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The DailySTEP 1
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  • 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.

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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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  • 36free practice questions every day
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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 5

Scaling and square and cubic units

Suppose every length of a figure is multiplied by the same number kk, the scale factor. Then every length, including the perimeter, is multiplied by kk. Every area, including surface area, is multiplied by k2k^2. Every volume is multiplied by k3k^3.

Why: an area multiplies two lengths, and each one grew by kk, so the area grows by k⋅kk \cdot k. A volume multiplies three lengths. In the figure below, rectangle B's sides are 2 times as long as rectangle A's, and its area is 22=42^2 = 4 times as large.

Work backward with roots. If two similar solids have volumes in the ratio 1,000 to 1, their lengths are in the ratio 1,0003=10\sqrt[3]{1{,}000} = 10 to 1, and their surface areas in the ratio 102=10010^2 = 100 to 1.

The rule needs every length to change by the same factor. If only some dimensions change, apply each change on its own: doubling only a box's length doubles its volume, and doubling its length and its width (not its height) multiplies the volume by 4.

Units follow the same pattern, because a unit is a length too. 1 foot is 12 inches, so 1 square foot is 12⋅12=14412 \cdot 12 = 144 square inches and 1 cubic foot is 12⋅12⋅12=1,72812 \cdot 12 \cdot 12 = 1{,}728 cubic inches. 1 meter is 100 centimeters, so 1 square meter is 1002=10,000100^2 = 10{,}000 square centimeters. Converting square or cubic units with the plain length factor, 12 instead of 144, is the classic mistake.

Rectangle B is rectangle A with every length doubled3264AB
Rectangle B is rectangle A with every length doubled Two rectangles side by side. Rectangle A, on the left, has a bottom side labelled 3 and a left side labelled 2, so its area is 6. Rectangle B, on the right, has a bottom side labelled 6 and a right side labelled 4, so its area is 24, which is 4 times A's area.

Worked example Easy

The length and the width of a rectangle are each multiplied by kk, where kk is a positive constant. The area of the new rectangle is 36 times the area of the original rectangle. What is the value of kk?

  1. 66Answer
  2. 1818
  3. 3636
  4. 1,2961{,}296

How to solve it

  1. Both dimensions grow by kk, so the area grows by k2k^2.
  2. k2=36k^2 = 36 and kk is positive, so k=6k = 6.
  3. Check: a 1-by-2 rectangle (area 2) becomes 6 by 12 (area 72), and 72=36⋅272 = 36 \cdot 2.

Why each choice is right or wrong

  • A. Correct. The area factor is k2k^2, so k2=36k^2 = 36 and k=6k = 6.
  • B. Incorrect. This divides 36 by 2 instead of taking the square root. With k=18k = 18, the area would grow by 182=32418^2 = 324.
  • C. Incorrect. 36 is the area factor, k2k^2. The lengths grow by its square root, 6.
  • D. Incorrect. This squares 36 instead of taking its square root: 362=1,29636^2 = 1{,}296. With k=1,296k = 1{,}296, the area would grow far more than 36 times.

Worked example Medium

A rectangular floor is 21 feet long and 9 feet wide. Carpet is sold by the square yard, and 1 yard is 3 feet. How many square yards of carpet are needed to cover the floor exactly?

  1. 2121Answer
  2. 6363
  3. 189189
  4. 1,7011{,}701

How to solve it

  1. Convert each length first: 21 feet is 7 yards and 9 feet is 3 yards.
  2. Area: 7⋅3=217 \cdot 3 = 21 square yards.
  3. Or find 21⋅9=18921 \cdot 9 = 189 square feet and divide by 9, because 1 square yard is 3 feet by 3 feet, 32=93^2 = 9 square feet.

Why each choice is right or wrong

  • A. Correct. The floor is 7 yards by 3 yards, so it is 7⋅3=217 \cdot 3 = 21 square yards.
  • B. Incorrect. This divides 189 square feet by 3, the length conversion, which gives 63. A square yard is 3 feet by 3 feet, which is 9 square feet.
  • C. Incorrect. 189 is the area in square feet. The question asks for square yards.
  • D. Incorrect. This multiplies by 9 instead of dividing: 189⋅9=1,701189 \cdot 9 = 1{,}701. A square yard is bigger than a square foot, so the floor has fewer square yards than square feet.

Worked example Hard

The radius of a right circular cylinder is doubled and its height is cut in half. How does the volume of the new cylinder compare with the volume of the original cylinder?

  1. The volume is unchanged.
  2. The volume is doubled.Answer
  3. The volume is multiplied by 4.
  4. The volume is multiplied by 8.

How to solve it

  1. V=πr2hV = \pi r^2 h. Replace rr with 2r2r and hh with h2\frac{h}{2}: π(2r)2⋅h2=π⋅4r2⋅h2=2πr2h\pi(2r)^2 \cdot \frac{h}{2} = \pi \cdot 4r^2 \cdot \frac{h}{2} = 2\pi r^2 h.
  2. The new volume is 2 times the original.
  3. Check with numbers: r=1r = 1 and h=2h = 2 give π(1)2(2)=2π\pi(1)^2(2) = 2\pi; r=2r = 2 and h=1h = 1 give π(2)2(1)=4π\pi(2)^2(1) = 4\pi, twice as much.

Why each choice is right or wrong

  • A. Incorrect. This assumes doubling one length and halving another cancel out. The radius is squared in πr2h\pi r^2 h, so doubling it multiplies the volume by 4, and halving the height only divides that by 2.
  • B. Correct. The radius change multiplies the volume by 22=42^2 = 4 and the height change multiplies it by 12\frac{1}{2}, so the volume is multiplied by 4⋅12=24 \cdot \frac{1}{2} = 2.
  • C. Incorrect. 4 is the effect of doubling the radius alone. Halving the height then cuts the volume in half: 4⋅12=24 \cdot \frac{1}{2} = 2.
  • D. Incorrect. 8 is 232^3, the factor when every length doubles. Here the height is halved, not doubled, so the k3k^3 rule doesn't apply.

Trap Using k instead of k² or k³

When lengths triple, the area doesn't triple. Ask what kind of quantity the question wants: a length gets kk, an area or surface area gets k2k^2, a volume gets k3k^3. Choices built from the wrong power are common distractors.

Trap Applying the scale rule when only some lengths change

k2k^2 and k3k^3 hold only when every length is multiplied by kk. When a question changes one dimension, or changes different dimensions by different factors, substitute into the formula instead.

Trap Converting square units with the length factor

1 yard is 3 feet, but 1 square yard is 32=93^2 = 9 square feet, not 3. Cubic units need the cube of the length factor. Safest of all: convert each length first, then multiply.

Desmos When Desmos isn’t faster

These questions turn on picking the right power of the scale factor, which is quicker by hand.

If you're unsure, test with numbers in Desmos. For the cylinder example, type pi112 on one line and pi221 on the next. Desmos shows about 6.28 and 12.57, and the second is twice the first.

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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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