Mathematics for 11th Grade at the 5-Unit Level – All Study Material for the Bagrut (Matriculation) and Exercises with Full

This book was specifically written for 11th-grade students studying mathematics at the level of 5 study units. It is designed to provide the knowledge and skills required for success in the current academic year in mathematics and the matriculation exam itself. The book will accompany students throughout the school year, helping them understand various topics, practice regularly, and prepare for the exam. The book is divided into two main parts: The first part is the theoretical section, which includes comprehensive explanations, simple and detailed examples, and key formulas according to the curriculum. In this section, students are introduced to various topics of study: algebra, sequences, induction, probability, plane geometry, trigonometry, and differential and integral calculus. The material is presented clearly and organized, with a focus on simplifying the understanding of complex concepts. The second part contains exercises of varying levels of difficulty and is aimed at enhancing students' independent learning and problem-solving skills. Each exercise is accompanied by a complete solution, emphasizing each stage of the solution process. This is done to strengthen various problem-solving techniques, establish a clearer understanding of the required level of detail in solving matriculation exam questions, and provide the essential tools for proper solution planning in an orderly and understandable manner. The combination of theory with diverse practice serves as an essential tool for success in exams and assignments.

Chapter Contents:
Sequences – Practice of geometric sequences using formulas for the general term and the sum of a sequence. A significant portion of the questions corresponds to the matriculation level and beyond. Many of the problems involve extensive use of parametric solutions, which are considered more complex. Induction – Application of the mathematical method for proving general claims related to sequences or series of numbers. This method is used to prove the validity of formulas, sequences, and mathematical laws.
Induction – The application of the mathematical method for proving general statements related to sequences or series of numbers. This method is used to prove the correctness of formulas, sequences, and mathematical laws.
Probability – Sample space, dependent and independent events. Intersection and union of events, conditional probability, and Bayes' formula. Two-dimensional diagrams and probability trees for various events. Bernoulli’s formula for accounting for possible combinations of a specific number of successes out of a given number of trials.
Plane Geometry – A full overview of all the theorems and axioms required up to the matriculation level. Theorems and exercises on triangles, quadrilaterals, circles, and their combinations.
Trigonometry – A section dedicated to recognizing and working with trigonometric functions such as sine, cosine, and tangent in right triangles, as well as the sine and cosine rules for "general" triangles. Includes calculations of triangle areas using the sine of the angle between two enclosing sides, parametric expressions for areas, perimeters, and more.
Differential and Integral Calculus – A deep understanding of derivatives, functions, tangents, differential, and integral concepts, including calculations of the area between curves. This section includes theoretical and practical material for analyzing rational functions, root functions and their combinations, and trigonometric functions.