Algebra
12–15% of the ACT math section
Linear, polynomial, radical and exponential relationships, and the systems they make. The ACT’s algebra is broader than the SAT’s and each question is shorter — one move, done fast, then the next question.
Linear, Polynomial & Radical Expressions
Solving an equation is undoing what was done to the variable, in reverse order. A radical is undone by squaring both sides, and squaring can create a solution that was not there — so a radical equation is not finished until the answer has been put back in.
- A
- B
- C
- D
- Square both sides to remove the root
Systems & Inequalities
A system of two lines has one solution, none, or infinitely many, and the ACT likes the last two: it gives one equation with an unknown coefficient and asks for the value that makes the lines coincide or run parallel. Coincident lines are the same equation twice, scaled.
- F
- G
- H
- J
- Infinitely many means the second equation is a multiple of the first
Quadratics & Factoring
Factor when the numbers allow it, complete the square when a vertex is wanted, and use the formula when nothing factors. The choices tell you which: radicals in the choices mean the formula; whole numbers and simple fractions mean it factors. A leading coefficient other than 1 means splitting the middle term.
- A and
- B and
- C and
- D and
- Two numbers with product and sum