Advanced Algebra and Functions practice
Work with quadratics, functions, logarithms, geometry and trigonometry.
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Back to ACCUPLACER subjectsFor f(x) = (x − 2)(x + 5), which values make f(x) = 0?
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Eight questions at your own pace, with explanations after each question or passage group.
Solve the system: 2x + y = 11; x − y = 1.
Linear equations and systems
Practice linear equations and systems with original questions and worked explanations.
Factor completely: x² − 7x + 12.
Factoring
Practice factoring with original questions and worked explanations.
Solve: x² + 2x − 15 = 0.
Quadratics
Practice quadratics with original questions and worked explanations.
f(x) = 2x + 1 and g(x) = x².
Find f(g(3)).
Functions
Practice functions with original questions and worked explanations.
Solve √(x + 5) = x − 1. Check possible solutions.
Rational and radical equations
Practice rational and radical equations with original questions and worked explanations.
What is the remainder when x³ − 2x + 4 is divided by x − 2?
Polynomials
Practice polynomials with original questions and worked explanations.
Solve: log₂(x) = 5.
Exponential and logarithmic equations
Practice exponential and logarithmic equations with original questions and worked explanations.
Find the radius of (x − 3)² + (y + 2)² = 25.
Geometry
Practice geometry with original questions and worked explanations.
A right triangle has opposite side 5 and hypotenuse 13.
What is sin θ for that opposite side?
Trigonometry
Practice trigonometry with original questions and worked explanations.
How to approach the questions
Develop higher algebra skills: systems, factoring, quadratics, functions, rational and radical equations, polynomials, exponential and logarithmic equations, geometry and trigonometry.
Identify the structure before choosing a method. Keep restrictions on denominators, radicals and logarithms visible, and substitute possible solutions into the original equation.
Watch for: Squaring both sides or multiplying by a variable expression can introduce an invalid solution. A correct algebraic manipulation still needs a domain check.
Read worked examplesFor f(x) = (x − 2)(x + 5), which values make f(x) = 0?
AAF practice test
Complete the subject test without feedback between questions. Confirm each answer before moving on; review the full explanation set at the end.
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