Free Practice Questions for FTCE Mathematics 6-12

Number Sense, Operations & Proportionality

Comparing and converting rational numbers across fractions, terminating and repeating decimals, percentages, and the number line; multi-step order of operations with rational exponents, radicals, grouping symbols, and absolute value; estimating irrational numbers; scientific notation; and ratio and proportion problems including mixtures, rates, measurement conversions, percent growth, taxes, and depreciation.

Algebra

Generating equivalent polynomial, radical, and rational expressions; key features of two-variable relationships and whether a relation is a function; function types and even/odd behavior; properties of equality and laws of exponents; slope, intercepts, and equations of lines; absolute value and quadratic inequalities; systems of linear equations and inequalities; quadratic features and solutions over the real and complex numbers; exponential growth and decay; shifting and scaling transformations; and inverses and composition of functions.

Geometry & Trigonometry

Classifying triangles, quadrilaterals, and solids; angle relationships and polygon angle sums; proofs about lines, angles, triangles, and quadrilaterals; SSS, SAS, ASA, AAS, AA, and HL criteria; rigid motions and dilations; coordinate geometry; cross sections and solids of revolution; scale factors between similar 2D and 3D figures; perimeter, area, surface area, and volume; compass-and-straightedge constructions; chords, secants, tangents, inscribed angles, and sectors; conic sections; right-triangle trigonometry; the laws of sines and cosines; graphs of the six trigonometric functions and periodic modeling; polar and parametric representations; and the language of logic.

Data Analysis, Statistics & Probability

Measures of central tendency and variation; fitting data to a normal distribution and estimating population percentages; interpreting distribution shape; univariate displays such as histograms, box plots, and frequency tables; population totals and margin of error; experimental design, randomized trials, and sources of bias; correlation in scatter plots and two-way tables; linear fits and intercepts; permutations, combinations, tree diagrams, and conditional probability; two-way relative frequency tables; sample spaces; experimental versus theoretical probability; and expected value and standard deviation of a random variable.

Precalculus & Calculus

Vector operations and applications; exponential and logarithmic functions including base e and natural logarithms; the Fundamental Theorem of Algebra and the Factor Theorem; rational functions and their key features; arithmetic and geometric sequences defined explicitly or recursively; limits of sums, products, and quotients; derivatives of algebraic, exponential, logarithmic, and trigonometric functions; applications of differentiation to intervals, concavity, extrema, and tangent lines; antiderivatives and substitution; definite integrals for distance, area, and volume; and binomial expansions.

Student Reasoning & Instructional Practices

Facilitating instruction in mathematical strategies, concepts, and procedures with fluency; giving students opportunities to evaluate reasonableness and assessing the validity of their mathematical arguments; connecting mathematics across contexts and analyzing sequences of concepts for continuity; selecting mathematical representations and instructional tools; analyzing learning progressions across concrete, representational, and abstract modes; interpreting individual student assessment data to differentiate instruction; and analyzing student misconceptions, errors, and gaps to choose instructional approaches.