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36 free practice questions a day, shared across all your practice, each with a full explanation. No card needed.

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  • English, Math, Reading and Science practice by category and skill
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Questions, answered

36 practice questions every day, each with a full explanation, shared across your SAT, ACT and AP practice. The SAT and ACT diagnostics, SAT full-length Test A and Challenge Test 1, ACT Practice Test 1, The Daily and all 1,023 SAT vocabulary words are free too. No card needed.

The digital SAT, the ACT and AP exams. Choose a test at the top of this page. The ACT side has English, Math, Reading and Science practice, lessons, a 20-question diagnostic and full-length practice tests. The AP side has practice by unit and topic and full-length practice exams. Every question is original.

ACT and AP practice use the same free daily questions as SAT practice. The 20-question ACT diagnostic and ACT Practice Test 1 are free too. Other ACT practice tests and the AP practice exams come with Pro.

Every day at midnight Central Time.

No. Peakscor is an independent practice tool, not affiliated with College Board or ACT Education Corp. Scores shown are estimates.

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. Free: one run every 24 hours.
  • Streaks pay. ×2 from three in a row, ×3 from six.
  • Your best run. Most right before three misses.

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

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  • 36free practice questions every day
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Free

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  • The Daily, every day
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  • The 20-question Learn diagnostic
  • PEAK Survivor’s first map, plus the opening levels of Peak Hoover and Peak Defense
Start free daily practice

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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.

Functions · Lesson 3

Transformations of graphs

A transformation question starts with a graph of y=f(x)y = f(x) and changes the equation. The key idea: **a change outside ff acts on the outputs (yy), and it does what it looks like. A change inside ff acts on the inputs (xx), and it does the opposite of what it looks like.**

So f(x)+2f(x) + 2 moves the graph up 2, and f(x)−2f(x) - 2 moves it down 2. But f(x−3)f(x - 3) moves the graph 3 units to the right: the output that ff used to give at x=0x = 0 now appears at x=3x = 3, because 3−3=03 - 3 = 0. Likewise f(x+4)f(x + 4) moves it 4 units left.

A negative sign outside, −f(x)-f(x), flips the graph over the xx-axis (every yy changes sign). A negative sign inside, f(−x)f(-x), flips it over the yy-axis (every xx changes sign).

To track one point (a,b)(a, b) through several changes, deal with the inside (the xx-coordinate) and the outside (the yy-coordinate) separately. For the outside, apply the changes in the order you would compute them: multiply first, then add.

Where the point (a,b)(a, b) on y=f(x)y = f(x) goes
New equationEffect on the graph(a,b)(a, b) moves to
y=f(x)+ky = f(x) + kUp kk units (down if k<0k < 0)(a,b+k)(a, b + k)
y=f(x−h)y = f(x - h)Right hh units (left if h<0h < 0)(a+h,b)(a + h, b)
y=−f(x)y = -f(x)Reflect over the xx-axis(a,−b)(a, -b)
y=f(−x)y = f(-x)Reflect over the yy-axis(−a,b)(-a, b)
y=c⋅f(x)y = c \cdot f(x), c>0c > 0Vertical stretch by a factor of cc (a squeeze if c<1c < 1)(a,cb)(a, cb)
y=f(cx)y = f(cx), c>0c > 0Horizontal squeeze toward the yy-axis by a factor of cc (a stretch if c<1c < 1)(ac,b)(\frac{a}{c}, b)
The graphs of y = |x| and y = |x - 3| + 2−5−4−3−2−112345678−2−112345678xy(0, 0)(3, 2)
The graphs of y=∣x∣y = |x| and y=∣x−3∣+2y = |x - 3| + 2 Two V-shaped graphs opening upward with the same shape. The first, y = |x|, has its vertex at (0, 0). The second, y = |x − 3| + 2, has its vertex at (3, 2): the whole V has moved 3 units right and 2 units up.

Worked example Easy

The graph of y=f(x)y = f(x) is translated 4 units to the left and 2 units down. Which equation describes the new graph?

  1. y=f(x−4)−2y = f(x - 4) - 2
  2. y=f(x+4)−2y = f(x + 4) - 2Answer
  3. y=f(x−4)+2y = f(x - 4) + 2
  4. y=f(x+4)+2y = f(x + 4) + 2

How to solve it

  1. Down 2 is a change to the output, outside ff: subtract 2.
  2. Left 4 is a change to the input, inside ff, and inside changes do the opposite of what they look like: left means x+4x + 4.
  3. Put them together: y=f(x+4)−2y = f(x + 4) - 2.

Why each choice is right or wrong

  • A. Incorrect. f(x−4)−2f(x - 4) - 2 moves the graph down 2 but 4 units to the right. Inside ff, subtracting moves the graph right.
  • B. Correct. x+4x + 4 inside ff moves the graph 4 units left, and −2-2 outside moves it 2 units down.
  • C. Incorrect. f(x−4)+2f(x - 4) + 2 reverses both directions: it moves the graph 4 right and 2 up.
  • D. Incorrect. f(x+4)+2f(x + 4) + 2 gets the left shift right but moves the graph 2 units up. Down 2 means subtract 2 outside ff.

Worked example Medium

The point (3,−5)(3, -5) lies on the graph of y=f(x)y = f(x). Which point must lie on the graph of y=−f(x−2)+1y = -f(x - 2) + 1?

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

How to solve it

  1. Inside: x−2x - 2 must equal 3 for ff to use its known input, so x=5x = 5. The point moves 2 units right.
  2. Outside, compute in order: f(3)=−5f(3) = -5, then the negative sign gives −(−5)=5-(-5) = 5, then add 1 to get 6.
  3. Check: at x=5x = 5, y=−f(5−2)+1=−f(3)+1=5+1=6y = -f(5 - 2) + 1 = -f(3) + 1 = 5 + 1 = 6. The point is (5,6)(5, 6).

Why each choice is right or wrong

  • A. Incorrect. (1,6)(1, 6) moves the point 2 units left. x−2x - 2 inside ff shifts the graph right, so the new xx is 3+2=53 + 2 = 5.
  • B. Incorrect. (5,−4)(5, -4) skips the reflection and just adds 1 to −5-5. The negative sign in front of ff changes −5-5 to 5 before you add 1.
  • C. Incorrect. (5,4)(5, 4) adds 1 before reflecting: −(−5+1)=4-(-5 + 1) = 4. In −f(x−2)+1-f(x - 2) + 1, the sign applies to ff alone, so you get 5+1=65 + 1 = 6.
  • D. Correct. The xx-coordinate becomes 3+2=53 + 2 = 5 and the yy-coordinate becomes −(−5)+1=6-(-5) + 1 = 6.

Trap Inside shifts go the opposite way

In f(x−3)f(x - 3), the minus sign tempts you to move left. A choice with the reversed shift is a common distractor. Test a point: the graph's old point at x=0x = 0 now shows up where x−3=0x - 3 = 0, at x=3x = 3, so the move is to the right.

Trap Stretching when the graph squeezes

In f(2x)f(2x), the 2 is inside, so it acts on xx in the opposite way: the graph squeezes toward the yy-axis and every xx-coordinate is halved. A choice that doubles the xx-coordinates is the classic wrong answer.

Calculator When a calculator is faster

When a question gives a specific function, Desmos settles transformation questions in seconds: graph the original, then graph each choice and see which one matches the described move. To learn the rules, add a slider: type y = abs(x - h) + k and drag hh and kk to watch the V move.

When the question only says y=f(x)y = f(x) with no formula, there is nothing to graph. Track one point by hand instead, using the table above.

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

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