100+ Free FTCE Mathematics 6-12 Practice Questions

Algebra

Linear equations and inequalities, slope and linear functions, systems of equations, polynomial operations, factoring, rational expressions, percent, and algebraic word problems.

Advanced Algebra

Quadratic equations and the quadratic formula, logarithms, complex numbers, arithmetic and geometric sequences and series, exponential and absolute-value equations, and inverse functions.

Functions

Domain and range, composition, transformations, exponential modeling, average rate of change, function families, and the definition of a function.

Geometry

Area and volume, the Pythagorean theorem, triangle and polygon angles, similarity and area ratios, circles, special right triangles, surface area, and congruence postulates.

Coordinate Geometry

Distance and midpoint formulas, equations of lines and circles, parallel and perpendicular slopes, and area in the coordinate plane.

Trigonometry

Unit circle and special angles, right-triangle trigonometry, radian-degree conversion, the Pythagorean identity, periodic functions, and real-world applications.

Statistics & Probability

Measures of center, basic and compound probability, the normal distribution and empirical rule, correlation and scatterplots, expected value, and independent events.

Calculus

Limits and indeterminate forms, derivatives and the power rule, tangent lines, integration and definite integrals, critical points, continuity, and the Intermediate Value Theorem.

Mathematical Reasoning

Logic and conditional statements, proof techniques, counterexamples, the contrapositive, and mathematical induction.

Instruction & Assessment (Math Pedagogy)

Diagnosing student misconceptions, error analysis, multiple representations, NCTM Standards for Mathematical Practice, formative and diagnostic assessment, productive struggle, and instructional next steps.