Digital SAT® practice

Reach your peak.

A quick run every day, an explanation for every question, and full-length tests on official timing.

Take the free diagnostic
Start here: 20 questions, about 28 minutes. You see your level in every domain and which lessons to take first. Free, no card. You also get 36 practice questions a day: 9 easy, 9 medium, 9 hard and 9 challenging. See what’s free
The DailySTEP 1
  • Three hearts. A miss costs one.
  • Streaks pay. ×2 from three in a row, ×3 from six.
  • Your longest streak. Try to beat it.

Full-length tests

Test day, rehearsed.

98 questions across four modules, in the same order and on the same timing as the digital SAT, with a highlighter, a question map and a timer you can see.

A Peakscor full-length test in progress: Reading and Writing, Test A, Module 1 of 4, question 7 of 27, with the passage, four answer choices, a highlighter, a 24:18 timer and Flag, Back and Next buttons.

How it works

A quick run every day. One skill at a time.

  1. 1

    Play the Daily.

    A quick run with three hearts. String right answers together and the questions get harder and the points multiply.

  2. 2

    Miss one, learn why.

    Every question is tagged by domain and skill, and every answer comes with an explanation.

  3. 3

    Drill that skill.

    Practice any single skill at any difficulty, or just the questions you got wrong.

  4. 4

    Beat your best.

    Come back tomorrow and climb. Progress shows your accuracy and your strongest skills.

Built on the digital SAT blueprint.

Every question is tagged by section, domain, skill and difficulty, so you can practice exactly what you need. Full tests run like test day: two Reading & Writing modules, a break, then two Math modules.

Explanations

Every answer, explained.

Not just the right letter: how to get there, and why the tempting answer is wrong.

MathProblem-Solving and Data AnalysisHard

A store raises the price of a jacket by 20%. Later, it lowers the new price by 20%. The final price is what percent of the original price?

A80%
B96%Correct
C100%The trap
D104%

Check with $100: $100then$120then$96

  1. Turn each change into a multiplier.

    Up 20% means × 1.20. Down 20% means × 0.80.

  2. Apply them in order.

    1.20 × 0.80 = 0.96

  3. Read the answer.

    The final price is 96% of the original. That’s B.

  4. Why not 100%?

    The 20% cut is taken from the higher price, so it removes more than the 20% increase added.

Test day

What test day looks like.

Every Peakscor full test follows this order. In the standard tests, the second module of each section adapts to how you did on the first.

  1. Reading & Writing · Module 1

    27 questions32 min

  2. Reading & Writing · Module 2

    27 questions32 min

    Adapts to how you did on Module 1.
  3. Break

    10 min

  4. Math · Module 1

    22 questions35 min

  5. Math · Module 2

    22 questions35 min

    Adapts to how you did on Module 1.

98 questions · 2 hr 14 min of testing, plus the break

Peakscor by the numbers

  • 36free practice questions every day
  • 98questions in every full-length test
  • 1,023SAT vocabulary words
  • 1.5×extended-time option on every test

Plans

Free every day. Pro when you’re serious.

The free plan is the real thing, not a trial. Pro removes the limits. Peak adds the full course and a plan to test day.

Free

$0no card needed

  • The Daily, every day
  • 36 practice questions a day, each with an explanation: 9 easy, 9 medium, 9 hard, 9 challenging
  • Full-length Test A and Challenge Test 1
  • All 1,023 vocabulary words: browse, flashcards and quiz
  • The 20-question Learn diagnostic
  • PEAK Survivor’s first map, plus the opening levels of Hole and Peak Defense
Start free daily practice

Pro

$20a month, or $200 a year

  • Everything in Free
  • Unlimited practice, no daily limit
  • Every full-length test and Challenge test
  • Every game map and level, with progress saved
See Pro

Peak

$29a month, or $280 a year

  • Everything in Pro
  • The full Learn course: every lesson and mastery quiz
  • Peak Plan, day by day to test day
See Peak

Prices in US dollars. Cancel anytime.

FAQ

Questions, answered.

The Daily, plus 36 practice questions every day: 9 easy, 9 medium, 9 hard and 9 challenging, each with a full explanation. Full-length Test A, Challenge Test 1 and all 1,023 vocabulary words are free too, as are the 20-question diagnostic and PEAK Survivor’s first map. No card needed.

Pro is $20 a month or $200 a year: unlimited practice with no daily limit, plus every full-length test and Challenge test, and every game map and level. Peak is $29 a month or $280 a year: everything in Pro, plus the full Learn course and Peak Plan. Cancel anytime from your account.

98 questions across four modules, in the same order as the digital SAT: Reading & Writing Module 1 and Module 2 (27 questions each), a 10-minute break, then Math Module 1 and Module 2 (22 questions each). On official timing that’s 2 hr 14 min of testing. You get estimated section scores and a total at the end.

Yes. In the standard full-length tests, Module 2 of each section is the harder version if you get 60% or more of Module 1 right, and the easier version if you don’t. Challenge tests are built from harder material in every module.

Official timing, extended 1.5× time, or untimed, on every test, including the free ones. Extended time allows 48 minutes for each Reading & Writing module and about 52 for each Math module. Untimed removes the clock so you can focus on accuracy.

A quick run with three hearts. Each right answer builds your streak: the questions get harder as it grows, and your points multiply (×2 from three in a row, ×3 from six). A miss costs a heart and drops you back to easy. Best is your longest streak.

Every day at midnight Central Time. You get a fresh 9 easy, 9 medium, 9 hard and 9 challenging.

No. Peakscor is an independent SAT practice tool, not affiliated with the College Board. Scores shown are estimates.

Your next point starts today.

Free, no card.

Nonlinear functions · Lesson 1

Function notation, graphs and transformations

f(x)f(x) is the output of the function ff when the input is xx. It does not mean ff times xx. To find f(−2)f(-2), replace every xx in the rule with (−2)(-2), in parentheses, and simplify. With f(x)=x2+1f(x) = x^2 + 1, f(−2)=(−2)2+1=5f(-2) = (-2)^2 + 1 = 5.

On a graph of y=f(x)y = f(x), the input is the xx-coordinate and the output is the yy-coordinate. The point (a,b)(a, b) is on the graph exactly when f(a)=bf(a) = b. So f(4)f(4) asks for the height of the graph at x=4x = 4, while f(x)=4f(x) = 4 asks for every xx where the graph has height 4. There can be more than one.

In context, read both units. If C(n)C(n) is the cost, in dollars, of printing nn posters, then C(40)=90C(40) = 90 means: printing 40 posters costs 90 dollars. The number in the parentheses is the input (posters) and the number after the equals sign is the output (dollars).

Transformations. If you know the graph of y=f(x)y = f(x), you can build related graphs. y=f(x)+ky = f(x) + k moves the graph up kk units (down if kk is negative). y=f(x−h)y = f(x - h) moves it right hh units, so y=f(x+3)y = f(x + 3) moves it left 3. y=−f(x)y = -f(x) flips it over the xx-axis. Every point moves the same way, so a vertex at (2,4)(2, 4) on y=f(x)y = f(x) becomes (2+h,4+k)(2 + h, 4 + k) on y=f(x−h)+ky = f(x - h) + k.

A quick way to remember the horizontal direction: in f(x−3)f(x - 3), the input that used to be 0 is now reached when x=3x = 3, so everything happens 3 units later, to the right.

The graphs of y = x^2 and y = (x - 3)^2 + 1−4−3−2−11234567−2−112345678910xy(3, 1)
The graphs of y=x2y = x^2 and y=(x−3)2+1y = (x - 3)^2 + 1 Two upward-opening parabolas with the same shape. The first has its lowest point at (0, 0). The second is the first moved 3 units right and 1 unit up, so its lowest point is at (3, 1). The first meets both axes at (0, 0); the second crosses the y-axis at (0, 10), the top edge of the window.

Worked example Easy

f(x)=3x2−5x+2f(x) = 3x^2 - 5x + 2

For the function ff defined above, what is the value of f(−2)f(-2)?

  1. 00
  2. 44
  3. 2424Answer
  4. 4848

How to solve it

  1. Replace every xx with (−2)(-2): f(−2)=3(−2)2−5(−2)+2f(-2) = 3(-2)^2 - 5(-2) + 2.
  2. Square first: (−2)2=4(-2)^2 = 4, so 3(−2)2=123(-2)^2 = 12.
  3. Multiply: −5(−2)=10-5(-2) = 10.
  4. Add: 12+10+2=2412 + 10 + 2 = 24.

Why each choice is right or wrong

  • A. Incorrect. This comes from treating (−2)2(-2)^2 as −4-4, which gives 3(−4)+10+2=03(-4) + 10 + 2 = 0. A negative number squared is positive: (−2)2=4(-2)^2 = 4.
  • B. Incorrect. This comes from writing −5(−2)-5(-2) as −10-10, which gives 12−10+2=412 - 10 + 2 = 4. A negative times a negative is positive, so the middle term is +10+10.
  • C. Correct. 3(4)−5(−2)+2=12+10+2=243(4) - 5(-2) + 2 = 12 + 10 + 2 = 24.
  • D. Incorrect. This comes from multiplying 3 by −2-2 before squaring, (3⋅(−2))2=36(3 \cdot (-2))^2 = 36, which gives 36+10+2=4836 + 10 + 2 = 48. The exponent applies only to xx, so square −2-2 first and then multiply by 3.

Worked example Medium

The graph of y = f(x)−2−1123456−5−4−3−2−11234560xy(2, 4)(0, 0)(4, 0)
The graph of y=f(x)y = f(x) A downward-opening parabola. Its highest point, the vertex, is at (2, 4). It crosses the x-axis at (0, 0), which is also where it crosses the y-axis, and at (4, 0).

The graph of y=f(x)y = f(x) is shown. The function gg is defined by g(x)=f(x+3)−1g(x) = f(x + 3) - 1. What are the coordinates of the vertex of the graph of y=g(x)y = g(x)?

  1. (−1,3)(-1, 3)Answer
  2. (5,3)(5, 3)
  3. (2,6)(2, 6)
  4. (−1,5)(-1, 5)

How to solve it

  1. Read the vertex of ff from the graph: (2,4)(2, 4).
  2. f(x+3)f(x + 3) moves the graph 3 units left, so the xx-coordinate becomes 2−3=−12 - 3 = -1.
  3. The −1-1 outside moves the graph 1 unit down, so the yy-coordinate becomes 4−1=34 - 1 = 3.
  4. The vertex of gg is (−1,3)(-1, 3). Check: g(−1)=f(2)−1=4−1=3g(-1) = f(2) - 1 = 4 - 1 = 3.

Why each choice is right or wrong

  • A. Correct. Adding 3 inside shifts the graph 3 units left and subtracting 1 outside shifts it 1 unit down: (2−3,4−1)=(−1,3)(2 - 3, 4 - 1) = (-1, 3).
  • B. Incorrect. This moves the vertex 3 units right. Adding 3 inside the parentheses moves the graph left: g(−1)=f(2)−1g(-1) = f(2) - 1, so the old vertex input 2 is now reached at x=−1x = -1.
  • C. Incorrect. This treats the +3+3 inside as a shift up, giving a height of 4+3−1=64 + 3 - 1 = 6, and leaves the xx-coordinate at 2. A number added inside the parentheses moves the graph sideways, not up.
  • D. Incorrect. This handles the horizontal shift correctly but also reverses the vertical one, giving 4+1=54 + 1 = 5. Only the shift inside the parentheses goes the opposite way from its sign. The −1-1 outside moves the graph down.

Trap Shifting the wrong way

f(x−3)f(x - 3) moves a graph 3 units right and f(x+3)f(x + 3) moves it 3 units left, the opposite of what the sign seems to say. Numbers outside the function behave as they look: f(x)−1f(x) - 1 moves the graph down 1. A choice with the horizontal shift reversed is often among the answers.

Trap Mixing up f(a) and f(x) = a

f(5)f(5) is an output: go to x=5x = 5 and read the height. f(x)=5f(x) = 5 asks for inputs: find every point at height 5 and read their xx-coordinates. When a question gives you an output and asks for the input, the output value itself is a likely wrong choice.

Desmos When Desmos is faster

When the function is given as a formula, define it in Desmos: type f(x) = 3x^2 - 5x + 2. On the next line type f(-2), and Desmos shows the value, 24. This avoids sign slips with negative inputs.

For transformations, define ff and then type g(x) = f(x + 3) - 1 on a new line. Desmos graphs both, and you can click the new graph to see points such as its vertex.

When the function is given only as a graph on the page, Desmos can't read it. Work from the points on the graph by hand, which is quick: a shift changes every point the same way.

Your progress

How you’re doing across daily practice and full-length tests.

Practice

Choose a section, then practice a whole domain or drill a single skill.

Difficulty
Status
Session
Timing

Full-length tests

Each test mirrors the digital SAT®: 98 questions across four modules, 2 hr 14 min on official timing.

A little harder on purpose. These tests can run slightly tougher than test day, which makes them good practice: if you can handle these, the real one should feel easier. No question appears in more than one test, Challenge Tests included.

Challenge Tests Hardest of the hardest

Same 98-question format, built from harder material: a hard Module 1, then a Module 2 made mostly of the hardest questions.

Vocab

Study the classic SAT® vocabulary list. Browse, flip flashcards, or quiz yourself.

Free every day. Pro when you're serious.

Practice free every day. Pro removes the limits. Peak adds the full course and a plan to test day.

FREE

$0forever
 
  • ✓ 9 easy + 9 medium + 9 hard + 9 challenging daily
  • ✓ Practice by any SAT domain
  • ✓ Explanations on every question
  • ✓ Test A and Challenge Test 1
  • ✓ The 20-question Learn diagnostic
  • ✓ PEAK Survivor’s first map, plus the opening levels of Hole and Peak Defense

PRO

$200/ year
About $16.67 a month, save $40
  • ✓ Everything in Free
  • ✓ Unlimited daily practice
  • ✓ Every full-length and Challenge test
  • ✓ Every game map and level, with progress saved
Full course and plan

PEAK

$280/ year
About $23.33 a month, save $68
  • ✓ Everything in Pro
  • ✓ Every Learn lesson, summary and mastery quiz
  • ✓ Peak Plan: a day-by-day plan to test day
  • ✓ Cancel anytime

Prices in USD. Switch or cancel your plan at any time.