Praxis Math 5165 study guide
Praxis Math 5165 · Work through your exam, one topic at a time.
The Praxis Mathematics (5165) test is one of the Praxis Subject Assessments, the family of content-knowledge tests that states and educator-preparation programs use as part of teacher licensure. It is built for candidates who intend to teach mathematics at the secondary level, and it measures mathematical content knowledge rather than classroom pedagogy - the separate Principles of Learning and Teaching tests cover instructional practice. The content is organized into three broad areas: number and quantity, algebra, and functions; geometry and trigonometry; and statistics, probability, and calculus. Because the exam samples widely across undergraduate mathematics, success depends less on memorizing formulas than on fluency with definitions, theorems, and multi-step reasoning under time pressure. The Praxis Math 5165 study guide has 3 sections and about 1,221 words.
01Number and Quantity, Algebra, and Functions
This domain tests structure as much as computation: subsets of the real numbers (natural, whole, integer, rational, irrational), field and closure properties, and why numbers like √2 are irrational. Expect rational exponents and radicals (x^(m/n) = ⁿ√(x^m)), scientific notation, proportional reasoning, percent change, and unit conversion by dimensional analysis.
616 words, about 3 min02Geometry and Trigonometry
Both synthetic and coordinate geometry appear. Know angle relationships formed by parallel lines and transversals, triangle congruence and similarity criteria, the Pythagorean theorem and its converse, special right triangles (45-45-90 and 30-60-90), perimeter, area, surface area, and volume formulas, and the scaling laws: lengths scale by k, areas by k², and volumes by k³.
302 words, about 2 min03Statistics, Probability, and Calculus
Descriptive statistics covers mean, median, mode, range, variance, standard deviation, quartiles, and boxplots; when data are skewed or contain outliers, the median and IQR are resistant while the mean and standard deviation are not. Expect the normal distribution with the 68-95-99.7 rule and z-scores, sampling methods and sources of bias, and the distinction between observational studies and experiments - correlation is not causation.
303 words, about 2 min