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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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1,023 essential SAT words. Browse the list, flip flashcards, or quiz yourself.

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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.

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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

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    Adapts to how you did on Module 1.

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  4. Math · Module 1

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  5. Math · Module 2

    22 questions35 min

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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.

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Probability and conditional probability · Lesson 1

Probability as favorable over total

A probability is a number from 0 to 1 that says how likely something is. When every outcome is equally likely, as when one item is chosen at random, P=favorable outcomestotal outcomesP = \frac{\text{favorable outcomes}}{\text{total outcomes}}. The favorable outcomes are the ones the question asks about. The total is every outcome you could get.

A box holds 6 lemon, 5 cherry and 13 grape candies. One candy is picked at random. There are 6+5+13=246 + 5 + 13 = 24 candies and 5 are cherry, so the probability of cherry is 524\frac{5}{24}.

Not means every other outcome. Count them directly, or subtract from 1. There are 6+13=196 + 13 = 19 candies that are not cherry, so the probability of not cherry is 1924\frac{19}{24}, and 1−5241 - \frac{5}{24} gives the same thing.

A probability can be a fraction, a decimal or a percent: 14\frac{1}{4}, 0.25 and 25% are the same. It is never below 0 or above 1. If your answer is greater than 1, recheck both counts: the total must be the whole group you are choosing from, and the favorable count can never be bigger than the total.

Here the choice is made from the whole group, so the total is everyone. When a question chooses from only part of the group, the total changes. Lesson 3 covers that.

Worked example Easy

A game box holds 12 red tiles, 9 blue tiles and 19 green tiles. One tile is taken from the box at random.

What is the probability that the tile is blue?

  1. 13\frac{1}{3}
  2. 940\frac{9}{40}Answer
  3. 931\frac{9}{31}
  4. 3140\frac{31}{40}

How to solve it

  1. Count every tile: 12+9+19=4012 + 9 + 19 = 40. That is the total.
  2. Count the favorable outcomes: 9 tiles are blue.
  3. Probability =940= \frac{9}{40}, which is 0.225 as a decimal.

Why each choice is right or wrong

  • A. Incorrect. 13\frac{1}{3} treats the three colors as equally likely: one favorable color out of three. The box has different numbers of tiles of each color, so count tiles, not colors.
  • B. Correct. There are 12+9+19=4012 + 9 + 19 = 40 tiles and 9 of them are blue, so the probability is 940\frac{9}{40}.
  • C. Incorrect. This divides the 9 blue tiles by the 12+19=3112 + 19 = 31 tiles that are not blue, which gives 931\frac{9}{31}. The total must include the blue tiles too, which makes it 40.
  • D. Incorrect. 3140\frac{31}{40} is the probability that the tile is not blue: 31 of the 40 tiles are red or green.

Worked example Medium

A playlist has 60 songs. Of these, 18 are rock songs, 25 are pop songs, and the rest are jazz songs. One song from the playlist is played at random.

What is the probability that the song is not a pop song?

  1. 512\frac{5}{12}
  2. 1760\frac{17}{60}
  3. 712\frac{7}{12}Answer
  4. 310\frac{3}{10}

How to solve it

  1. Find the number of jazz songs: 60−18−25=1760 - 18 - 25 = 17.
  2. Not pop means rock or jazz: 18+17=3518 + 17 = 35 songs.
  3. Probability =3560=712= \frac{35}{60} = \frac{7}{12}.
  4. Or use the complement: P(pop)=2560=512P(\text{pop}) = \frac{25}{60} = \frac{5}{12}, so P(not pop)=1−512=712P(\text{not pop}) = 1 - \frac{5}{12} = \frac{7}{12}.

Why each choice is right or wrong

  • A. Incorrect. 512\frac{5}{12} is the probability that the song is pop: 2560=512\frac{25}{60} = \frac{5}{12}.
  • B. Incorrect. This counts only the 17 jazz songs (60−18−25=1760 - 18 - 25 = 17) as not pop, which gives 1760\frac{17}{60}. The 18 rock songs are not pop either.
  • C. Correct. The songs that are not pop are the 18 rock songs and the 17 jazz songs, 35 in all, so the probability is 3560=712\frac{35}{60} = \frac{7}{12}. Check: 1−2560=35601 - \frac{25}{60} = \frac{35}{60}.
  • D. Incorrect. This counts only the 18 rock songs as not pop: 1860=310\frac{18}{60} = \frac{3}{10}. The 17 jazz songs are not pop either.

Trap Leaving the favorable outcomes out of the total

The total is every outcome, including the ones you want. A drawer with 3 black socks and 9 white socks holds 12 socks, so the probability of picking black is 312\frac{3}{12}, not 39\frac{3}{9}. Dividing one group by the other compares the two groups; it isn't a probability.

Trap Counting kinds instead of items

Two colors of socks don't make the chance of black 12\frac{1}{2}. The equally likely outcomes are the individual socks, tiles or people, so count those, not the number of categories.

Trap Answering the opposite event

When a question asks for not something, the probability of the thing itself is often among the choices, and the reverse is true too. Reread the last line of the stem before you pick.

Desmos When Desmos isn’t faster

There is nothing to graph in a counting question. The work is deciding which outcomes count and what the total is, and that happens on paper or in your head.

Desmos still works as a calculator. Type a sum such as 12 + 9 + 19 on a line to see the total, or type a fraction such as 9/40 to see its decimal value, 0.225. That helps when the answer choices are decimals or percents.

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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.

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Same 98-question format, but every question is drawn from the toughest SAT material: Challenging-tier math throughout and the hardest reading.

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

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