SAT Math

Algebra is the largest area: linear equations in one and two variables, inequalities, systems, and interpreting the parts of a linear model. A question that gives a joining fee and a monthly rate is asking whether you can tell which number multiplies the variable.

Advanced Math covers quadratics in their several forms, exponential growth and decay, polynomial expressions, radical equations, and function notation including composition and inverses.

Problem Solving and Data Analysis covers ratios and proportions, percentages, unit conversion, rates, probability from tables, and statistics including mean, median and the effect of an outlier on each. It also covers sampling: whether a conclusion about a population is supported by the group that was actually surveyed.

Geometry and Trigonometry covers angles, triangles including similarity and the Pythagorean theorem, circles in the coordinate plane, area and volume, and right-triangle trigonometry.

A graphing calculator is built into the testing application and available for every question. You may also bring an approved handheld one.

The reference sheet provides area and circumference of a circle, area of a triangle and rectangle, the Pythagorean theorem, the special right triangles, volumes of the common solids, and the number of degrees and radians in a circle.

It does not provide the quadratic formula, the slope formula, the equation of a circle, the laws of exponents or of logarithms, or anything about functions. Those have to be known.

The calculator changes what the questions can ask. Because arithmetic is free, the difficulty sits in setting the problem up rather than in working it out, and a question whose answer requires no thought to compute may require a good deal to formulate.

Answering the wrong quantity. A system of equations produces both x and y, a ratio problem produces two shares and their difference, and a question about a discount may want the reduction or the final price. All of these appear among the options.

Stopping one step early. The value of 5x is not the value of x. The square of the hypotenuse is not the hypotenuse. The work done is not the power. Each of these is a correct number reported at the wrong stage.

Percentage base. A price reduced by 20% and then by 25% has not fallen by 45%, because the second reduction applies to the already reduced amount. Two successive changes always combine to less than their sum.

Unit conversion. A rate given per minute and a time given in hours cannot be multiplied until one of them is converted, and the wrong product is always among the options.

Reversing a relationship. Perpendicular gradients are negative reciprocals, so both the sign and the fraction change. Ohm's law multiplies rather than divides. A check on the units catches most of these in a few seconds.