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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.

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    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

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Start free daily practice

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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.

Area and volume · Lesson 2

Circles in area problems

Two circle formulas are on the reference sheet: area A=πr2A = \pi r^2 and circumference C=2πrC = 2\pi r. The circumference is the circle's perimeter. Both formulas use the radius rr, the distance from the center to the circle. The diameter goes all the way across through the center and is twice the radius, so C=πdC = \pi d too.

A circle with radius 7 has area π(7)2=49π\pi(7)^2 = 49\pi and circumference 2π(7)=14π2\pi(7) = 14\pi. Many SAT answers keep π\pi as a symbol, so leave it in unless the choices are decimals.

When a figure or question gives the diameter, halve it before you use A=πr2A = \pi r^2. When it gives the circumference or the area, work back to rr first: a circumference of 14π14\pi means 2πr=14π2\pi r = 14\pi, so r=7r = 7.

Shaded regions with circles work like any other region: outer area minus inner area. A ring between two circles with the same center has area πR2−πr2\pi R^2 - \pi r^2, where RR is the outer radius and rr the inner one. A circle that just fits inside a square, touching all four sides, has a diameter equal to the square's side.

A semicircle is half a circle, with area 12πr2\frac{1}{2}\pi r^2. The perimeter of a semicircle shape is half the circumference plus the straight edge, which is a diameter. A semicircle with diameter 12 has a curved edge of 12π(12)=6π\frac{1}{2}\pi(12) = 6\pi and a perimeter of 6π+126\pi + 12.

Worked example Easy

Circle with center O18O
Circle with center O A circle with center O. A segment through O joins two points on the circle, so it is a diameter; it is labelled 18.

In the circle shown, O is the center, and the segment through O is a diameter of length 18. What is the area of the circle?

  1. 18π18\pi
  2. 36π36\pi
  3. 81π81\piAnswer
  4. 324π324\pi

How to solve it

  1. The segment passes through the center and ends on the circle, so it is a diameter: d=18d = 18.
  2. The radius is half of that: r=9r = 9.
  3. A=π(9)2=81πA = \pi(9)^2 = 81\pi.

Why each choice is right or wrong

  • A. Incorrect. 18π18\pi is the circumference, πd=π(18)\pi d = \pi(18). The question asks for the area.
  • B. Incorrect. This puts the diameter into the circumference formula as if it were the radius: 2π(18)=36π2\pi(18) = 36\pi. It uses the wrong formula and the wrong length.
  • C. Correct. The radius is half the diameter, 9, and π(9)2=81π\pi(9)^2 = 81\pi.
  • D. Incorrect. This uses the diameter as the radius: π(18)2=324π\pi(18)^2 = 324\pi. Halve the diameter first.

Worked example Medium

Two circles with the same center O410O
Two circles with the same center O Two circles share the center O. A radius of the smaller circle is labelled 4, and a radius of the larger circle is labelled 10. The ring between the two circles is shaded; the inside of the smaller circle is not.

The figure shows two circles with the same center, O. What is the area of the shaded region, inside the larger circle and outside the smaller circle?

  1. 36π36\pi
  2. 84π84\piAnswer
  3. 100π100\pi
  4. 116π116\pi

How to solve it

  1. Larger circle: π(10)2=100π\pi(10)^2 = 100\pi.
  2. Smaller circle: π(4)2=16π\pi(4)^2 = 16\pi.
  3. The region between them: 100π−16π=84π100\pi - 16\pi = 84\pi.

Why each choice is right or wrong

  • A. Incorrect. This subtracts the radii first and then squares: π(10−4)2=36π\pi(10 - 4)^2 = 36\pi. Subtract the areas, not the radii. π(10)2−π(4)2\pi(10)^2 - \pi(4)^2 is not the same as π(10−4)2\pi(10 - 4)^2.
  • B. Correct. The larger circle's area minus the smaller circle's area: 100π−16π=84π100\pi - 16\pi = 84\pi.
  • C. Incorrect. 100π100\pi is the area of the whole larger circle. The smaller circle's area, 16π16\pi, is not part of the region.
  • D. Incorrect. This adds the two areas, 100π+16π=116π100\pi + 16\pi = 116\pi. The smaller circle is a hole in the region, so its area is subtracted.

Trap Radius or diameter

Every circle formula on the reference sheet uses rr. If the figure labels a segment through the center, or the words say diameter, halve it first. Using the diameter as the radius makes an area 4 times too big, and the SAT can list that value as a choice.

Trap Subtracting before squaring

For a ring, πR2−πr2\pi R^2 - \pi r^2 is not π(R−r)2\pi(R - r)^2. Find each circle's area, then subtract.

Trap Area or circumference

πr2\pi r^2 and 2πr2\pi r look alike. Area is in square units and squares the radius; circumference is a length and doesn't. Reread what the question asks for before you choose a formula.

Desmos When Desmos isn’t faster

When the choices are written with π\pi, the work is choosing the right radius and formula, which is faster by hand.

Desmos helps when the choices are decimals. Type pi for π\pi: typing 84pi shows about 263.89, so you can match an answer such as 84π84\pi to a decimal choice.

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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.

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