TExES Mathematics 7-12 (235) Practice Course

This is Part 1 of a 6-part refresher series covering every domain of the TExES Mathematics 7-12 (235) exam. It's built for candidates who have already studied the material and just need a fast, structured recall before test day, not a first-time introduction. Today: real numbers, complex numbers, and number theory (Competencies 001-003). Lesson Objectives ▼ Place rational, irrational, and complex numbers correctly within the nested structure of the number system. Apply field properties, order axioms, and absolute value as distance on the number line. Perform arithmetic with complex numbers, including conjugates and modulus, and explain why the complex numbers are not an ordered field. Apply the Fundamental Theorem of Algebra to count and locate polynomial roots. Use core number theory tools: primes, GCF/LCM, divisibility rules, and modular arithmetic. Lesson Outline ▼ The Real Number System ...

Part 2 of the 6-part TExES Mathematics 7-12 (235) refresher series (see Part 1: Number Concepts ). This is the largest domain on the exam, spanning functions, algebra, exponentials and logarithms, trigonometry, and an introduction to calculus (Competencies 004-010). Lesson Objectives ▼ Work with function basics: domain and range, even/odd symmetry, transformations, inverses, and composition. Analyze linear and quadratic functions, including the quadratic formula and the discriminant. Apply the Fundamental Theorem of Algebra and the Rational Root Theorem to polynomial, rational, and radical functions. Convert between exponential and logarithmic form and apply the log rules. Use the unit circle, trig identities, and the Law of Sines and Law of Cosines. Apply basic differentiation and integration rules, including the Fundamental Theorem of Calculus. Lesson Outline ▼ Functions: The Basics Linear and Quadratic Functions Polynomial, Rational, Radical & Piece...

Part 3 of the 6-part TExES Mathematics 7-12 (235) refresher series (see Part 2: Patterns and Algebra ), covering measurement, the axiomatic structure of Euclidean geometry, triangle and circle theorems, and coordinate and vector geometry (Competencies 011-014). Lesson Objectives ▼ Apply measurement formulas for area, surface area, and volume, and use dimensional analysis to convert units. Understand Euclidean geometry as an axiomatic system built from undefined terms, postulates, and theorems. Apply triangle congruence and similarity shortcuts, the Pythagorean Theorem, and special right triangles. Apply circle theorems and properties of quadrilaterals. Use the distance and midpoint formulas, and analyze geometric transformations and vectors. Lesson Outline ▼ Measurement as a Process Euclidean Geometry as an Axiomatic System Results and Applications of Euclidean Geometry Coordinate, Transformational, and Vector Geometry Exercises Measurement as a Proce...

Part 4 of the 6-part TExES Mathematics 7-12 (235) refresher series (see Part 3: Geometry and Measurement ), covering data description, probability rules, sampling, and statistical inference (Competencies 015-017). Lesson Objectives ▼ Choose appropriate measures of center and spread, and identify distribution shape. Apply the rules of probability, including the complement, addition, and conditional probability rules. Apply counting methods: permutations and combinations. Evaluate sampling methods and sources of bias, and distinguish correlation from causation. Interpret the Central Limit Theorem, confidence intervals, and margin of error. Lesson Outline ▼ Exploring Data Probability Sampling and Statistical Inference Exercises Exploring Data Three measures of center each have a job: the mean is sensitive to outliers, the median resists them and is best for skewed data, and the mode is the only measure that works for categorical data. Spread is measured ...

Part 5 of the 6-part TExES Mathematics 7-12 (235) refresher series (see Part 4: Probability and Statistics ), covering mathematical reasoning, proof, and communication (Competencies 018-019). Lesson Objectives ▼ Apply Polya's four-step problem-solving model and common problem-solving strategies. Distinguish inductive from deductive reasoning, and recognize valid proof structures. Move fluently between verbal, numerical, graphical, and algebraic representations of the same idea. Evaluate whether a given mathematical argument or "proof" is logically valid. Lesson Outline ▼ Mathematical Reasoning and Problem Solving Mathematical Connections and Communication Exercises Mathematical Reasoning and Problem Solving Polya's four-step model is the classic framework: understand the problem, devise a plan, carry out the plan, then look back and check. Common strategies for the second step include drawing a diagram, looking for a pattern, working backward, g...

Part 6, the final part of the TExES Mathematics 7-12 (235) refresher series (see Part 5: Mathematical Processes and Perspectives ), covering how students learn mathematics, instructional design, and assessment (Competencies 020-021). Lesson Objectives ▼ Describe the Van Hiele levels of geometric thinking and the Concrete-Representational-Abstract sequence. Use prior knowledge and common misconceptions to inform instructional planning and differentiation. Distinguish formative, summative, and diagnostic assessment. Distinguish validity from reliability, and weigh selected-response against constructed-response items. Lesson Outline ▼ Mathematics Learning and Instruction Assessment Exercises Mathematics Learning and Instruction The Van Hiele levels describe how geometric thinking develops in order: visualization, analysis, informal deduction, formal deduction, and rigor. Instruction should match a student's current level rather than skip ahead. The Concre...