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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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    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.

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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.

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.

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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

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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FAQ

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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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Right triangles and trigonometry · Lesson 1

The Pythagorean theorem and common triples

A right triangle has one 90° angle, marked with a small square. The two sides that form the right angle are the legs. The side across from the right angle is the hypotenuse, and it is always the longest side.

The Pythagorean theorem, on the reference sheet, says a2+b2=c2a^2 + b^2 = c^2, where aa and bb are the legs and cc is the hypotenuse. In the triangle below, the legs are 3 and 4, so c2=9+16=25c^2 = 9 + 16 = 25 and c=5c = 5.

Finding a leg: subtract. If the hypotenuse is 4 and one leg is 3, the other leg is 42−32=7\sqrt{4^2 - 3^2} = \sqrt{7}, not 5. Square the sides, add or subtract, then take the square root at the end.

Common triples are whole-number sides that fit the theorem. Two worth memorizing are 3-4-5 and 5-12-13. Any multiple of a triple is a triple too: 6-8-10 is 3-4-5 doubled. When two sides of a right triangle match a triple, or a multiple of one, in the right positions, you can write down the third side without the arithmetic. The largest number of the triple must be the hypotenuse.

Not every right triangle has whole-number sides. Legs of 2 and 6 give c2=4+36=40c^2 = 4 + 36 = 40, so c=40c = \sqrt{40}. To simplify a square root, pull out the largest perfect-square factor: 40=4⋅10=210\sqrt{40} = \sqrt{4 \cdot 10} = 2\sqrt{10}.

A right triangle with legs 3 and 4435
A right triangle with legs 3 and 4 A right triangle with the right angle at the bottom left, marked with a square. The vertical leg is labelled 3, the horizontal leg is labelled 4, and the hypotenuse, the slanted side across from the right angle, is labelled 5.

Worked example Easy

A right triangle with one leg unknownx1026
A right triangle with one leg unknown A right triangle with the right angle at the bottom left, marked with a square. The vertical leg is labelled 10, the horizontal leg is labelled x, and the hypotenuse is labelled 26.

In the right triangle shown, what is the value of xx?

  1. 2424Answer
  2. 3636
  3. 576576
  4. 21942\sqrt{194}

How to solve it

  1. The hypotenuse is across from the right angle, so it is 26. The legs are 10 and xx.
  2. x2+102=262x^2 + 10^2 = 26^2, so x2+100=676x^2 + 100 = 676 and x2=576x^2 = 576.
  3. x=576=24x = \sqrt{576} = 24.
  4. Shortcut: 10 and 26 are 5 and 13 doubled, so this is the 5-12-13 triangle doubled, and x=2⋅12=24x = 2 \cdot 12 = 24.

Why each choice is right or wrong

  • A. Correct. x2=262−102=676−100=576x^2 = 26^2 - 10^2 = 676 - 100 = 576, so x=24x = 24. Check: 242+102=576+100=676=26224^2 + 10^2 = 576 + 100 = 676 = 26^2.
  • B. Incorrect. This adds the two lengths, 10+26=3610 + 26 = 36. The theorem works with squares, and a leg must be shorter than the hypotenuse, 26.
  • C. Incorrect. 576 is x2x^2. Take the square root to get x=24x = 24.
  • D. Incorrect. This treats 26 as a leg and adds the squares: 262+102=77626^2 + 10^2 = 776, and 776=2194\sqrt{776} = 2\sqrt{194}. The side across from the right angle, 26, is the hypotenuse, so subtract: 262−10226^2 - 10^2.

Worked example Medium

A rectangle has a diagonal of length 41 and a side of length 9. What is the perimeter of the rectangle?

  1. 4949
  2. 9898Answer
  3. 100100
  4. 360360

How to solve it

  1. A diagonal splits the rectangle into two right triangles. The diagonal is the hypotenuse, and the sides of the rectangle are the legs.
  2. The other side is 412−92=1,681−81=1,600=40\sqrt{41^2 - 9^2} = \sqrt{1{,}681 - 81} = \sqrt{1{,}600} = 40.
  3. The perimeter is 2(40)+2(9)=80+18=982(40) + 2(9) = 80 + 18 = 98.

Why each choice is right or wrong

  • A. Incorrect. This adds one length and one width, 40+9=4940 + 9 = 49. A rectangle's perimeter has two of each.
  • B. Correct. The other side is 412−92=40\sqrt{41^2 - 9^2} = 40, so the perimeter is 2(40)+2(9)=982(40) + 2(9) = 98.
  • C. Incorrect. This uses the diagonal as a side of the rectangle: 2(41)+2(9)=1002(41) + 2(9) = 100. The diagonal runs across the inside; find the missing side with the Pythagorean theorem.
  • D. Incorrect. 360 is the area, 40⋅940 \cdot 9. The question asks for the perimeter.

Trap Adding squares when the hypotenuse is given

Before you use a2+b2=c2a^2 + b^2 = c^2, find the side across from the right angle. If that side is given, you are finding a leg, so subtract its square. A choice built from adding the squares would be longer than the hypotenuse, which a leg can never be.

Trap Forcing a triple

A triple works only when its largest number is the hypotenuse. A leg of 3 and a hypotenuse of 4 is not a 3-4-5 triangle; the missing leg is 7\sqrt{7}. Check the positions before you skip the arithmetic.

Trap Stopping at the square

a2+b2a^2 + b^2 gives c2c^2, not cc. A choice equal to the sum of the squares, or to the difference of the squares when you are finding a leg, is waiting for anyone who forgets the square root.

Desmos When Desmos isn’t faster

When the sides match a triple, writing down the answer is faster than typing anything. Otherwise the theorem is two squares and a root, and Desmos is a handy calculator for that last step.

Type sqrt(2626-1010) on a line and Desmos shows 24. Typing sqrt creates the root sign, and what you type in the parentheses goes under it. Writing each square as a product, such as 26*26, saves you from stepping out of an exponent.

When the answer isn't a whole number, Desmos shows a decimal, such as about 6.3246 for 40\sqrt{40}. Compare it with the choices as decimals, or simplify the root by hand.

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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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