Free digital SAT practice questions, by topic, with explanations

Answer: C ($7$)

A: Five hours would cost $6+3(5)=21$ dollars, not 27.

B: Six hours would cost $6+3(6)=24$ dollars, not 27.

C: The hours cost $27-6=21$ dollars, and $21\div 3=7$ hours.

D: Divides the whole $27 by $3 and forgets to take off the $6 fee first.

Answer: A ($12$)

A: Twelve cookies bring in $2(12)=24$ dollars, leaving $36$, and $36\div 3=12$ muffins.

B: Would bring in $3(8)+24=48$ dollars, not 60.

C: Would bring in $3(10)+24=54$ dollars, not 60.

D: Subtracts 12 from 60 and divides by 3, treating the 12 as dollars instead of cookies.

Answer: B (The number of gallons that drain from the tank each minute)

A: That is $480$, the value of $W(0)$.

B: Each minute $t$ goes up by 1 and $W$ goes down by 15, so 15 gallons drain per minute.

C: The tank empties when $480-15t=0$, at $t=32$ minutes.

D: After 1 minute, $480-15=465$ gallons are left.

Answer: D ($4$)

A: The lines would have different slopes ($-\tfrac{2}{3}$ and $-\tfrac{1}{3}$) and cross once.

B: The lines would have different slopes ($-\tfrac{2}{3}$ and $-\tfrac{1}{2}$) and cross once.

C: The slopes would be $-\tfrac{2}{3}$ and $-1$: different, so one solution.

D: Doubling the first equation gives $4x+6y=36$. With $k=4$ the second is $4x+6y=20$: same slope, different line, so the lines are parallel and never meet.

Answer: B ($9$)

A: Squares 4 as 8: $8-12+5=1$.

B: $16-12+5=9$.

C: Drops the $-3x$ term: $16+5=21$.

D: Adds $3x$ instead of subtracting it: $16+12+5=33$.

Answer: C ($(3,5)$)

A: On the parabola ($1-4=-3$) but not the line: $2(1)-1=1$.

B: On the parabola ($4-4=0$) but not the line: $2(2)-1=3$.

C: $3^2-4=5$ and $2(3)-1=5$, so it satisfies both equations.

D: On neither: at $x=-1$ both equations give $y=-3$, not 1.

Answer: A ($P(t)=12{,}000(1.03)^t$)

A: Growth of 3% a year multiplies the population by $1.03$ each year.

B: Multiplying by $0.03$ each year would shrink the population to 3% of itself.

C: Multiplying by $1.3$ is 30% growth a year, not 3%.

D: Adds $0.03$ of a person a year: linear and far too small.

Answer: C ($-2$)

A: That is the minimum value of $f$, reached at $x=-2$: $(-4)(4)=-16$.

B: A zero of $f$, where the graph crosses the $x$-axis.

C: The vertex of a parabola lies halfway between its zeros, $2$ and $-6$: $\tfrac{2+(-6)}{2}=-2$.

D: The other zero of $f$.

Answer: A ($120$)

A: That is $\tfrac{18}{45}=0.4$ pages a second, and 5 minutes is 300 seconds: $0.4\times 300=120$.

B: Five times 18: treats 45 seconds as one minute.

C: Six times 18, as if 5 minutes held six 45-second blocks; it holds $\tfrac{300}{45}=6\tfrac{2}{3}$.

D: Uses the wrong rate, $0.5$ pages a second.

Answer: B ($66)

A: Takes $18 off rather than working out the two steps.

B: 25% off $80 is $60, and 10% tax on $60 is $6, so the price is $66.

C: Combines the two as a single 15% discount: $80\times 0.85=68$.

D: Applies only a 10% discount: $80\times 0.90=72$.

Answer: B (The mean increases and the median stays the same.)

A: The median is the middle value, 7, and stays 7.

B: The total goes from 40 to 50, so the mean goes from 8 to 10. The middle value is still 7.

C: It is the other way round: only the mean changes.

D: The total rises by 10, so the mean must change.

Answer: C ($\dfrac{2}{5}$)

A: The probability of blue only.

B: The probability of red only.

C: 10 of the 25 marbles are not green: $\tfrac{10}{25}=\tfrac{2}{5}$.

D: The probability that it is green, $\tfrac{15}{25}$.

Answer: B ($120$)

A: The surface area: $2(40+24+15)=158$ square centimetres.

B: $8\times 5\times 3=120$ cubic centimetres.

C: The area of the base only, $8\times 5$.

D: Adds the three dimensions instead of multiplying them.

Answer: D ($90^\circ$)

A: That is angle $R$.

B: Splits the remaining $135^\circ$ in half instead of in the ratio $2:1$.

C: The sum of angles $Q$ and $R$, not angle $Q$ alone.

D: Angles $Q$ and $R$ share $180^\circ-45^\circ=135^\circ$. With $Q=2R$, $3R=135^\circ$, so $R=45^\circ$ and $Q=90^\circ$.

Answer: A ($\dfrac{5}{12}$)

A: With opposite side 5 and hypotenuse 13, the adjacent side is 12 ($5^2+12^2=13^2$), so $\tan A=\tfrac{5}{12}$.

B: That is $\cos A$.

C: That is $\tan B$, for the other acute angle.

D: Hypotenuse over opposite: the reciprocal of $\sin A$.

Answer: B ($6$)

A: Reads the radius from the right-hand side without completing the square.

B: Completing the square gives $(x-3)^2+(y+4)^2=11+9+16=36$, so the radius is $\sqrt{36}=6$.

C: Takes the constant as the radius.

D: That is the radius squared.

Answer: D (Ecologists have found that mussels hold large amounts of microfibre from river water.)

The passage defines microfibres, names the research question, and reports the finding, which is the tonnage the mussels retain. D states it. C stops at the definition. A shifts the subject to bed building, and B says the effect is still an open question, when the passage reports a result.

Answer: A (The model with the broad tail completed a sharp turn in significantly less time than the model with the narrow tail.)

The hypothesis concerns pursuing prey that changes direction abruptly, so the relevant measure is how quickly the model can turn. A reports it. B measures displacement, which follows from the tail's size without showing any advantage. C and D describe greater energy use and slower straight-line speed, both of which count against the hypothesis.

Answer: D (the cycling survey can be done well without collecting data over many years.)

The passage attributes the cohort study's cost to decades of data collection, so the cheaper survey must be one that does not need them. D completes the contrast. A recommends the expensive method for the cheap study. B and C comment on the cohort study rather than explaining the survey's budget.

Answer: A (These leaves have most likely been exposed to stressful conditions.)

The red pigments appear only after cold nights and strong light have begun to damage the leaf, so red signals that the stress has occurred. A follows. B reverses the point, since the anthocyanins are protection against that light. C denies the pigment's role. D concerns leaf survival over winter, which the passage never discusses.

Answer: D (depended on)

She could not travel everywhere herself and so relied on others to find material for her. "Depended on" fits. "Admired" describes an attitude rather than a working arrangement, and "disagreed with" and "warned" describe interactions that would not produce a collection.

Answer: D (To portray Aunty Ruruhira's determination in gathering signatures)

Every sentence adds another circumstance in which she gets someone to sign, which builds a picture of relentlessness. D says that. A and C describe how others feel, which the passage does not report. B claims a change over time that the text does not show.

Answer: A (Thomas Betterton's writing has a distinctive and readily recognized style.)

Both texts treat Betterton's metrical habit as unmistakable enough to identify his scenes. A states the shared premise. C is the point on which they divide, since Halden denied Behn's hand. B and D make claims about Centlivre that only Text 1 approaches, and not in those terms.

Answer: B (superseded)

The sentence says this is the largest genome yet measured and that the costs of a still larger one would be prohibitive, so what is unlikely is that some other genome will take the record. "Superseded" means displaced from that position. "Curtailed" and "protracted" describe the genome shrinking or lengthening rather than losing its rank, and "obviated" would mean rendered unnecessary, which makes no sense of a genome.

Answer: A (Kando's traction system and Holst's drum brake both improved on designs already in use.)

Both notes say the invention improved on something already in use, and A names that shared feature. C sets the two effects against each other, which is a contrast. B and D describe one invention each.

Answer: A (In addition,)

The last sentence adds a second way Perry made her ancestry felt, beyond how she described herself, so an additive transition is needed. "In addition" supplies it. "However" and "Regardless" would set the two sentences against each other, and "Actually" would correct the previous statement rather than extend it.

Answer: A (Sotelo's team analyzed eDNA in water samples from the Rio Negro for evidence of river dolphins, which are difficult to observe directly.)

For an audience that already knows what eDNA is, the sentence should get straight to the study, which A does. C and D spend most of their length defining the term. B states the general capability rather than presenting this study.

Answer: D (that is,)

The phrase after the blank defines "lexical turnover," so the transition must introduce a definition. "That is" does. "For example" would present the definition as an instance, and "likewise" and "in addition" would present it as a second, parallel point rather than a gloss on the term just used.

Answer: B (years,)

The colon introduces a list of three abilities, and the items are separated by commas. B supplies the comma after the first item, matching the comma before "and colonise." A uses a semicolon where the other items take commas, C breaks the list into a fragment, and D runs the first two items together.

Answer: D (looking)

The sentence already has its main verb, "opens," so the interrupter between the commas must be a participial phrase. D supplies one. A, B, and C are finite verbs and would give the sentence two main verbs with no conjunction between them.

Answer: A (frameworks—which)

The clause "which assume a shared vocabulary" interrupts the sentence and closes with a dash before "cannot," so it must open with a dash. A matches the pair. B opens with a comma against a closing dash. C omits the opening mark, and D puts the dash after "which," splitting the clause from its own subject.

Answer: D (was)

The subject is "Her exhaustive breeding survey," a singular noun, so the verb is "was." The long modifier between subject and verb ends in plural nouns, "waterbird" and "migrants," which is what makes the plural forms in A, B, and C sound plausible.