cdot x$. Taking the cube root gives$x^2\sqrt$[3]{x}$.
3. Variable $y^{12}$: Divide the exponent 12 by 3. The quotient is 4 with a remainder of 0. This means $y^{12} = (y^4)^3$. Taking the cube root gives $y^4$.

Combine the terms outside the radical (2, $x^2$, $y^4$) and the terms inside the radical (2, $x$): $2 \cdot x^2 \cdot y^4 \cdot \sqrt[3]{2 \cdot x} = 2x^2y^4\sqrt[3]{2x}$.

Answer: A

To find the effect on the mean, calculate the change in the total sum of the house prices. The corrected price of the most expensive house is $2,100,000 dollars instead of $600,000 dollars. This is an increase of $2,100,000 - 600,000 = 1,500,000$ dollars in the total sum.

Because there are 15 houses, this increase in the total sum is distributed evenly across all data points when calculating the new mean. The mean increases by $$\frac{1,500,000}{15} = 100$,000$ dollars.

The median is the middle value of an ordered list. For 15 houses, the median is the 8th house price. Because the highest price simply increased to an even higher value, its position in the ordered list does not change (it remains the 15th value). Therefore, the middle value (8th value) is completely unaffected, and the median remains unchanged. Answer: A

The sentence presents a simple list of three actions farmers should take: (1) "test their soil's pH levels", (2) "rotate their crops", and (3) "use natural fertilizers". According to Standard English conventions, items in a list of three or more must be separated by commas, including the comma immediately preceding the coordinating conjunction "and" (known as the Oxford comma).

Option A correctly applies the comma before "and". Option B is missing the required Oxford comma. Option C includes an unnecessary comma after the conjunction. Option D incorrectly uses a semicolon instead of a comma for a simple list.

To find the equivalent expression, we can use the Select Strategic Numbers strategy by picking an easy-to-manage number for $x$ and plugging it in.

Why we avoid $x = 0$ or $x = 1$:

• If $x = 0$, every answer choice evaluates to 0.
• If $x = 1$, the original expression equals $3(1)(7) - 4(0) = 21$. Both Option B ($2(1)^2 + 19(1) = 21$) and Option C ($10(1)^2 + 11(1) = 21$) evaluate to 21, meaning we would have to test another number to break the tie.

Using a strategic number like $x = 2$: Original expression: $3(2)(2(2) + 5) - 4(2^2 - 2)$ = 6(4 + 5) - 4(4 - 2) $= 6(9) - 4(2)$ $= 54 - 8 = 46$

Now, substitute $x = 2$ into the answer choices to find the matching value of 46:

• A: $2(2)^2 + 11(2) = 8 + 22 = 30$
• B: $2(2)^2 + 19(2) = 8 + 38 = 46$
• C: $10(2)^2 + 11(2) = 40 + 22 = 62$
• D: $10(2)^2 + 19(2) = 40 + 38 = 78$

Only Choice B matches our target value!

Algebraic method: Distribute the terms: $3x(2x) + 3x(5) = 6x^2 + 15x$ and $-4(x^2) - 4(-x) = -4x^2 + 4x$. Combine like terms: $(6x^2 - 4x^2) + (15x + 4x) = 2x^2 + 19x$. Answer: B

To isolate $m$, first subtract the other terms on the right side of the equation from $C$.

$C = 35d + 0.25m + f$

Subtract $35d$ and $f$ from both sides:

$C - 35d - f = 0.25m$

To solve for $m$, divide both sides by $0.25. Since dividing by $0.25 is the same as multiplying by 4 (because $0.$25 = \frac{1}{4}$$), we multiply the entire left side by 4:

$m = 4(C - 35d - f)$

Answer: A

Since $\overline{DE} \parallel \overline{AC}$, $\angle BDE \cong \angle BAC$ and $\angle BED \cong \angle BCA$ because they are corresponding angles. This makes $\triangle BDE$ similar to $\triangle BAC$.

Because the triangles are similar, the lengths of their corresponding sides are proportional: $\frac{BD}{AB} = \frac{BE}{BC}$

We are given $BD = 6$ and $AD = 9$, so the total length of AB is $6 + 9 = 15$. We also know$BE = 8$.

Substitute the known values into the proportion: $\frac{6}{15} = \frac{8}{BC}$ $6 \cdot BC = 15 \cdot 8$ $6 \cdot BC = 120$ $BC = 20$

The question asks for the length of $\overline{CE}$. Since $BC = BE + CE$, we can solve for CE: $20 = 8 + CE$ $CE = 12$

(Alternatively, using the Triangle Proportionality Theorem: A line parallel to one side of a triangle divides the other two sides proportionally. $$\frac{BD}{AD} = \frac{BE}{CE} \rightarrow \frac{6}{9} = \frac{8}{CE} \rightarrow 6 \cdot$CE$= 72 \rightarrow$CE = 12$.)

Answer: B

The passage explicitly states that Elias views the skyscrapers as 'imposing cage bars that blocked out the sky' rather than 'monuments of human achievement.' Choice A correctly captures this feeling of being trapped and disconnected from nature. Choice B is an 'opposite trap'—it uses positive words like 'inspiring' and 'progress' to describe the skyscrapers, which is the exact opposite of Elias's negative viewpoint and directly contradicts his belief that they are not monuments of achievement. Choices C and D also introduce positive or comforting attributes that contradict the text.

To find the machine's painting rate in square feet per minute, we must convert the given rate using dimensional analysis.

Step 1: Convert square meters to square feet Because the rate involves area, we must square the linear conversion factor. Given $1 meter = 3.28 feet$, squaring both sides gives:$(1 meter)^2 = (3.28 feet)^2$$1 \text{ square meter} \approx 10.7584 \text{ square feet}$

Multiply the original rate by this area conversion factor: $2.$5 \frac{m^2}{hour} \times \frac{10.7584 ft^2}{1 m^2} = 26.896 \frac{ft^2}{hour}$$

Step 2: Convert hours to minutes There are 60 minutes in 1 hour. To cancel out hours in the denominator, multiply by the ratio $\frac{1 hour}{60 minutes}$: $26.896 \frac{\text{ft}^2}{\text{hour}} \times \frac{1 \text{ hour}}{60 \text{ minutes}} = \frac{26.896}{60} \frac{\text{ft}^2}{\text{minute}} \approx 0.44827 \frac{\text{ft}^2}{\text{minute}}$

Rounding to the nearest hundredth gives $0.45 square feet per minute.

Common Distractor Analysis:

• Option A comes from forgetting to square the conversion factor ($2.$5 \times 3.28 / 60 \approx 0.14$$).
• Option C is the rate in square feet per hour ($26.896 \approx 26.90$).
• Option D comes from mistakenly multiplying by 60 instead of dividing when converting hours to minutes ($26.$896 \times 60 \approx 1613.76$$).

Answer: B

To support the claim, we must identify the core argument made in the passage. Patel's team claims two things: first, that a high density of "third places" fosters greater civic engagement (defined in the text as volunteering or attending council meetings); and second, that this correlation occurs regardless of a neighborhood's socioeconomic status. Option A directly supports both parts of this claim by demonstrating that as third places increased across "various income brackets," there was a corresponding rise in a form of civic engagement (attending community meetings). Option B addresses income but fails to mention civic engagement. Option C focuses on personal relationships rather than civic participation. Option D addresses economic growth rather than civic engagement. Answer: A

To answer this question, we must identify the true subject of the sentence and ensure the verb agrees with it in number. Mentally cross out the distracting prepositional phrase ("of specialized bacteria") and the non-essential describing clause (", thriving within the fibrous setae on the crabs' claws,"). This reveals the true subject: the collective noun "colony," which is singular. Therefore, the sentence requires a singular verb. Choice B ("converts") is the only singular main verb. Choices A ("convert") and C ("have converted") are plural and incorrectly pair with the trap nouns "bacteria" or "claws." Choice D ("converting") is an -ing word, which cannot act as a main verb on its own and would create a sentence fragment. Answer: B

To isolate $m$, first subtract the other terms on the right side of the equation from $C$.

$C = 35d + 0.25m + f$

Subtract $35d$ and $f$ from both sides:

$C - 35d - f = 0.25m$

To solve for $m$, divide both sides by $0.25. Since dividing by $0.25 is the same as multiplying by 4 (because $0.$25 = \frac{1}{4}$$), we multiply the entire left side by 4:

$m = 4(C - 35d - f)$

Answer: A

The sentence presents a list of three key speakers. Because the individual items in the list contain internal commas (e.g., "Dr. Elena Rostova, a marine biologist..."), semicolons must be used instead of commas to separate the items to prevent confusion. This is known as a complex list. Therefore, a semicolon is required after "conservation" to separate the first speaker from the second speaker. Additionally, a comma is needed after "Marcus Thorne" to properly introduce the appositive phrase ("an urban planner...") that describes him. Answer: A

An independent clause can stand on its own as a complete sentence. A subordinating word (such as "although," "because," "since," or "when") takes an independent clause and turns it into a dependent clause. For example, "Although the architects finalized the blueprints for the new library" cannot stand on its own as a complete sentence; it now depends on another independent clause to finish the thought. Options B, C, and D are transition words (conjunctive adverbs), not subordinating words, so adding them does not make the clause dependent. Answer: A