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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.

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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.

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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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Games

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

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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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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 4

Surface area as the sum of the faces

Surface area is the total area of all the outside faces of a solid, in square units. It is not on the reference sheet, and you don't need a formula for it: list the faces, find each one's area and add.

Rectangular prism (box): six rectangles in three matching pairs, so the surface area is 2(ℓw+ℓh+wh)2(\ell w + \ell h + wh). A box 2 by 3 by 4 has 2(6+8+12)=522(6 + 8 + 12) = 52 square units of surface. A cube with edge ss has six square faces, 6s26s^2 in all.

Cylinder: two circles plus the curved side. Unroll the side and it becomes a rectangle. Its width is the circle's circumference, 2πr2\pi r, and its height is the cylinder's height, so the side's area is 2πrh2\pi rh and the whole surface is 2πr2+2πrh2\pi r^2 + 2\pi rh.

Pyramid: the base plus the triangular faces. Each triangle's height is measured on that face, from the top vertex at a right angle to the face's base edge, not the pyramid's height. When the base is a square and the top vertex is directly above its center, all four faces share this height, the slant height, and the pyramid's height, half of a side of the base and the slant height form a right triangle with the slant height as the hypotenuse.

Read the situation for which faces count. A box with no lid has five faces, and a label wrapped around a can covers only the curved side.

Worked example Easy

A rectangular prism835
A rectangular prism A rectangular box drawn in 3D with its three hidden edges dashed. The front bottom edge is labelled 8, the front left edge (the height) is labelled 3, and the bottom edge running back from the front right corner is labelled 5.

The rectangular prism shown is 8 units long, 5 units wide and 3 units tall. What is the surface area of the prism, in square units?

  1. 6464
  2. 7979
  3. 120120
  4. 158158Answer

How to solve it

  1. The faces come in three pairs: top and bottom are 8⋅5=408 \cdot 5 = 40 each, front and back are 8⋅3=248 \cdot 3 = 24 each, and the two ends are 5⋅3=155 \cdot 3 = 15 each.
  2. Add one face from each pair and double: 2(40+24+15)=2(79)=1582(40 + 24 + 15) = 2(79) = 158.

Why each choice is right or wrong

  • A. Incorrect. 64 is the total length of all 12 edges, 4(8+5+3)4(8 + 5 + 3). Surface area adds the areas of the faces.
  • B. Incorrect. This adds one face from each pair, 40+24+15=7940 + 24 + 15 = 79. A box has six faces, two of each size, so double it.
  • C. Incorrect. 120 is the volume, 8⋅5⋅38 \cdot 5 \cdot 3, in cubic units. Surface area is the total area of the faces.
  • D. Correct. Two faces of each size: 2(40+24+15)=1582(40 + 24 + 15) = 158 square units.

Worked example Medium

A closed right circular cylinder76
A closed right circular cylinder A right circular cylinder standing on one circular base. A diameter across the top face is labelled 6, and the right side is labelled 7, the height. The back half of the bottom edge is dashed because it is hidden.

The closed right circular cylinder shown has a diameter of 6 and a height of 7. What is the total surface area of the cylinder, including both circular ends?

  1. 42π42\pi
  2. 51π51\pi
  3. 60π60\piAnswer
  4. 156π156\pi

How to solve it

  1. The radius is half the diameter: r=3r = 3.
  2. The two circular ends: 2⋅π(3)2=18π2 \cdot \pi(3)^2 = 18\pi.
  3. The curved side unrolls into a rectangle 2π(3)=6π2\pi(3) = 6\pi wide and 7 tall: 6π⋅7=42π6\pi \cdot 7 = 42\pi.
  4. Total: 18π+42π=60π18\pi + 42\pi = 60\pi.

Why each choice is right or wrong

  • A. Incorrect. 42π42\pi is only the curved side. The cylinder is closed, so add the two circular ends, 18π18\pi.
  • B. Incorrect. This adds only one circular end: 9π+42π=51π9\pi + 42\pi = 51\pi. A closed cylinder has a top and a bottom.
  • C. Correct. Two ends, 2π(3)2=18π2\pi(3)^2 = 18\pi, plus the curved side, 2π(3)(7)=42π2\pi(3)(7) = 42\pi, make 60π60\pi.
  • D. Incorrect. This uses the diameter, 6, as the radius: 2π(6)2+2π(6)(7)=72π+84π=156π2\pi(6)^2 + 2\pi(6)(7) = 72\pi + 84\pi = 156\pi. The radius is 3.

Trap Answering with the volume

Volume and surface area of the same box use the same three numbers, and the volume is often among the choices. Surface area is in square units and adds faces; volume is in cubic units and multiplies three lengths.

Trap Missing faces or extra faces

Count the faces before you add. A box has six, in three pairs; a closed cylinder has two ends; an open box or an open can has one fewer. Adding only one face from each pair gives half the right total.

Desmos When Desmos isn’t faster

Surface area is careful bookkeeping: listing every face is the work, and Desmos can't do it for you.

Use Desmos for the final arithmetic if you like. Type 2(40+24+15) on a line and it shows 158.

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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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