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Digital SAT practice questions with answers

Practise Digital SAT (Math · Reading and Writing) with 649 exam-style practice questions, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

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Digital SAT practice questions with answers

Practise Digital SAT (Math · Reading and Writing) with 649 exam-style practice questions, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

649 questions · 8 chapters

What each chapter covers 8 chapters

The questions follow the syllabus chapter by chapter. You can test the whole subject or one chapter at a time.

  1. Math · Algebra 119 questionsLinear equations in one variable, Linear functions, Linear equations in two variables, Systems of two linear equations, Linear inequalities
  2. Math · Advanced Math 103 questionsEquivalent expressions, Nonlinear equations and systems, Nonlinear functions
  3. Math · Problem-Solving and Data Analysis 133 questionsRatios, rates, proportions and units, Percentages, One-variable data, Two-variable data, Probability, Samples, studies and margin of error
  4. Math · Geometry and Trigonometry 92 questionsArea and volume, Lines, angles and triangles, Right triangles and trigonometry, Circles
  5. Reading and Writing · Craft and Structure 50 questionsWords in context, Text structure and purpose, Cross-text connections
  6. Reading and Writing · Information and Ideas 54 questionsCentral ideas and details, Command of evidence: text, Command of evidence: data, Inferences
  7. Reading and Writing · Standard English Conventions 56 questionsBoundaries, Form, structure and sense
  8. Reading and Writing · Expression of Ideas 42 questionsTransitions, Rhetorical synthesis
Sample Digital SAT practice questions with answers 12 questions

12 questions from the test, one or two from each chapter. Try each one, then open the answer.

1. A student sells handmade cards for $3.50 each. Each card costs $0.80 in materials, and the student also paid a one-time $60 fee for a booth. What is the minimum number of cards the student must sell to earn a profit of at least $200?

  1. A
    75
  2. B
    96
  3. C
    97
  4. D
    130
Show answer

Answer: C. Profit is 3.5c − 0.8c − 60 ≥ 200, so 2.7c ≥ 260 and c ≥ 96.3. The minimum whole number is 97. Choosing 96 rounds down and 75 ignores the cost of materials.

2. The graph of y = x2 in the xy-plane is shifted 3 units to the right and 2 units down. Which equation represents the resulting graph?

  1. A
    y = (x + 3)2 − 2
  2. B
    y = (x − 2)2 − 3
  3. C
    y = (x − 3)2 − 2
  4. D
    y = (x − 3)2 + 2
Show answer

Answer: C. A shift of 3 units right replaces x with x − 3, and a shift of 2 units down subtracts 2 from the output: y = (x − 3)2 − 2. Using x + 3 would shift the graph to the left.

3. A faucet leaks 3 drops of water every 2 seconds. If 20 drops of water make 1 milliliter, how many liters of water does the faucet leak in one day? (1 liter = 1,000 milliliters)

  1. A
    2.88
  2. B
    6.48
  3. C
    64.8
  4. D
    6,480
Show answer

Answer: B. One day has 24 × 60 × 60 = 86,400 seconds, so the faucet leaks 1.5 × 86,400 = 129,600 drops, which is 129,600 ÷ 20 = 6,480 milliliters, or 6.48 liters. 2.88 turns the rate upside down (2/3 drop per second), and 6,480 stops at milliliters.

4. A circle has a circumference of 18π centimeters. What is the area of the circle, in square centimeters?

  1. A
    9π
  2. B
    18π
  3. C
    81π
  4. D
    324π
Show answer

Answer: C. 2πr = 18π gives r = 9, so the area is π(9)2 = 81π. 324π uses the diameter, 18, as the radius.

5. The committee's report recommends replacing the city's buses with electric models by 2030, but the authors are careful to qualify that recommendation, noting that the schedule is realistic only if the promised federal funding arrives on time.

As used in the text, what does the word “qualify” most nearly mean?

  1. A
    certify
  2. B
    pass
  3. C
    train
  4. D
    limit
Show answer

Answer: D. Adding a condition (“only if the funding arrives”) limits or restricts the recommendation. “Certify” and “pass” belong to the sense of qualifying for a job or contest, which does not fit a recommendation.

6. The following text is from Paul Laurence Dunbar's 1895 poem “We Wear the Mask.”

We wear the mask that grins and lies,
It hides our cheeks and shades our eyes,—
This debt we pay to human guile;
With torn and bleeding hearts we smile,
And mouth with myriad subtleties.

Which choice best states the main idea of the text?

  1. A
    People conceal their pain behind a cheerful outward appearance.
  2. B
    The speaker is preparing to wear a costume at a celebration.
  3. C
    People who smile often are usually happy.
  4. D
    The speaker regrets having lied to a close friend.
Show answer

Answer: A. The “mask that grins and lies” hides “torn and bleeding hearts,” so the smile covers suffering. The mask is a figure of speech, not a costume, and the poem suggests smiles can hide unhappiness.

7. Some plants defend themselves by recruiting help from other ______ caterpillars chew on corn leaves, the plants release airborne chemicals that attract parasitic wasps, which lay their eggs inside the caterpillars.

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

  1. A
    species, when
  2. B
    species when
  3. C
    species, which when
  4. D
    species: when
Show answer

Answer: D. The first clause is complete, and the sentence after it gives an example of that claim, so a colon is correct. A comma creates a comma splice (two main clauses joined by only a comma), no punctuation creates a run-on, and 'which when' is ungrammatical.

8. Many desert plants have features that help them conserve water. ______ the leaves of most cacti have been reduced to spines, which lose far less water than broad leaves do, and photosynthesis takes place in the plants' thick green stems instead.

Which choice completes the text with the most logical transition?

  1. A
    In contrast,
  2. B
    Nevertheless,
  3. C
    Consequently,
  4. D
    For example,
Show answer

Answer: D. Cacti, with leaves reduced to spines, are one case of desert plants with water-saving features, so 'For example' is correct.

9. A caterer can spend at most $600 on sandwiches that cost $6 each and salads that cost $8 each. She needs at least 80 items in all. Which system of inequalities represents this situation, where s is the number of sandwiches and d is the number of salads?

  1. A
    6s + 8d ≥ 600 and s + d ≤ 80
  2. B
    6s + 8d ≤ 600 and s + d ≤ 80
  3. C
    8s + 6d ≤ 600 and s + d ≥ 80
  4. D
    6s + 8d ≤ 600 and s + d ≥ 80
Show answer

Answer: D. "At most $600" means the cost 6s + 8d is less than or equal to 600, and "at least 80 items" means s + d ≥ 80. The system with both signs flipped reverses both conditions.

10. f(x) = 3x2 + kx − 4
In the given function, k is a constant and f(2) = 10. What is the value of f(−1)?

  1. A
    −2
  2. B
    0
  3. C
    2
  4. D
    6
Show answer

Answer: A. f(2) = 12 + 2k − 4 = 10 gives k = 1. Then f(−1) = 3(1) + (1)(−1) − 4 = −2. The value 0 is f(1), and 6 is f(−2).

11. Machine A makes 45 parts per hour, and Machine B makes 30 parts per hour. If both machines work at the same time, how many minutes will it take them to make a total of 300 parts?

  1. A
    240
  2. B
    400
  3. C
    480
  4. D
    1,200
Show answer

Answer: A. Together the machines make 45 + 30 = 75 parts per hour, so 300 parts take 300 ÷ 75 = 4 hours, or 240 minutes. 400 is the time for Machine A alone, and 480 uses the average of the two rates instead of their sum.

12. In the xy-plane, the equation of a circle is x2 + y2 − 8x + 6y − 11 = 0. What is the radius of the circle?

  1. A
    √11
  2. B
    5
  3. C
    6
  4. D
    36
Show answer

Answer: C. Completing the square gives (x − 4)2 + (y + 3)2 = 11 + 16 + 9 = 36, so the radius is 6. √11 uses the constant term before completing the square, 5 leaves out the 11, and 36 is r2.

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Ways to practise 5 ways

When you get a question wrong, a short note called "The idea behind this" explains the topic it belongs to, with the rules to remember and a worked example.

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Digital SAT: frequently asked questions

Is this Digital SAT test free?

Yes. Every test, answer and explanation is free, and you do not need an account. Sign in only if you want your results kept across devices.

How many Digital SAT questions are there?

649 practice questions with answers, covering 8 chapters of the syllabus. Each test draws new questions, so you can practise many times.

Are these Digital SAT past paper questions?

No. The 649 practice questions are our own, written to the syllabus in the style of the exam.

How is the test marked?

Instantly. You see your score, the right answer and an explanation for every question, and the topics to work on next. Questions you got wrong are saved so you can retry them.

Can I practise one chapter or only my weak topics?

Yes. Pick a chapter, build your own test from chosen topics, or practise your weakest topics and your past mistakes.

Is there a full-length mock test?

Yes: 98 questions in four timed modules, Reading and Writing 2 × 27 (32 minutes each) and Math 2 × 22 (35 minutes each).

Does it work on a phone?

Yes. It runs in the browser on any phone or computer, and you can add it to your home screen like an app.

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