Free SAT Skill Check

1. Algebra

If 4(x − 2) = 2x + 10, what is the value of x?

1. 5
2. 7
3. 9
4. 11

Answer C: Distribute first: 4x − 8 = 2x + 10. Subtract 2x and add 8 to obtain 2x = 18, so x = 9. Check: both sides equal 28. The other values fail when substituted into the original equation.

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2. Words in Context

The first map gave only a rough outline of the coast. After several surveys, the team produced a more ______ chart, showing even small inlets.

Which choice most logically completes the text?

1. precise
2. temporary
3. distant
4. controversial

Answer A: Precise means exact or detailed. The small inlets show the revised chart had finer detail than the rough outline. Nothing in the passage concerns how long the chart lasted, how far away it was, or whether people disputed it.

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3. Advanced Math

The equation x² − 6x + 9 = 0 has exactly one distinct real solution. What is it?

1. −3
2. 0
3. 3
4. 6

Answer C: Factor the left side as (x − 3)². It equals zero only when x = 3. Substituting −3, 0, or 6 gives a positive value, not zero.

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4. Transitions

The first prototype needed a separate power source. ______, the revised model runs on a rechargeable battery built into its case.

Which choice best connects the two sentences?

1. For example
2. By contrast
3. Likewise
4. Consequently

Answer B: By contrast marks the change from a separate power source to an integrated battery. For example introduces an instance; likewise signals similarity; consequently claims that the second design resulted from the first, which the text does not say.

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5. Problem-Solving and Data Analysis

A price of $80 rises by 25% and then falls by 20% of the new price. What is the final price?

1. $76
2. $80
3. $84
4. $100

Answer B: A 25% increase gives $80 × 1.25 = $100. The later 20% decrease uses $100 as its base, so $100 × 0.80 = $80. The two percentage changes cancel in this particular order and magnitude; percentages should never be added without checking their bases.

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6. Standard English Conventions

The new telescope recorded the comet’s path ______ the research team compared the images with observations from the previous night.

Which choice completes the text so that it conforms to Standard English conventions?

1. , and
2. ,
3. and,
4. ; and

Answer A: Both sides are independent clauses. A comma plus the coordinating conjunction and joins them correctly. A comma alone is a comma splice. “And,” places the comma after the conjunction, while “; and” unnecessarily combines two joining methods.

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7. Geometry and Trigonometry

A right triangle has legs of 5 and 12 units. What is the length of its hypotenuse?

1. 7 units
2. 13 units
3. 17 units
4. 60 units

Answer B: The Pythagorean theorem gives c² = 5² + 12² = 25 + 144 = 169. The positive length is c = 13. Adding the legs, subtracting them, or multiplying them does not give the hypotenuse.

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8. Rhetorical Synthesis

Student notes: The Cedar Garden program began in 2019. Participants grow vegetables on a shared plot. The Maple Garden program began in 2022. Its participants grow vegetables in individual containers. Both programs donate some produce to a local food pantry.

The student wants to emphasize a similarity in the programs’ community contributions. Which choice best accomplishes this goal?

1. Cedar Garden began three years before Maple Garden.
2. Cedar Garden uses a shared plot, whereas Maple Garden uses individual containers.
3. Both Cedar Garden and Maple Garden donate some produce to a local food pantry.
4. Maple Garden was created because Cedar Garden’s donations were insufficient.

Answer C: C states the shared contribution and is supported by the notes. A and B are supported but address dates and growing methods, not contributions. D invents a causal reason and a judgment about donations that the notes do not provide.

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