Digital SAT practice

Reach your peak.

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

See what’s free
Free, no card. You also get 36 practice questions a day: 12 easy, 12 medium and 12 hard.
The DailySTEP 1
  • Three hearts. A miss costs one.
  • Streaks pay. ×2 from three in a row, ×3 from six.
  • Your longest streak. Beat it tomorrow.

Full-length tests

The real test, rehearsed.

98 questions across four modules, in the digital SAT’s order and on its timing, 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

One run a 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 around the real 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.

Free daily practice

12 easy, 12 medium and 12 hard questions free every day, each with a full explanation. Filter by section, domain, skill and difficulty. Resets at midnight.

Real SAT timing

Take any test on official timing, extended 1.5× time, or untimed to focus purely on accuracy.

Adaptive full-length tests

Four modules in official order. The second module of each section adapts to how you did on the first.

Vocabulary

1,023 essential SAT words. Browse the list, flip flashcards, or quiz yourself.

Your progress

Accuracy across daily practice and full tests, your strongest skills, and the ones that need the most help.

Games

PEAK Survivor, Hole and Peak Defense: three games powered by SAT practice questions.

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: 12 easy, 12 medium, 12 hard
  • Full-length Test A and Challenge Test 1
  • All 1,023 vocabulary words: browse, flashcards and quiz
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
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: 12 easy, 12 medium and 12 hard, each with a full explanation. Full-length Test A, Challenge Test 1 and all 1,023 vocabulary words are free too. 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. 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 digital SAT’s order: 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 use the hardest material throughout.

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. You get a fresh 12 easy, 12 medium and 12 hard.

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.

Circles · Lesson 4

The equation of a circle

A circle is every point at the same distance rr, the radius, from a center (h,k)(h, k). The distance formula turns that into the standard form of a circle's equation: (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2.

Reading it. Each coordinate of the center is the value that makes its square zero. In (x−5)2+(y+7)2=16(x - 5)^2 + (y + 7)^2 = 16, x−5=0x - 5 = 0 when x=5x = 5, and y+7=0y + 7 = 0 when y=−7y = -7, so the center is (5,−7)(5, -7). The right side is r2r^2, so the radius is 16=4\sqrt{16} = 4.

Writing it. Given the center and the radius, substitute. Given the center and a point on the circle, the radius is the distance between them, and you don't need the square root: r2r^2 is the square of the horizontal change plus the square of the vertical change.

Inside, on or outside. Substitute the point into the left side and compare the result with r2r^2. Less than r2r^2: inside. Equal: on the circle. Greater: outside. For the circle above, the point (6,−4)(6, -4) gives (6−5)2+(−4+7)2=1+9=10(6 - 5)^2 + (-4 + 7)^2 = 1 + 9 = 10, which is less than 16, so (6,−4)(6, -4) is inside.

A circle touches the xx-axis at exactly one point when its center is rr units above or below the axis, and it touches the yy-axis when its center is rr units to the left or right of it.

The circle (x - 5)^2 + (y + 7)^2 = 16123456789101112−12−11−10−9−8−7−6−5−4−3−2−1xy(5, −7)
The circle (x−5)2+(y+7)2=16(x - 5)^2 + (y + 7)^2 = 16 A circle on a coordinate grid, below the x-axis and to the right of the y-axis, touching neither. Its center (5, −7) is marked and labelled. It passes through (9, −7), (1, −7), (5, −3) and (5, −11), each 4 units from the center; (9, −7) and (5, −3) are marked.

Worked example Easy

(x+4)2+(y−3)2=49(x + 4)^2 + (y - 3)^2 = 49

The given equation defines a circle in the xyxy-plane. What are the center and the radius of the circle?

  1. Center (−4,3)(-4, 3), radius 77Answer
  2. Center (4,−3)(4, -3), radius 77
  3. Center (−4,3)(-4, 3), radius 4949
  4. Center (4,−3)(4, -3), radius 4949

How to solve it

  1. Match the equation to (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2.
  2. x+4=0x + 4 = 0 when x=−4x = -4, and y−3=0y - 3 = 0 when y=3y = 3. The center is (−4,3)(-4, 3).
  3. r2=49r^2 = 49, so r=7r = 7.

Why each choice is right or wrong

  • A. Correct. x+4x + 4 is x−(−4)x - (-4), so h=−4h = -4, and k=3k = 3. The center is (−4,3)(-4, 3), and r=49=7r = \sqrt{49} = 7.
  • B. Incorrect. This copies the signs shown in the equation. The center's coordinates are the values that make each square zero: x=−4x = -4 and y=3y = 3.
  • C. Incorrect. 49 is r2r^2, the right side of the equation. The radius is 49=7\sqrt{49} = 7.
  • D. Incorrect. This makes both mistakes: it copies the signs shown in the equation, and it uses r2=49r^2 = 49 as the radius.

Worked example Medium

A circle in the xyxy-plane has its center at (3,−2)(3, -2) and passes through the point (4,1)(4, 1). Which equation defines the circle?

  1. (x+3)2+(y−2)2=10(x + 3)^2 + (y - 2)^2 = 10
  2. (x−3)2+(y+2)2=10(x - 3)^2 + (y + 2)^2 = 10Answer
  3. (x−3)2+(y+2)2=16(x - 3)^2 + (y + 2)^2 = 16
  4. (x−4)2+(y−1)2=10(x - 4)^2 + (y - 1)^2 = 10

How to solve it

  1. The center (3,−2)(3, -2) gives (x−3)2+(y+2)2(x - 3)^2 + (y + 2)^2 on the left side.
  2. r2r^2 is the squared distance from the center to (4,1)(4, 1). The horizontal change is 4−3=14 - 3 = 1 and the vertical change is 1−(−2)=31 - (-2) = 3, so r2=12+32=10r^2 = 1^2 + 3^2 = 10.
  3. The equation is (x−3)2+(y+2)2=10(x - 3)^2 + (y + 2)^2 = 10. Check: (4−3)2+(1+2)2=1+9=10(4 - 3)^2 + (1 + 2)^2 = 1 + 9 = 10.

Why each choice is right or wrong

  • A. Incorrect. This flips both signs of the center: (x+3)2+(y−2)2(x + 3)^2 + (y - 2)^2 is a circle centered at (−3,2)(-3, 2).
  • B. Correct. The center gives (x−3)2+(y+2)2(x - 3)^2 + (y + 2)^2, and the squared distance to (4,1)(4, 1) is 12+32=101^2 + 3^2 = 10.
  • C. Incorrect. This adds the changes before squaring: (1+3)2=16(1 + 3)^2 = 16. Square each change first, then add: 12+32=101^2 + 3^2 = 10.
  • D. Incorrect. This uses the point on the circle as the center. (4,1)(4, 1) lies on the circle; the center is (3,−2)(3, -2).

Trap Copying the signs

(x+5)2(x + 5)^2 means the center's xx-coordinate is −5-5, not 5. Find each coordinate of the center by asking what value makes that square zero.

Trap Radius or radius squared

The right side of standard form is r2r^2. If it is 50, the radius is 50=52\sqrt{50} = 5\sqrt{2}, not 50. Going the other way, a radius of 5 makes the right side 25.

Trap Comparing with r instead of r²

To test a point, compare the left side with r2r^2 itself. Comparing it with rr, or comparing the point's distance from the center with r2r^2, mixes a squared quantity with a plain one: the first can call an inside point outside, and the second can call an outside point inside.

Desmos When Desmos is faster

Type the equation exactly as written, such as (x-5)^2+(y+7)^2=16, and Desmos draws the circle. Desmos doesn't mark a circle's center as a point, but when the center and the radius are whole numbers you can read them off the grid.

For a which equation question, type the given points first, such as (3,-2) and (4,1), then type each choice on its own line. The right equation's circle is centered on the first point and passes through the second.

To test whether a point is inside, on or outside, type the point and look. If it sits very close to the circle, the picture can't tell on from just inside, so substitute by hand to be sure.

Your progress

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

Build your study plan

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 than the real SAT. 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, but every question is drawn from the toughest SAT material: Challenging-tier math throughout and the hardest reading.

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
 
  • ✓ 12 easy + 12 medium + 12 hard daily
  • ✓ Practice by any SAT domain
  • ✓ Explanations on every question
  • ✓ Test A and Challenge Test 1
  • ✓ The first lesson of every Learn module

PRO

$200/ year
About $16.67 a month, save $40
  • ✓ Everything in Free
  • ✓ Unlimited daily practice
  • ✓ Every full-length and Challenge test
  • ✓ Every timing mode
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.

▦ Calculator
Drag the bar to move it, and the corner to resize it