SAT Algebra: what your AP classes already cover

Linear equations, linear functions, systems and inequalities. For an AP student this is the most familiar domain: it is the arithmetic of straight lines, which every AP math course leans on.

Each row is one SAT Algebra skill and the AP units on this site where you already practice it. Revisit those notes, then work through the two examples below before opening the answers.

Algebra skills, matched to AP units

SAT skill	Where it comes up in AP	Why it carries over
Linear equations in one variable	AP Precalculus, Unit 1	Solving for an unknown is routine in every Precalculus unit; on the SAT the equations are simpler but the clock is tighter.
Linear functions	AP Precalculus, Unit 1 AP Calculus AB, Unit 2	Slope as a constant rate of change (Precalculus Unit 1) is the same idea as a tangent line's slope (Calculus Unit 2).
Linear equations in two variables	AP Precalculus, Unit 1 AP Statistics, Unit 5	Reading the slope and intercept of a line in context is exactly what you do with a least-squares regression line.
Systems of two linear equations in two variables	AP Precalculus, Unit 4	Two equations in two unknowns; Precalculus Unit 4 solves the same systems with a 2x2 matrix inverse.
Linear inequalities in one or two variables	AP Precalculus, Unit 1	Sign charts and inequality reasoning from polynomial and rational functions, in their simplest linear form.

Worked example 1: Linear functions

A line passes through \((2, 7)\) and \((6, 19)\). What is its \(y\)-intercept?

Show the answer and working

Answer: 1

The slope is \(\frac{19-7}{6-2}=3\), so \(7=3(2)+b\) and \(b=1\). In AP Statistics you would read this \(b\) as the predicted value when the explanatory variable is 0.

Worked example 2: Systems of two linear equations in two variables

If \(3x+2y=16\) and \(x-y=2\), what is the value of \(x+y\)?

Show the answer and working

Answer: 6

Substitute \(x=y+2\): \(3(y+2)+2y=16\), so \(5y=10\), \(y=2\) and \(x=4\). Then \(x+y=6\). The same system is \(\begin{bmatrix}3&2\\1&-1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}16\\2\end{bmatrix}\) in AP Precalculus Unit 4.