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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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    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

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    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.

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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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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.

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Ratios, rates, proportions and units · Lesson 5

Density and other per quantities

Density is mass per unit of volume: density = mass ÷ volume, in units such as grams per cubic centimeter. Ice has a density of about 0.92 gram per cubic centimeter, so 50 cubic centimeters of ice has a mass of about 0.92×50=460.92 \times 50 = 46 grams.

Rearrange the same relationship as needed: mass = density × volume and volume = mass ÷ density.

Many other quantities work the same way. Population density is people per square mile or per square kilometer. Fuel efficiency is kilometers per liter. A price is dollars per pound. Each one is the first quantity divided by the second.

Let the units guide you. Write the units next to each number. Grams per cubic centimeter times cubic centimeters leaves grams. If a mass is in kilograms but the density uses grams, convert first: 1 kilogram is 1,000 grams.

Chain per quantities so the units cancel. If you know kilometers per liter and dollars per liter, find the liters first (kilometers ÷ kilometers per liter), then multiply by dollars per liter. Adding a per amount to a total mixes units and is never right.

Worked example Easy

A rock sample has a mass of 156 grams and a volume of 20 cubic centimeters.

What is the density of the sample, in grams per cubic centimeter?

  1. 539\frac{5}{39}
  2. 7.87.8Answer
  3. 136136
  4. 3,1203{,}120

How to solve it

  1. Density is mass divided by volume.
  2. 156÷20=7.8156 \div 20 = 7.8 grams per cubic centimeter.

Why each choice is right or wrong

  • A. Incorrect. This divides volume by mass, 20÷156=53920 \div 156 = \frac{5}{39}. That is cubic centimeters per gram, the upside-down rate.
  • B. Correct. Density = mass ÷ volume =156÷20=7.8= 156 \div 20 = 7.8 grams per cubic centimeter.
  • C. Incorrect. This subtracts the volume from the mass, 156−20=136156 - 20 = 136. Grams and cubic centimeters can't be subtracted; density divides them.
  • D. Incorrect. This multiplies mass by volume, 156×20=3,120156 \times 20 = 3{,}120. Density is mass divided by volume.

Worked example Medium

Gold has a density of 19.3 grams per cubic centimeter. A gold bar has a mass of 1.93 kilograms. (1 kilogram = 1,000 grams)

What is the volume of the bar, in cubic centimeters?

  1. 0.010.01
  2. 0.10.1
  3. 100100Answer
  4. 37,24937{,}249

How to solve it

  1. The density uses grams, so convert the mass: 1.93×1,000=1,9301.93 \times 1{,}000 = 1{,}930 grams.
  2. Volume = mass ÷ density: 1,930÷19.3=1001{,}930 \div 19.3 = 100 cubic centimeters.
  3. Check: 19.3×100=1,93019.3 \times 100 = 1{,}930 grams.

Why each choice is right or wrong

  • A. Incorrect. This divides density by mass, 19.3÷1,930=0.0119.3 \div 1{,}930 = 0.01. Volume is mass divided by density.
  • B. Incorrect. This divides 1.93 by 19.3 without converting kilograms to grams, giving 0.1. The density is in grams per cubic centimeter, so the mass must be in grams.
  • C. Correct. 1.93 kilograms is 1,930 grams, and 1,930÷19.3=1001{,}930 \div 19.3 = 100 cubic centimeters.
  • D. Incorrect. This multiplies mass by density, 1,930×19.3=37,2491{,}930 \times 19.3 = 37{,}249. Density times volume gives mass, so to find volume, divide mass by density.

Trap Dividing the wrong way

Density is mass ÷ volume, and population density is people ÷ area. The upside-down quotient is often a choice. Say the units out loud, grams per cubic centimeter, and put the first unit on top.

Trap Units that don't match

A density in grams per cubic centimeter needs a mass in grams and a volume in cubic centimeters. A mass in kilograms or a volume in cubic meters must be converted first, and cubic units use the cubed factor.

Trap Adding a per amount instead of multiplying

When one rate leads to another, such as kilometers per liter and then dollars per liter, the second rate multiplies the amount you found. Adding a price per liter to a number of liters mixes units and gives a distractor.

Desmos When Desmos is faster

These questions are one or two operations once the units match, so Desmos works best as a calculator for decimals. Type 1930/19.3 on an expression line and it shows 100.

Desmos can't tell you which way to divide or whether a mass needs converting, so do the unit check first. When a result is a long decimal, Desmos shows it rounded, so compare it with the choices carefully.

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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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