About the Exercises for Grades 11-12

Learn Basic Algebra, Functions, Graphs and more. This tutorial contains over 800 practice exercises and lessons in the following topics:
  • Unit I. Review of Basic Algebra
    The Real Number System, Absolute Values, Exponents and Radicals, Polynomials: Special Products and Factoring, Quadratic Equations, Solving Equations, Solving Inequalities.
  • Unit II. Functions and Graphs
    The Cartesian Plane, Graphs of Equations, Lines in the Plane, Functions, The Graph of Functions, Combinations of Functions, Inverse Functions.
  • Unit III. Systems of Equations and Inequalities
    System Of Linear Equations, Linear System in More Than two Variables, System of Inequalities.
  • Unit IV. Matrices and Determinants
    Matrices and Systems of Linear Equations, Operations with Matrices, The Inverse of a Square Matrix, The Determinants of a Square Matrix.
  • Unit V. Polynomial and Rational Functions
    Quadratic Functions, Polynomial Functions of Higher Degree, Polynomial Division and Synthetic Division, Complex Numbers, The Fundamental Theorem of Algebra, Rational Functions, Partial Functions, The Binomial Theorem.
  • Unit VI. Exponential and Logarithmic Functions
    Quadratic Functions, Polynomial Functions of Higher Degree, Polynomial Division and Synthetic Division, Solving Exponential and Logarithmic Equations, Exponential and Logarithmic Applications.
  • Unit VII. Sequences, Counting Principles, and Probability
    Sequences and Summation Notation, Arithmetic Sequences, Geometric Sequences, Mathematical Induction, Probability, Counting Principles, Permutations, and Combinations.
  • Unit VIII. Explorations with Similarities in Right Triangles
    Exploring Similarities in Right Triangles, The Pythagorean Theorem and the Converse of the Pythagorean, Special Right Triangles, Area of Squares, Rectangles, Parallelograms, Triangles, Trapezoids, and Regular Polygons, Area of Sector and Segments of a circle, Circumference of a Circle and Length of an Arc.
  • Unit IX. Trigonometry
    Radian and Degree Measure, The Trigonometric Functions and the unit Circle, Right Triangle Trigonometry, Trigonometric Functions of Any Angles, Graphs of Sine and Cosine Functions, Graphs of Sine and Cosine Functions, Graphs of Other Trigonometric Functions, Inverse Trigonometric Functions, Applications of Trigonometry.
  • Unit X. Analytic Trigonometry
    Radian and Degree Measure, The Trigonometric Functions and the unit Circle, Right Triangle Trigonometry, Graphs of Sine and Cosine Functions, Graphs of Other Trigonometric Functions.
  • Unit XI. Additional Topics in Trigonometry
    Law of Sines, Law of Cosines, Vectors in the Plane.
  • Unit XII. Some Topics in Analytic Geometry
    Introduction to Conics: Parabolas, Ellipses, Hyperbolas, Polar Coordinates, Plane Curves and Parametric Equations.

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