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

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

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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.

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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.

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

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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.

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

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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

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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.

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Circles · Lesson 1

Arc length and sector area

A central angle has its vertex at the center of a circle, and its sides are two radii. It cuts off an arc, a piece of the circle, and a sector, the pie slice between the two radii. The key idea: the arc and the sector are the same fraction of the whole circle as the central angle is of a full turn.

In degrees a full turn is 360°, so arc length =θ360⋅2πr= \frac{\theta}{360} \cdot 2\pi r and sector area =θ360⋅πr2= \frac{\theta}{360} \cdot \pi r^2. In the figure below, r=10r = 10 and the angle is 72°, which is 72360=15\frac{72}{360} = \frac{1}{5} of the circle. The arc is 15\frac{1}{5} of the circumference 20π20\pi, so it is 4π4\pi, and the sector is 15\frac{1}{5} of the area 100π100\pi, so it is 20π20\pi.

In radians a full turn is 2π2\pi. The reference sheet gives both facts: a circle has 360 degrees and 2π2\pi radians. The fraction of the circle is θ2π\frac{\theta}{2\pi}, which gives two short formulas for an angle θ\theta in radians: arc length s=rθs = r\theta and sector area =12r2θ= \frac{1}{2}r^2\theta. To convert degrees to radians, multiply by π180\frac{\pi}{180}: 72° is 72π180=2π5\frac{72\pi}{180} = \frac{2\pi}{5} radians, and s=10⋅2π5=4πs = 10 \cdot \frac{2\pi}{5} = 4\pi, the same arc as before.

Questions also run backward: given an arc length or a sector area, find the angle or the radius. Set up the same fraction and solve. Whatever is asked, start with one question: what fraction of the circle is this?

A central angle of 72° and the arc it cuts off72°10OAB
A central angle of 72° and the arc it cuts off A circle with center O. Radii OA and OB are drawn, and OA is labelled 10. The angle AOB at the center is marked 72°. The arc from A to B inside that angle is drawn in bold.

Worked example Easy

A circle with center O and central angle AOB45°8OAB
A circle with center O and central angle AOB A circle with center O. Radii OA and OB are drawn, and OA is labelled 8. The angle AOB at the center is marked 45°. The minor arc AB, inside that angle, is drawn in bold.

In the circle shown, O is the center, the radius is 8 and angle AOB measures 45°. What is the length of minor arc AB, shown in bold?

  1. π\pi
  2. 2π2\piAnswer
  3. 4π4\pi
  4. 8π8\pi

How to solve it

  1. The central angle is 45° out of a full 360°, so the arc is 45360=18\frac{45}{360} = \frac{1}{8} of the circle.
  2. The circumference is 2π(8)=16π2\pi(8) = 16\pi.
  3. The arc is 18⋅16π=2π\frac{1}{8} \cdot 16\pi = 2\pi.

Why each choice is right or wrong

  • A. Incorrect. This uses πr=8π\pi r = 8\pi as the circumference, so 18⋅8π=π\frac{1}{8} \cdot 8\pi = \pi. The circumference is 2πr=16π2\pi r = 16\pi.
  • B. Correct. The arc is 45360=18\frac{45}{360} = \frac{1}{8} of the circumference, 16π16\pi, which is 2π2\pi.
  • C. Incorrect. This divides by 180 instead of 360: 45180⋅16π=4π\frac{45}{180} \cdot 16\pi = 4\pi. A full circle is 360°, so 45° is one eighth of it, not one fourth.
  • D. Incorrect. 8π8\pi is the area of the sector, 18⋅π(8)2=18⋅64π\frac{1}{8} \cdot \pi(8)^2 = \frac{1}{8} \cdot 64\pi. An arc is a length, so take the fraction of the circumference.

Worked example Medium

In a circle with center O, central angle AOB measures 5π6\frac{5\pi}{6} radians, and the area of sector AOB is 15π15\pi. What is the radius of the circle?

  1. 323\sqrt{2}
  2. 66Answer
  3. 1818
  4. 3636

How to solve it

  1. A full circle is 2π2\pi radians, so the sector is 5π6÷2π=512\frac{5\pi}{6} \div 2\pi = \frac{5}{12} of the circle.
  2. So 512⋅πr2=15π\frac{5}{12} \cdot \pi r^2 = 15\pi. Divide both sides by π\pi and multiply by 125\frac{12}{5}: r2=36r^2 = 36.
  3. r=6r = 6. The radian formula gives the same equation: 12r2⋅5π6=15π\frac{1}{2}r^2 \cdot \frac{5\pi}{6} = 15\pi.

Why each choice is right or wrong

  • A. Incorrect. This divides the angle by π\pi instead of 2π2\pi, so the sector seems to be 56\frac{5}{6} of the circle: 56πr2=15π\frac{5}{6}\pi r^2 = 15\pi gives r2=18r^2 = 18 and r=32r = 3\sqrt{2}. A full circle is 2π2\pi radians.
  • B. Correct. The sector is 512\frac{5}{12} of the circle, so 512πr2=15π\frac{5}{12}\pi r^2 = 15\pi, r2=36r^2 = 36 and r=6r = 6.
  • C. Incorrect. This uses the arc length formula as if 15π15\pi were a length: r⋅5π6=15πr \cdot \frac{5\pi}{6} = 15\pi gives r=18r = 18. 15π15\pi is an area, so use 12r2θ\frac{1}{2}r^2\theta or the fraction of πr2\pi r^2.
  • D. Incorrect. 36 is r2r^2. Take the square root to get the radius, 6.

Trap Arc length or sector area

An arc is a length and uses the circumference, 2πr2\pi r. A sector is a region and uses the area, πr2\pi r^2. The value from the other formula can appear among the choices, so reread which one the question asks for.

Trap Dividing by the wrong full turn

In degrees a whole circle is 360, and in radians it is 2π2\pi. Dividing a degree measure by 180, or a radian measure by π\pi, measures the angle against half a circle, so the fraction of the circle comes out twice as big. That doubles an arc length or a sector area; when you work backward to a radius, an angle or the whole circle, it throws the answer off in other ways.

Trap Degrees in a radian formula

s=rθs = r\theta and 12r2θ\frac{1}{2}r^2\theta work only when θ\theta is in radians. If the angle is in degrees, either convert it with π180\frac{\pi}{180} or use the fraction θ360\frac{\theta}{360}.

Desmos When Desmos isn’t faster

These questions come down to one fraction of the circle, and setting it up is the real work. That part is faster by hand.

Desmos is still a good calculator for the last step. Type 2pi1072/360 and it shows about 12.57; type 4pi on the next line and it shows the same value, so the arc is 4π4\pi. Keep the division at the end of what you type: in Desmos, what you type right after the slash goes into the denominator until you leave the fraction.

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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.

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

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