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.

Right triangles and trigonometry · Lesson 4

Complementary angles and finding a side from an angle

The angles of a triangle add up to 180°, so in a right triangle the two acute angles add up to 90°. Angles that add up to 90° are complementary.

Look at the figure below. Side aa is across from angle AA, and it is also the leg that touches angle BB. So sin⁡A=ac\sin A = \frac{a}{c} and cos⁡B=ac\cos B = \frac{a}{c}: the sine of one acute angle equals the cosine of the other. In degrees, sin⁡(x∘)=cos⁡((90−x)∘)\sin(x^\circ) = \cos((90 - x)^\circ), and likewise cos⁡(x∘)=sin⁡((90−x)∘)\cos(x^\circ) = \sin((90 - x)^\circ). For example, sin⁡(20∘)=cos⁡(70∘)\sin(20^\circ) = \cos(70^\circ).

Working backward: if sin⁡(a∘)=cos⁡(b∘)\sin(a^\circ) = \cos(b^\circ) and both angles are between 0∘0^\circ and 90∘90^\circ, then a+b=90a + b = 90. Without that condition other angles can work too, so look for it in the question.

Finding a side from an angle. When you know one acute angle and one side, choose the ratio that links the side you know to the side you want. With a hypotenuse of 10 and a 35° angle, the side opposite the angle is 10sin⁡(35∘)10\sin(35^\circ) and the adjacent side is 10cos⁡(35∘)10\cos(35^\circ). If the unknown is on the bottom of the ratio, you divide: when the side adjacent to a 35° angle is 10, the hypotenuse hh satisfies cos⁡(35∘)=10h\cos(35^\circ) = \frac{10}{h}, so h=10cos⁡(35∘)h = \frac{10}{\cos(35^\circ)}.

Some answer choices keep the expression, such as 10sin⁡(35∘)10\sin(35^\circ). Others are decimals, and then you need a calculator in degree mode. The Desmos block below shows how to switch.

Side a is opposite angle A and adjacent to angle BabcCAB
Side a is opposite angle A and adjacent to angle B Right triangle ABC with the right angle at C, the bottom left corner, marked with a square. A is at the right end of the horizontal leg and B is at the top of the vertical leg. Side BC, the vertical leg, is labelled a. Side AC, the horizontal leg, is labelled b. The hypotenuse AB is labelled c.

Worked example Easy

Which of the following is equal to sin⁡(34∘)\sin(34^\circ)?

  1. cos⁡(34∘)\cos(34^\circ)
  2. cos⁡(56∘)\cos(56^\circ)Answer
  3. cos⁡(124∘)\cos(124^\circ)
  4. cos⁡(146∘)\cos(146^\circ)

How to solve it

  1. The sine of an angle equals the cosine of its complement: sin⁡(x∘)=cos⁡((90−x)∘)\sin(x^\circ) = \cos((90 - x)^\circ).
  2. 90−34=5690 - 34 = 56, so sin⁡(34∘)=cos⁡(56∘)\sin(34^\circ) = \cos(56^\circ).
  3. Check in Desmos, in degree mode: sin(34) and cos(56) both show about 0.5592.

Why each choice is right or wrong

  • A. Incorrect. For an angle between 0° and 90°, the sine and cosine are different unless the angle is 45°. In degree mode, cos⁡(34∘)≈0.8290\cos(34^\circ) \approx 0.8290, while sin⁡(34∘)≈0.5592\sin(34^\circ) \approx 0.5592.
  • B. Correct. 34° and 56° are complementary, because 34+56=9034 + 56 = 90, so sin⁡(34∘)=cos⁡(56∘)\sin(34^\circ) = \cos(56^\circ).
  • C. Incorrect. This adds 90 instead of subtracting from 90: 34+90=12434 + 90 = 124. In degree mode, cos⁡(124∘)≈−0.5592\cos(124^\circ) \approx -0.5592, which is negative, so it doesn't equal sin⁡(34∘)\sin(34^\circ).
  • D. Incorrect. This subtracts from 180 instead of 90: 180−34=146180 - 34 = 146. Angles that add up to 180° are supplementary, not complementary, and cos⁡(146∘)≈−0.8290\cos(146^\circ) \approx -0.8290.

Worked example Medium

A right triangle with a 21° angle21°19x
A right triangle with a 21° angle A right triangle with the right angle at the bottom left, marked with a square. The angle at the right end of the horizontal leg is marked 21°. The hypotenuse is labelled 19. The vertical leg, across from the 21° angle, is labelled x. The horizontal leg is not labelled.

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

  1. 6.86.8Answer
  2. 7.37.3
  3. 15.915.9
  4. 17.717.7

How to solve it

  1. The side labelled xx is across from the 21° angle, and 19 is the hypotenuse. Sine links them: sin⁡(21∘)=x19\sin(21^\circ) = \frac{x}{19}.
  2. Multiply both sides by 19: x=19sin⁡(21∘)x = 19\sin(21^\circ).
  3. In Desmos, in degree mode, type 19sin(21). It shows about 6.809, so x≈6.8x \approx 6.8.

Why each choice is right or wrong

  • A. Correct. x=19sin⁡(21∘)≈19(0.3584)≈6.8x = 19\sin(21^\circ) \approx 19(0.3584) \approx 6.8.
  • B. Incorrect. This uses tangent: 19tan⁡(21∘)≈7.319\tan(21^\circ) \approx 7.3. Tangent compares the two legs, and 19 is the hypotenuse, so the ratio is sine.
  • C. Incorrect. This is what radian mode gives: Desmos reads 19sin(21) as 19 times the sine of 21 radians and shows about 15.9. Switch to degree mode first.
  • D. Incorrect. This uses cosine: 19cos⁡(21∘)≈17.719\cos(21^\circ) \approx 17.7 is the horizontal leg, the side that touches the 21° angle. The side labelled xx is across from the angle.

Trap A calculator in radian mode

Desmos starts in radian mode, so sin(21) there means the sine of 21 radians, a different and wrong number for a question in degrees. Switch to degrees before you type any sine, cosine or tangent of an angle measured in degrees. In the example above, radian mode turns 6.8 into about 15.9, and a radian-mode value can appear among the choices.

Trap Complement, not supplement

The complement of x∘x^\circ is (90−x)∘(90 - x)^\circ. Subtracting from 180 gives the supplement instead. Setting the two angles equal is a mistake too: sin⁡(x∘)=cos⁡(x∘)\sin(x^\circ) = \cos(x^\circ) only when x=45x = 45, for xx between 0 and 90.

Trap Multiplying when the unknown is on the bottom

When the side you want is the hypotenuse, it sits on the bottom of the sine or cosine ratio, so you divide the known side by the sine or cosine. With tangent, the side you want can be on the bottom too. Multiplying instead of dividing gives a value that doesn't fit the triangle, and it can appear among the choices.

Desmos When Desmos is faster

Desmos starts in radian mode. To switch, click the wrench icon (Graph Settings) at the top right of the graph area and choose Degrees. Do this at the start of any question that gives an angle in degrees.

Then type the expression with parentheses around the angle: 19sin(21) shows about 6.809. When the unknown is on the bottom, type the division, such as 10/cos(35), which shows about 12.208.

Quick mode check: in degree mode, sin(30) shows 0.5. If it shows about −0.988, you're still in radians.

Desmos also confirms complement questions. Type sin(34) and cos(56) on two lines in degree mode, and both show about 0.5592.

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