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The DailySTEP 1

Three hearts. A miss costs one.
Streaks pay. ×2 from three in a row, ×3 from six.
Your longest streak. Beat it tomorrow.

Full-length tests

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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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1
Play the Daily.

A quick run with three hearts. String right answers together and the questions get harder and the points multiply.
Expression of IdeasTransitions

Jazz pianist Mary Lou Williams composed hundreds of works. ______ she wrote arrangements for bands led by Duke Ellington and Benny Goodman.

AHowever,Your pick

BIn addition,Correct

Why: the second sentence adds another accomplishment. Nothing is being contrasted.

2
Miss one, learn why.

Every question is tagged by domain and skill, and every answer comes with an explanation.
3
Drill that skill.

Practice any single skill at any difficulty, or just the questions you got wrong.
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

9 easy, 9 medium, 9 hard and 9 challenging questions free every day, each with a full explanation. Filter by section, domain, skill and difficulty. Resets at midnight Central Time.

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.

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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

C~~100%~~The trap

D104%

Check with $100: $100then$120then$96

Turn each change into a multiplier.
Up 20% means × 1.20. Down 20% means × 0.80.
Apply them in order.
1.20 × 0.80 = 0.96
Read the answer.
The final price is 96% of the original. That’s B.
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.

Reading & Writing · Module 1
27 questions32 min
Reading & Writing · Module 2
27 questions32 min

Adapts to how you did on Module 1.
Break
10 min
Math · Module 1
22 questions35 min
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

Peakscor by the numbers

36free practice questions every day
98questions in every full-length test
1,023SAT vocabulary words
1.5×extended-time option on every test

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The Daily, every day
36 practice questions a day, each with an explanation: 9 easy, 9 medium, 9 hard, 9 challenging
Full-length Test A and Challenge Test 1
All 1,023 vocabulary words: browse, flashcards and quiz
Each Learn module’s overview and first lesson, and the 20-question diagnostic
PEAK Survivor’s first map, plus the opening levels of Hole and Peak Defense

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Peak Plan, day by day to test day

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FAQ

Questions, answered.

The Daily, plus 36 practice questions every day: 9 easy, 9 medium, 9 hard and 9 challenging, each with a full explanation. Full-length Test A, Challenge Test 1 and all 1,023 vocabulary words are free too, as are the 20-question diagnostic, each Learn module’s overview and first lesson, and PEAK Survivor’s first map. 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, and every game map and level. 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 Central Time. You get a fresh 9 easy, 9 medium, 9 hard and 9 challenging.

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.

Nonlinear equations and systems · Lesson 1

Solving quadratic equations

A quadratic equation has $x^2$ as its highest power. Before solving, get it into standard form: everything on one side and 0 on the other, $ax^2 + bx + c = 0$ . A quadratic can have two real solutions, one, or none (Lesson 2 shows how to tell).

Square roots, when there is no separate $x$ -term. In $(x - 3)^2 = 16$ , the inside is 4 or $-4$ , so $x - 3 = \pm 4$ and $x = 7$ or $x = -1$ . The $\pm$ matters: both 4 and $-4$ square to 16.

Factoring, when the numbers are friendly. For $x^2 - 5x - 14 = 0$ , find two numbers that multiply to $-14$ and add to $-5$ : $-7$ and 2. So $(x - 7)(x + 2) = 0$ . A product is 0 only when one of its factors is 0, so $x - 7 = 0$ or $x + 2 = 0$ , which gives $x = 7$ or $x = -2$ . When each factor is $x$ plus or minus a number, the solutions have the opposite signs of those numbers. With a coefficient, as in $2x - 5 = 0$ , solve the factor: $x = \frac{5}{2}$ .

The quadratic formula always works: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Use it when factoring isn't quick or the answer choices contain square roots. The whole numerator is divided by $2a$ , not just the $-b$ .

Completing the square turns the equation into the square-root kind. For $x^2 + 6x = 7$ , add the square of half of 6, which is 9, to both sides: $(x + 3)^2 = 16$ , so $x + 3 = \pm 4$ and $x = 1$ or $x = -7$ . It is quickest when $a = 1$ and $b$ is even.

Two habits save points. Divide out a common number first: $2x^2 - 8x - 10 = 0$ becomes $x^2 - 4x - 5 = 0$ . But never divide both sides by $x$ : in $3x^2 = 12x$ , dividing by $x$ loses the solution $x = 0$ . Move everything to one side and factor instead: $3x(x - 4) = 0$ , so $x = 0$ or $x = 4$ .

The solutions of $ax^2 + bx + c = 0$ are the $x$ -intercepts of the graph of $y = ax^2 + bx + c$ , as the graph below shows.

The graph of

y = x^2 - 2x - 8

An upward-opening parabola with its vertex at (1, -9). It crosses the x-axis at (-2, 0) and (4, 0), so the equation x^2 - 2x - 8 = 0 has the two solutions -2 and 4.

Worked example Easy

x^2 - 5x - 14 = 0

What are the solutions to the given equation?

$x = -7$ and $x = 2$
$x = -2$ and $x = 7$ Answer
$x = -4$ and $x = 14$
$x = -1$ and $x = 14$

How to solve it

Look for two numbers that multiply to $-14$ and add to $-5$ : $-7$ and 2.
Factor: $(x - 7)(x + 2) = 0$ .
Set each factor equal to 0: $x - 7 = 0$ gives $x = 7$ , and $x + 2 = 0$ gives $x = -2$ .
Check $x = 7$ : $49 - 35 - 14 = 0$ . Check $x = -2$ : $4 + 10 - 14 = 0$ .

Why each choice is right or wrong

A. Incorrect. These are the numbers inside the factors, $-7$ and 2, with their signs kept. Each solution makes its factor 0, so $x - 7 = 0$ gives $x = 7$ and $x + 2 = 0$ gives $x = -2$ .
B. Correct. $x^2 - 5x - 14 = (x - 7)(x + 2)$ , and each factor is 0 at $x = 7$ or $x = -2$ . Both values make the left side 0.
C. Incorrect. This comes from the quadratic formula without dividing by $2a$ : $5 \pm \sqrt{25 + 56} = 5 \pm 9$ , which gives 14 and $-4$ . Dividing by $2a = 2$ gives 7 and $-2$ .
D. Incorrect. This uses $(x - 14)(x + 1)$ , whose numbers multiply to $-14$ but add to $-13$ , so it expands to $x^2 - 13x - 14$ . The two numbers must also add to $-5$ .

Worked example Medium

2(x + 1)^2 - 128 = 0

What is the positive solution to the given equation?

$7$ Answer
$9$
$8\sqrt{2} - 1$
$63$

How to solve it

There is no separate $x$ -term, so isolate the square. Add 128: $2(x + 1)^2 = 128$ . Divide by 2: $(x + 1)^2 = 64$ .
Take square roots, both signs: $x + 1 = 8$ or $x + 1 = -8$ .
Subtract 1: $x = 7$ or $x = -9$ . The positive solution is 7.
Check: $2(8)^2 - 128 = 128 - 128 = 0$ .

Why each choice is right or wrong

A. Correct. $(x + 1)^2 = 64$ gives $x + 1 = \pm 8$ , so $x = 7$ or $x = -9$ , and 7 is the positive one.
B. Incorrect. This adds 1 to 8 instead of subtracting it, which gives $x = 9$ . From $x + 1 = 8$ , subtract 1 to get $x = 7$ .
C. Incorrect. This skips dividing by 2 and takes the square root of 128: $x + 1 = \sqrt{128} = 8\sqrt{2}$ , so $x = 8\sqrt{2} - 1$ . The 2 multiplies the square, so divide by it first to get $(x + 1)^2 = 64$ .
D. Incorrect. This forgets to take the square root: it treats $(x + 1)^2 = 64$ as $x + 1 = 64$ , so $x = 63$ . Undo the square with a square root, $x + 1 = \pm 8$ .

Worked example Hard

x^2 - 6x + 4 = 0

Which of the following is a solution to the given equation?

$-3 + \sqrt{5}$
$3 + \sqrt{5}$ Answer
$3 + 2\sqrt{5}$
$6 + 2\sqrt{5}$

How to solve it

No two integers multiply to 4 and add to $-6$ , and the choices contain square roots, so use the formula or complete the square.
Formula with $a = 1$ , $b = -6$ , $c = 4$ : $x = \frac{6 \pm \sqrt{36 - 16}}{2} = \frac{6 \pm \sqrt{20}}{2}$ .
$\sqrt{20} = 2\sqrt{5}$ , so $x = \frac{6 \pm 2\sqrt{5}}{2} = 3 \pm \sqrt{5}$ . Divide both terms by 2.
Completing the square gives the same result: $x^2 - 6x = -4$ , add 9 to both sides, $(x - 3)^2 = 5$ , so $x = 3 \pm \sqrt{5}$ .

Why each choice is right or wrong

A. Incorrect. This uses $b = -6$ in place of $-b$ at the start of the formula, which gives $\frac{-6 \pm 2\sqrt{5}}{2} = -3 \pm \sqrt{5}$ . The formula starts with $-b$ , which is 6 here.
B. Correct. The formula gives $\frac{6 \pm 2\sqrt{5}}{2} = 3 \pm \sqrt{5}$ , and completing the square gives $(x - 3)^2 = 5$ , the same two solutions.
C. Incorrect. This divides only the 6 by 2 and leaves $2\sqrt{5}$ whole. The fraction bar divides the entire numerator, so both terms are halved.
D. Incorrect. This is the numerator $6 + \sqrt{20}$ written as $6 + 2\sqrt{5}$ without dividing by $2a = 2$ .

Trap Keeping the signs from the factors

$(x - 7)(x + 2) = 0$ has solutions 7 and $-2$ , not $-7$ and 2. The SAT often lists the pair with the factors' signs kept as a choice. Plug one solution back in for a two-second check.

Trap Losing a solution

Two moves lose solutions. Taking only the positive square root turns $(x - 3)^2 = 16$ into $x = 7$ alone and loses $x = -1$ . Dividing both sides by $x$ turns $3x^2 = 12x$ into $x = 4$ alone and loses $x = 0$ . Write $\pm$ every time you take a square root, and factor out $x$ instead of dividing by it.

Desmos When Desmos is faster

Move everything to one side and graph the result as $y =$ , such as $y = x^2 - 5x - 14$ . Click the curve and Desmos marks its $x$ -intercepts with gray points. Click each one to see its coordinates, here $(-2, 0)$ and $(7, 0)$ . The $x$ -coordinates are the solutions.

If you'd rather not rearrange, graph each side as its own $y =$ and click the points where the graphs cross. Their $x$ -coordinates are the solutions.

When the solutions are irrational, Desmos shows rounded decimals, such as 5.236 for $3 + \sqrt{5}$ . Type each answer choice on a new line, such as 3 + sqrt(5), to see its decimal and compare. For an equation that factors at a glance, solving by hand is just as fast.

Your progress

How you’re doing across daily practice and full-length tests.

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Practice

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Difficulty

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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.

Free every day. Pro when you're serious.

Practice free every day. Pro removes the limits. Peak adds the full course and a plan to test day.

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✓ 9 easy + 9 medium + 9 hard + 9 challenging daily
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✓ The 20-question Learn diagnostic
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Level up your SAT skills.

The real test, rehearsed.

One run a day. One skill at a time.

Play the Daily.

Miss one, learn why.

Drill that skill.

Beat your best.

Built around the real SAT blueprint.

Free daily practice

Real SAT timing

Adaptive full-length tests

Vocabulary

Your progress

Games

Every answer, explained.

Turn each change into a multiplier.

Apply them in order.

Read the answer.

Why not 100%?

What test day looks like.

Reading & Writing · Module 1

Reading & Writing · Module 2

Break

Math · Module 1

Math · Module 2

Peakscor by the numbers

Free every day. Pro when you’re serious.

Free

Pro

Peak

Questions, answered.

What’s free?

What do Pro and Peak cost?

What does a full-length test include?

Do the tests adapt to me?

Which timing options are there?

How does the Daily work?

When do my free questions reset?

Is Peakscor affiliated with the College Board?

Your next point starts today.

Solving quadratic equations

Worked example Easy

How to solve it

Why each choice is right or wrong

Worked example Medium

How to solve it

Why each choice is right or wrong

Worked example Hard

How to solve it

Why each choice is right or wrong

Trap Keeping the signs from the factors

Trap Losing a solution

Desmos When Desmos is faster

Your progress

Practice

Full-length tests

Challenge Tests Hardest of the hardest

Vocab

Free every day. Pro when you're serious.

FREE

PRO

PEAK