Algebra

The SAT asks for a variable less often than it asks for something built from one — $3x + 2$, or $\frac{3}{4}x + 2$ — and the equation it gives you is usually arranged so that the chunk falls out directly. Solving all the way to $x$ works, but it is the long way round on a test that gives you about 95 seconds a question.

A line on the SAT is usually a sentence: a plumber charges, a tank drains, a plant grows. The slope is the rate — what changes per unit of $x$ — and the $y$-intercept is the amount at zero. Given two points, the slope is rise over run, and the test’s favourite question is not what the slope is but what it means.

Recognising when to substitute, when to eliminate, and when a system has no solution because the two lines are parallel. The numbers decide the method: look at the coefficients before you start moving anything.

Solve an inequality the way you solve an equation, with one exception: multiply or divide by a negative and the sign turns round. The other shape the SAT uses is a system of two inequalities and a list of points — and for that you solve nothing. Put each point into both inequalities and see whether both hold.