Math
What the domain tests
The Math section is 70 minutes across two modules, with multiple-choice and student-produced response (SPR) questions; a calculator is allowed throughout. Content falls into four areas: Algebra (linear equations, inequalities, systems, functions), Advanced Math (quadratic, exponential, polynomial, radical, and rational relationships), Problem-Solving and Data Analysis (ratios, percentages, rates, statistics, probability, sampling), and Geometry and Trigonometry (area, volume, angles, right-triangle relationships, trigonometric ratios).
Core rules
- Translate the wording into an equation before computing; define the variable, including its units.
- Linear models: slope is a rate per unit; the y-intercept is the starting value when the input is zero.
- Percent change is (new minus old) divided by old; percent of a number is multiplication, not a change.
- For systems, solve for the requested quantity, not automatically for x.
- SPR answers must be entered without units or commas; fractions and decimals are generally accepted, but an exact fraction is safer when the decimal repeats.
- Check whether a quadratic or radical solution is extraneous in the original equation.
Worked example
A gym charges a $40 joining fee plus $25 per month. A second gym charges $15 per month with a $100 joining fee. After how many months is the total cost equal?
Set 40 + 25m = 100 + 15m. Subtract 15m: 40 + 10m = 100. Subtract 40: 10m = 60, so m = 6. At 6 months both total $190. The trap is stopping at 10m = 60 and answering 60, or solving for the cost instead of the month count.
Traps
- Rounding intermediate values and then choosing an answer that differs by a small amount.
- Confusing percent more than with percent of.
- Missing a second solution after taking a square root.
- Using the wrong units, such as minutes instead of hours, in rate problems.
- In geometry, using diameter as radius or forgetting that volume scales by the cube of a length factor.