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

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

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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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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 5

Radians and degrees

Angles can be measured in degrees or in radians. The reference sheet says a full circle is 360 degrees and also 2π2\pi radians, so 180∘=π180^\circ = \pi radians. Every conversion comes from that one fact.

Degrees to radians: multiply by π180\frac{\pi}{180}. For 120∘120^\circ: 120⋅π180=2π3120 \cdot \frac{\pi}{180} = \frac{2\pi}{3}. Radians to degrees: multiply by 180π\frac{180}{\pi}. For 3π2\frac{3\pi}{2} radians: 3π2⋅180π=270∘\frac{3\pi}{2} \cdot \frac{180}{\pi} = 270^\circ. A quick way to do the second one: replace π\pi with 180 and simplify.

Know the common angles: 30∘=π630^\circ = \frac{\pi}{6}, 45∘=π445^\circ = \frac{\pi}{4}, 60∘=π360^\circ = \frac{\pi}{3}, 90∘=π290^\circ = \frac{\pi}{2} and 180∘=π180^\circ = \pi. So the angles of any triangle add up to π\pi radians, and the two acute angles of a right triangle add up to π2\frac{\pi}{2}.

A radian measure doesn't have to include π\pi. An angle of 1 radian is 180π\frac{180}{\pi} degrees, about 57.3∘57.3^\circ.

Worked example Easy

What is the measure, in radians, of an angle of 150∘150^\circ?

  1. 5π6\frac{5\pi}{6}Answer
  2. 6π5\frac{6\pi}{5}
  3. 5π3\frac{5\pi}{3}
  4. 27,000π\frac{27{,}000}{\pi}

How to solve it

  1. Multiply by π180\frac{\pi}{180}: 150⋅π180=150π180150 \cdot \frac{\pi}{180} = \frac{150\pi}{180}.
  2. Simplify by dividing the top and bottom by 30: 5π6\frac{5\pi}{6}.
  3. Check: 5π6\frac{5\pi}{6} is a bit less than π\pi, and 150∘150^\circ is a bit less than 180∘180^\circ.

Why each choice is right or wrong

  • A. Correct. 150⋅π180=5π6150 \cdot \frac{\pi}{180} = \frac{5\pi}{6}.
  • B. Incorrect. This flips the fraction, using 180150=65\frac{180}{150} = \frac{6}{5}. 6π5\frac{6\pi}{5} radians is 216∘216^\circ, more than 180∘180^\circ.
  • C. Incorrect. This uses 90∘90^\circ for π\pi radians: 15090π=5π3\frac{150}{90}\pi = \frac{5\pi}{3}. π\pi radians is 180∘180^\circ.
  • D. Incorrect. This multiplies by 180π\frac{180}{\pi}, the factor for radians to degrees: 150⋅180π=27,000π150 \cdot \frac{180}{\pi} = \frac{27{,}000}{\pi}. From degrees to radians, multiply by π180\frac{\pi}{180}.

Worked example Medium

An angle measures 7π12\frac{7\pi}{12} radians. What is the measure of the angle, in degrees?

  1. 52.552.5
  2. 105105Answer
  3. 210210
  4. 7π22,160\frac{7\pi^2}{2{,}160}

How to solve it

  1. Multiply by 180π\frac{180}{\pi}: 7π12⋅180π\frac{7\pi}{12} \cdot \frac{180}{\pi}.
  2. The π\pis cancel: 7⋅18012=7⋅15=105\frac{7 \cdot 180}{12} = 7 \cdot 15 = 105.
  3. The shortcut gives the same thing: replace π\pi with 180 to get 7⋅18012=105\frac{7 \cdot 180}{12} = 105.

Why each choice is right or wrong

  • A. Incorrect. This uses 90∘90^\circ for π\pi: 7⋅9012=52.5\frac{7 \cdot 90}{12} = 52.5. π\pi radians is 180∘180^\circ.
  • B. Correct. 7π12⋅180π=7⋅18012=105\frac{7\pi}{12} \cdot \frac{180}{\pi} = \frac{7 \cdot 180}{12} = 105 degrees.
  • C. Incorrect. This uses 360∘360^\circ for π\pi: 7⋅36012=210\frac{7 \cdot 360}{12} = 210. A full circle, 2π2\pi radians, is 360∘360^\circ, so π\pi alone is 180∘180^\circ.
  • D. Incorrect. This multiplies by π180\frac{\pi}{180}, the factor for degrees to radians: 7π12⋅π180=7π22,160\frac{7\pi}{12} \cdot \frac{\pi}{180} = \frac{7\pi^2}{2{,}160}. To get degrees, the π\pi has to cancel.

Trap Using the wrong conversion factor

Degrees to radians multiplies by π180\frac{\pi}{180}; radians to degrees multiplies by 180π\frac{180}{\pi}. When a radian measure is written with π\pi, such as 7π12\frac{7\pi}{12}, the π\pi cancels on the way to degrees; if your answer in degrees still has π\pi in it, or has π2\pi^2, you used the wrong factor.

Trap π radians is 180°, not 360°

A full circle is 2π2\pi radians, so π\pi alone is half a circle, 180∘180^\circ. Using 360 for π\pi doubles every answer in degrees, and using 90 halves it.

Trap Answering in the wrong unit

When a question gives an angle in radians and asks for degrees, or the other way around, make sure your last step converts. A value in the wrong unit can appear among the choices.

Desmos When Desmos isn’t faster

Conversions are one multiplication, so they're quick by hand, and the radian or degree setting doesn't change plain arithmetic.

To check radians to degrees, replace π\pi with 180 as you type: 180*7/12 shows 105. For degrees to radians, divide by 180: 150/180 shows about 0.8333, which is 56\frac{5}{6}, so the angle is 5π6\frac{5\pi}{6} radians.

Desmos also knows pi: typing 7pi/12 shows about 1.8326, the angle in radians as a decimal, if a choice is written that way.

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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.

Vocab

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

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