ACT Math · 15% of the test
Intermediate Algebra
Intermediate Algebra covers quadratic and polynomial equations, rational expressions, radicals, exponents, and basic function notation.
What's actually tested
These items test material typically covered in an Algebra 2 course. They overlap heavily with the SAT's Passport to Advanced Math category.
Subtopics
Click any subtopic to see filed practice questions, worked solutions, and a short tactical guide.
Quadratic equations
Solving quadratics by factoring or formula.
Function notation and composition
Evaluating f(x), composing f(g(x)), and inverse functions.
Arithmetic and geometric sequences
Finding the nth term of arithmetic and geometric sequences.
Systems of equations and matrices
Solving 2-by-2 systems and basic matrix arithmetic.
Sample practice questions in this topic
- Easy Quadratic equations What is the sum of the solutions to the equation x² + 2x − 15 = 0?
- Easy Quadratic equations What is the sum of the solutions to the equation x² − 13x + 42 = 0?
- Medium Quadratic equations What is the sum of the solutions to the equation x² − 13x + 42 = 0?
- Medium Quadratic equations What is the sum of the solutions to the equation x² − 7x + 12 = 0?
- Medium Quadratic equations What is the sum of the solutions to the equation x² − 6x + 8 = 0?
- Hard Quadratic equations What is the sum of the solutions to the equation x² + 1x = 0?
- Easy Quadratic equations What is the sum of the solutions to the equation x² − 1x = 0?
- Easy Quadratic equations What is the sum of the solutions to the equation x² + 6x + 5 = 0?
- Medium Quadratic equations What is the sum of the solutions to the equation x² − 2x − 15 = 0?
- Medium Quadratic equations What is the sum of the solutions to the equation x² + 6x + 5 = 0?
- Medium Quadratic equations What is the sum of the solutions to the equation x² − 5x + 4 = 0?
- Hard Quadratic equations What is the sum of the solutions to the equation x² − 5x + 4 = 0?
See all 56 questions in Intermediate Algebra →
How students lose points here
Forgetting both roots of a quadratic, sign errors when applying the quadratic formula, and dropping the negative root of a radical. The good news: nearly every common mistake on this topic comes from one of three or four recurring patterns. Spend an hour reviewing those patterns and your accuracy on this topic typically jumps two or three percentage points immediately, which on a balanced test is worth ten to twenty scaled score points depending on your band.
How to study this topic
Drill the surface forms — every Intermediate Algebra item is one of about a dozen recognizable shapes. A reasonable session looks like fifteen practice items, untimed, with you reading the worked solution after every one — even the questions you got right, because being right by accident teaches nothing. After two or three such sessions, attempt a timed mini-set of ten items. If your accuracy stays above 80%, move on. If it doesn't, drill the lowest-accuracy subtopic for another session before you push forward.