Algebra

The biggest domain, tied with Advanced Math. Linear relationships in every form: equations, systems, inequalities, and the word problems that hide them.

#Linear equations and their forms

Know all three fluently, and know which one a question wants:

• Slope-intercept: y = mx + b — m is the rate, b the starting value. Best for reading a graph or interpreting a context.
• Standard: Ax + By = C — best when you need intercepts fast (set the other variable to 0).
• Point-slope: y − y₁ = m(x − x₁) — best when you're given a point and a slope.

Slope = (y₂ − y₁)/(x₂ − x₁). Parallel lines share it; perpendicular lines have slopes whose product is −1.

#Interpretation questions

A large share of Algebra questions don't ask you to solve anything — they give a model like C = 45h + 120 and ask what the 120 means.

The rule: the coefficient is the rate (per unit of the variable), the constant is the value when the variable is zero. Here, $45 per hour and a $120 fixed charge. Read the units off the variable definitions in the stem, which are always given.

#Systems of two equations

Three methods, in order of how often they're fastest on this test:

1. Graph both in Desmos and read the intersection. Often the whole solve. Works even when the algebra is ugly.
2. Substitution when one variable is already isolated.
3. Elimination when coefficients line up.

Number of solutions is a favourite:

• Different slopes → exactly one solution.
• Same slope, different intercept → no solution (parallel).
• Same slope, same intercept → infinitely many (identical line).

If a question gives ax + by = c and asks for what a makes there be no solution, it's asking you to match slopes.

#Inequalities

Same as equations, with one rule: multiplying or dividing by a negative flips the sign. That's the entire difference and it's where the errors are.

For systems of inequalities, graph them in Desmos — it shades the feasible region for you.

#Absolute value

|x − a| = b → two cases: x − a = b and x − a = −b. Read |x − a| as the distance between x and a, which makes |x − 7| < 3 obviously mean "within 3 of 7", i.e. between 4 and 10.

#Word problems

The translation table, which is most of the work:

Define your variables in writing. h = hours worked. Half of all word-problem errors are solving correctly for a variable you'd defined as something else two minutes earlier.