SAT Math: domains, examples, and pacing

01The four tested domains

All four domains appear across the Math section. The counts below are College Board’s approximate section distribution, not a prediction of the topics in your next module.

02Algebra: define the variable before solving

A rental costs 12 dollars plus 4 dollars per hour. If the bill is 36 dollars, write $12+4h=36$, then $h=6$. The fixed fee is the intercept; the hourly charge is the slope.

For a system such as $y=2x+1$ and $y=-x+10$, equate the right sides to get $3x=9$, so the intersection is $(3,7)$. If the question asks for $x+y$, entering only the x-coordinate would miss the requested quantity.

In linear-function practice, explain what each coefficient means in the scenario. That check helps detect a correctly solved equation built from the wrong quantities.

03Advanced Math: preserve structure

For $x^2-5x+6=0$, factoring gives $(x-2)(x-3)=0$, so the roots are 2 and 3. A graph can confirm the intercepts, but factoring also gives their exact values and their sum.

For growth $P(t)=200(1.08{)}^t$, the initial value is 200 and the growth rate per time unit is 8%, not 108%. If the problem changes the time unit, change the exponent before reading the rate.

Before dividing by an expression containing a variable, consider when it is zero. Simplifying $(x^2-9)/(x-3)$ to $x+3$ preserves a restriction: $x\ne 3$. A graph or simplification alone can hide the excluded value.

04Data analysis: use the right denominator

An item falls from 80 dollars to 60 dollars. The decrease is 20 dollars, and the percent decrease is $20/80=25\%$. Reversing the change gives $20/60$, a different percentage.

For a probability drawn from a two-way table, circle the eligible group first. “Among students who take art” uses the art group as the denominator, not the whole school.

Separate association from causation. A survey can describe a relationship, but a claim that one variable causes another needs support from the study design, not just a trend line.

05Geometry: mark the relevant length

If a circle has diameter 10, its radius is 5 and its area is $\pi (5{)}^2=25\pi$. Entering 10 as the radius quadruples the area. Mark radius or diameter next to the number before using the formula.

For a right triangle with legs 6 and 8, $c^2=6^2+8^2=100$, so $c=10$. For an acute angle, label opposite, adjacent, and hypotenuse before choosing sine, cosine, or tangent.

The supplied reference information includes several geometry formulas and special right triangles. Know how to identify the quantities the formulas require; having the formula does not label the diagram for you.

06Choose Desmos or algebra deliberately

Graph both equations when an intersection answers the question. Use a table to evaluate a function repeatedly. For exact coefficient relationships or restrictions, algebra can be the shorter, clearer route. The Desmos guide shows both methods.

Zooming until two curves appear to touch is not proof of one solution. Check the coordinates and substitute where appropriate. A decimal close to a fraction also needs the precision requested by the item.

07Pacing and student-produced responses

Thirty-five minutes for 22 presented questions averages about 95 seconds each; it is not a required limit for each item. Let short problems create time for longer ones, and leave a best attempt before marking an unfinished question.

For numeric entry, read Bluebook’s response instructions. Do not enter units, an equation, or a mixed number when the field asks for a number. Keep exact fractions where allowed rather than rounding intermediate values.

Review a module by error type: translation, algebra, calculator entry, graph reading, answer format, or timing. Pick the repeated cause for the next small practice set instead of assuming a section score tells you which domain to skip.

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