ILTS Mathematics for Beginners – ILTS 208 Math Study Guide & Practice Tests

Becoming a teacher means proving you know the mathematics you will teach. ILTS Mathematics for Beginners is written for exactly that moment: a beginner-friendly guide to the ILTS Mathematics (test 208) with lessons that explain the reasoning, worksheets and answer keys after every chapter, and two practice tests with detailed explanations.

For busy future teachers

What is inside

• 24 content chapters covering the ILTS Mathematics (test 208)
• Clear lessons that build each topic one idea at a time
• Worksheets after every chapter, with complete answer keys
• Two practice tests with an answer sheet, answer key and detailed explanations
• Includes Number Theory, Proof, and Mathematical Reasoning; Trigonometric Identities, Equations, and Applications; and Teaching Secondary Mathematics: Student Thinking and Instruction
• Printable 456-page PDF, available to download the moment your order is complete

How the chapters are organized

The book moves one chapter at a time through The Real and Complex Number Systems; Number Theory, Proof, and Mathematical Reasoning; Vectors, Matrices, and Linear Systems; Exponents, Radicals, and Rational Expressions; Linear Equations, Inequalities, and Their Systems; Polynomial Expressions, Factoring, and Equations; Quadratic Functions and Conic Sections; Functions, Transformations, Composition, and Inverses; Rational, Radical, Absolute Value, and Piecewise Functions; Exponential and Logarithmic Functions; Sequences, Series, and Mathematical Induction; Trigonometric Functions and the Unit Circle; Trigonometric Identities, Equations, and Applications; Limits and Continuity; Derivatives and Their Applications; Integrals and Their Applications; Lines, Angles, Triangles, and Polygons; Congruence, Similarity, and Geometric Proof; Circles and Coordinate Geometry; Transformations, Solids, and Measurement; Descriptive Statistics and Data Displays; Probability, Distributions, and Expected Value; Sampling, Study Design, and Statistical Inference; and Teaching Secondary Mathematics: Student Thinking and Instruction. Every chapter ends with worksheets and a full answer key, and the final chapter holds the two practice tests with an answer sheet, answer key and detailed explanations.

Who it helps

Designed for future teachers preparing for the ILTS Mathematics (test 208) in Illinois. It also works for teacher-education students, substitute and paraprofessional staff moving toward full licensure, and tutors supporting candidates — anyone who wants a clear path through the mathematics without gaps.

How to study with it

Pick a steady pace — a chapter every few days works well — and finish each chapter’s worksheets before moving on. Use the answer keys to find exactly where a solution went wrong. Finish with the two practice tests, one per sitting, and read every explanation, including the ones you got right.

Helpful links

National context on teacher preparation is available from the U.S. Department of Education and the National Center for Education Statistics. Check your state’s current licensure testing requirement before you register. For more from Mathfa, see the Mathfa Illinois math learning page, ILTS Middle Grades 5-8 Mathematics for Beginners, and the full Mathfa library.

Frequently asked questions