100+ Free GACE Mathematics (522) Practice Questions

Number and Quantity (Test I, Subarea I)

The real number system and properties of exponents, including rational exponents and radicals; rational and irrational numbers and their interactions; vector and matrix quantities and operations; ratios, proportions, averages, percents, and unit conversions; scientific notation and orders of magnitude; the complex number system in rectangular and polar form; and precision, accuracy, and absolute and relative error.

Algebra (Test I, Subarea II)

Seeing structure in expressions and rewriting them; arithmetic with polynomials and rational expressions; the remainder theorem and the binomial theorem; creating equations and inequalities to model relationships; solving linear, quadratic, rational, and radical equations and analyzing extraneous solutions; systems of equations including matrix methods; rate of change; intercepts and slope; and finding the zeros of functions.

Discrete Mathematics and Calculus (Test I, Subarea III)

Arithmetic, geometric, and recursive sequences and series; discrete versus continuous models; vertex-edge graphs, trees, networks, and linear programming; logic, quantifiers, and set theory; counting techniques; and calculus topics including limits, the derivative as a limit and rate of change, continuity and differentiability, standard differentiation and integration, the foundational theorems of calculus, and applications such as related rates and optimization.

Functions (Test II, Subarea I)

The function concept and notation, domain and range; interpreting key features of graphs and tables; building functions from contexts and recursive processes; transformations, compositions, and inverses; linear, quadratic, and exponential models; logarithms; constructing and using the unit circle; modeling periodic phenomena; and applying trigonometric identities such as the Pythagorean, double-angle, and sum and difference identities.

Geometry (Test II, Subarea II)

Transformations in the plane and rigid motions; congruence and similarity, including triangle criteria and the AA similarity criterion; geometric proofs and constructions; right-triangle and general trigonometry with the Law of Sines and Law of Cosines; circles, arcs, and sectors; perimeter, area, surface area, and volume; conic sections; cross sections of three-dimensional figures; and coordinate geometry.

Probability and Statistics (Test II, Subarea III)

Summarizing and interpreting categorical and quantitative data with plots and statistics; the normal distribution; two-way frequency tables and conditional relative frequencies; linear regression, correlation, and the distinction from causation; statistical inference and study design; independence and conditional probability; the addition and multiplication rules; the binomial distribution; and expected value and decision making.