Intermediate Algebra
Quadratics, complex numbers, sequences, matrices and functions.
8 skill topics sit under Intermediate Algebra on the ACT Math taxonomy. Each one has its own dedicated page with concept notes and six worked practice questions. Work through the list top to bottom, or jump straight to the topic you struggle with.
This category accounts for a meaningful slice of your overall math score, so spend the time. The fastest way to gain points is to convert one weak topic per week into a strong one — not to skim every topic at surface depth.
Need the formulas at a glance? See the Intermediate Algebra formula sheet. Studying for a specific score range? Use the score-band guides to focus on the topics that move the needle for your current score.
All Intermediate Algebra topics
The Quadratic Formula
Apply x = (−b ± √(b² − 4ac))/(2a) and use the discriminant to count real solutions.
Open topic
Complex Numbers
Operate on a + bi using i² = −1 and find the modulus.
Open topic
Systems of Equations
Solve linear-linear and linear-quadratic systems algebraically.
Open topic
Functions
Evaluate f(x), interpret domain and range, and recognise function notation in problems.
Open topic
Sequences and Series
Use arithmetic and geometric formulas a_n = a_1 + (n−1)d and a_n = a_1·r^{n−1}.
Open topic
Matrices (Basic)
Add, subtract and multiply small matrices and find a 2×2 determinant.
Open topic
Logarithms
Convert between log and exponential form and apply the basic log laws.
Open topic
Quadratic Inequalities
Solve ax² + bx + c > 0 by factoring and reasoning about sign on intervals.
Open topic
Recommended study order
If this category is brand new to you, start with the first three topics in the list above — they tend to be the most foundational. Then work outward to the others. If you're already comfortable, go straight to a recent past paper, identify which Intermediate Algebra question you missed, and drill that specific topic page.
For broader test-prep advice, see our study tips. For real test reference, browse the ACT Math past paper index.