GACE Mathematics (522) study guide
GACE Mathematics (522) · Work through your exam, one topic at a time.
This independent study page provides practice for GACE Mathematics (522). Its editorial learning areas include Algebra and functions; Number and quantity; Geometry and measurement; Calculus foundations; Discrete mathematics and reasoning; Probability and statistics. The GACE Mathematics (522) study guide has 6 sections and about 2,550 words.
01Algebra and Functions
Algebra and function practice asks you to move fluently between symbolic, graphical, and verbal representations of relationships. Expect manipulation of polynomial, rational, radical, exponential, and logarithmic expressions; solving equations and inequalities; and reasoning about domain, range, inverse functions, and transformations.
462 words, about 2 min02Number and Quantity
This number and quantity chapter develops whether you can move fluently among fractions, decimals, percents, integers, exponents, radicals, and scientific notation, and whether you can justify why a number is rational or irrational. Items rarely ask for a bare computation; they ask you to choose the representation or operation that fits a situation.
472 words, about 2 min03Geometry and Trigonometry
This geometry and trigonometry chapter covers triangle congruence and similarity, circle properties, coordinate geometry, area and volume, and the trigonometric ratios extended to the unit circle. You should be able to prove relationships, apply the sine and cosine laws to non-right triangles, work in radians, and connect trigonometric functions to their graphs and identities.
425 words, about 2 min04Calculus
Calculus practice develops the ability to move fluently between a function, its rate of change, and its accumulated total. Expect differentiation of composite, implicit and parametric forms, evaluation of definite and improper integrals, and questions that require you to justify a limit before differentiating.
348 words, about 2 min05Discrete Mathematics and Mathematical Reasoning
This domain tests formal reasoning and finite structures: logic and truth values, proof technique, sets, counting, relations, and basic graph and recurrence ideas. Questions reward precision - a correct conclusion with an invalid justification loses marks.
446 words, about 2 min06Statistics and Probability
This statistics and probability chapter explores how data are collected, summarized, and interpreted, and how probability models uncertainty. Expect measures of centre and spread, graphical displays, normal distributions and z-scores, counting-based probability, conditional probability, and critical evaluation of study design and correlation versus causation.
397 words, about 2 min