SAT Math section guide: pacing and Desmos

How the section is built

Math comes after Reading and Writing and a 10-minute break. It has two modules of 22 questions, and each module gets 35 minutes on its own clock. That's 44 questions in 70 minutes.

How you do on Module 1 decides whether you get the easier or the harder Module 2. The test doesn't tell you which one you got, and you can't tell from how hard it feels. What the adaptive second module means explains how that works.

Inside a module you can skip ahead, go back, flag a question with Mark for Review, and change any answer. Click the question number at the bottom of the screen to open the question list and jump anywhere. On test day you can't move on until the module's clock runs out, so if you finish early, use the time on your flagged questions. Once a module ends, you can't go back to it.

Most questions have four choices. About a quarter have none, and you type your answer in a box. Those are called , and you'll get five or six in each module. They can turn up anywhere, even as the first question of Module 2.

Two buttons at the top right stay with you through both modules. Reference opens the reference sheet, and Calculator opens Desmos.

Pacing a module

Every Math module starts with easier questions and gets harder toward the end. That holds for Module 1 and for both versions of Module 2, and the last five questions are the hardest.

35 minutes for 22 questions is about 95 seconds each. Aim for about a minute each on the early questions when the work is short, and spend what you save on the last ones. Check the clock twice:

At question 12, you'd like at least 17:30 left.
At question 18, about 10:00 left gives you two minutes for each of the last five.

If you've spent about 90 seconds on a question and don't know what to write next, pick your best guess, flag it, and move on. With 2:00 left, put an answer in every blank, including a number in every empty grid-in. A wrong answer and a blank both score zero, so a guess can only help.

Pacing each module has the full plan, and Flag and move on covers leaving a question and coming back to it.

Answering the question that was asked

A common way to lose a question you've solved is to hand in the wrong number. Here's a short example.

If $6x-5=31$ , what is the value of $x+3$ ?

Start. Write “find $x+3$ ” at the top of your scratch paper.
$6x-5=31$
Add 5 to both sides.
$6x=36$
Divide both sides by 6.
$x=6$
Add 3, because the question asks for $x+3$ .
$x+3=9$

Write down what the question asks for before you start, and check your last number against it.

Do this: Check the 6 against what you wrote at the top, see that it's $x$ , and add 3.
Not this: Pick 6 because solving for $x$ is what you always do.

6 is the right value of $x$ and still the wrong answer. On a multiple-choice question, 6 is often one of the choices, waiting for anyone who stops one step early.

Stopping early is one way it goes wrong. You can also solve for the letter the question mentions most instead of the one it asks for. Or you can give the wrong one of a pair: $y$ when it asks for $x$ , the smaller solution when it asks for the larger, or one coordinate when it asks for their sum.

Units count too. If the times are in minutes and the last line asks for hours, divide by 60 before you answer. Units, percents, and grid-in entry rules works through these.

On a grid-in, no list of choices can show you that your number is off. Read the last line once more before you type.

Figures

When a question has a figure, copy it onto your scratch paper and write every given length, angle and mark on it. You can't mark the screen in Math. When a geometry question has no figure, sketch one.

A math figure is drawn to scale unless a note under it says “Figure not drawn to scale.” Without that note, you can estimate from the picture. If you work out an angle as $30^\circ$ and it's drawn wider than a square corner, recheck your work. With the note, go by the numbers and marks only.

Either way, a corner that looks square isn't a right angle until the figure shows the small square or the question says so. The same goes for lines that look parallel.

What the reference sheet gives you

The reference sheet has these formulas:

Shape	Formula
Circle	$A = \pi r^2$ and $C = 2\pi r$
Rectangle	$A = \ell w$
Triangle	$A = \tfrac{1}{2}bh$
Right triangle	$c^2 = a^2 + b^2$
Box	$V = \ell wh$
Cylinder	$V = \pi r^2h$
Sphere	$V = \tfrac{4}{3}\pi r^3$
Cone	$V = \tfrac{1}{3}\pi r^2h$
Rectangular pyramid	$V = \tfrac{1}{3}\ell wh$

It also shows the two special right triangles:

Angles	Sides, shortest to longest
$30^\circ, 60^\circ, 90^\circ$	$x,\ x\sqrt{3},\ 2x$
$45^\circ, 45^\circ, 90^\circ$	$s,\ s,\ s\sqrt{2}$

It also says that a full circle is $360$ degrees, or $2\pi$ , and that the angles of a triangle add up to $180$ degrees.

That's the whole sheet. Learn it before test day, so you only open it to check a special triangle or a volume. Anything not on it has to come from memory, including the formula, the formula, percent change, sine, cosine and tangent, the of a circle, and the mean. Formulas that are not on the reference sheet covers them.

When to open Desmos

Practice on the free College Board version so nothing in it is new on test day. In Bluebook it opens on the Graphing tab, with the graph on top and the rows you type in underneath. The practice site puts the rows to the left of the graph instead.

Opening it and typing takes about ten seconds before you see anything, so a short hand solution is often done first. Open it when typing is shorter than the hand work, or when it checks a step you'd worry about.

The question	What to do
An equation with $x^2$ , a square root or fractions	Put each side on its own `y=` row, then click where they cross
Two equations at once, or “how many solutions”	Put each on its own row, then click or count the crossings
“Which is equivalent”	Graph the original and each choice
Several values of one	Define it once with `f(x)=`
A table of points and a line or curve through them	Type the points into a table and fit the line
Sine, cosine or tangent of an angle in degrees	Switch to Degrees first, since it starts in radians
Area, volume, percents and rates	Type the arithmetic on one row
An equation that's already factored or one step from solved	Solve it by hand
A table, a study, an angle figure, or “What does 45 represent?”	Nothing to graph, so use a row for arithmetic at most

Learn one typing rule before anything else. After you type /, everything you type stays in the bottom of the fraction until you press the right arrow. Fractions and the right arrow shows it, and Exponents and roots covers powers.

Solving by graphing and Desmos for data and regression go further, and each math skill lesson says how Desmos helps on its questions, or that it doesn't.

Checks that catch slips

Count the facts the question gives you and tick each one off on scratch paper as you use it. When you're down to two choices, check both against every fact. The wrong one fits part of the question and fails another part.

When a minus sign sits in front of parentheses, write out the next line and change every sign inside.

Change the sign of every term inside the parentheses.

Right: $5-(x-3)=5-x+3=8-x$
Wrong: $5-(x-3)=5-x-3=2-x$

The minus in front applies to the $-3$ too, and minus $-3$ is plus 3.

Put your answer back into the original equation or sentence. If you copied something wrong partway through, checking a later line won't catch it.

When the choices are numbers or expressions, you can sometimes test them instead of solving. Plugging in numbers and working backward shows when that's quicker.

Typing a grid-in answer

The left side of the screen lists the entry rules, the same ones on every grid-in, and the Answer Preview under the box shows what you typed. Check the preview before you move on. Here are the rules in short:

A positive answer can use up to 5 characters. A negative answer gets 6, because the minus sign takes its own character. The decimal point and the slash count too.
Leave out dollar signs, percent signs, commas and units. $1,250 goes in as 1250.
A fraction doesn't have to be reduced. If it won't fit in 5 characters, type its decimal.
Type a mixed number like $1\frac{2}{5}$ as 7/5 or 1.4, never as 1 2/5.
A decimal that keeps going has to fill all five characters. As a decimal, $\frac{1}{6}$ goes in as .1666, .1667, 0.166 or 0.167. A shorter .17 is marked wrong.
When more than one answer works, type just one of them.

What the box accepts and Fractions and decimals that don't fit go through each rule with examples.

Which lesson to read

The questions come from four areas, mixed together through each module. By College Board's published breakdown, Algebra and Advanced Math are about 35% of the section each and the other two areas about 15% each, so practice on the first two pays off most. Under each area below is roughly how many questions that makes in a module, and the lesson for each kind of question.

Algebra, about 7 or 8 questions a module:

The question is about	Read
Solving an equation with one , or writing one from a story	Linear equations in one variable
A linear function's values, its equation, or what a number in it means	Linear functions
A line's slope and , or a parallel or perpendicular line	Linear equations in two variables
Two linear equations at once	Systems of two linear equations
“At most,” “at least,” or a shaded graph	Linear inequalities

Advanced Math, about 7 or 8:

The question is about	Read
Rewriting an expression to match a choice	Equivalent expressions
Equations with squares, square roots or , or a line meeting a curve	Nonlinear equations and systems
Quadratic and functions and their graphs	Nonlinear functions

Problem-Solving and Data Analysis, about 3 or 4:

The question is about	Read
Rates, and converting units	Ratios, rates, proportional relationships, and units
Percent of a number and percent change	Percentages
Mean, , range, and data plots	One-variable data
A or a model that fits data	Two-variable data
Probability from a table or a description	Probability
A sample's estimate and	Inference from sample statistics
What a study or experiment can show	Evaluating statistical claims

Geometry and Trigonometry, about 3 or 4:

The question is about	Read
Area and volume, including surface area	Area and volume
Angles, parallel lines and	Lines, angles, and triangles
Right triangles, sine, cosine and tangent	Right triangles and trigonometry
A circle's equation, and radians	Circles

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