Mathematics

About this course

The tenth-grade math course is more advanced than the grade label suggests. It opens with complex numbers, taking your student from the imaginary unit and standard form through complex arithmetic, the complex plane, modulus and argument, polar form, and De Moivre's theorem for powers and roots, then moves into arithmetic and geometric sequences, infinite geometric series, sigma notation, recursive sequences, and proof by mathematical induction. A function unit covers sums, differences, products, and quotients of functions, composition, inverse functions and the horizontal line test, polynomial long division and synthetic division, the remainder theorem, the rational root theorem, Descartes' rule of signs, the fundamental theorem of algebra, multiplicity of roots, and polynomial inequalities solved with sign charts. Rational and radical functions follow, with domain, vertical, horizontal, and oblique asymptotes, holes, extraneous solutions, rational exponents, and partial fraction decomposition.

Two full units are given to the conic sections. Your student analyzes the parabola by focus and directrix, the ellipse by foci and eccentricity, and the hyperbola by foci and asymptotes, identifies conics by completing the square, solves systems involving conics, and then meets parametric equations, polar coordinates, polar curves such as roses and limacons, and conics written in polar form. Trigonometry enters through right triangle ratios, the special 45-45-90 and 30-60-90 triangles, the law of sines, the law of cosines, and the SAS area formula, alongside triangle congruence and similarity, circle geometry, coordinate geometry, geometric proof, and the surface area and volume of composite solids. The algebra units add matrices, determinants, Cramer's rule, augmented matrices and row operations, logarithms and their properties, and exponential growth and decay. The statistics units cover center and spread, the normal distribution and z-scores, scatter plots and least-squares regression, permutations and combinations, geometric probability, inference from a sample, statistical bias, two-way tables, and reading published statistics critically.

The course is 180 lessons across 15 units, one per school day, at about 55 minutes each. The first eight units introduce each strand and the last seven return to the same material with new examples and harder problems. Lessons are written to your student as dense textbook pages, typically a statement of the theorem or formula, two or three fully worked examples, an application, and a practice set, with a KJV verse woven in. Every lesson ends with a ten-question quiz that grades itself. Before starting, your student should have finished a full Algebra I course: factoring, the quadratic formula, exponent rules, function notation, and graphing lines and parabolas are all assumed rather than taught. Freedom Homeschool also offers a separate, dedicated Geometry course at this grade for families who want a full year of proof-based plane geometry; this math course touches geometry but is chiefly an advanced algebra and precalculus course.

What the course covers

• Complex numbers, polar form, and De Moivre's theorem
• Arithmetic and geometric sequences, series, and mathematical induction
• Function operations, composition, and inverse functions
• Polynomial division, the rational root theorem, and graphing polynomials
• Rational and radical functions, asymptotes, and partial fractions
• Conic sections: parabolas, ellipses, and hyperbolas
• Parametric equations, polar coordinates, and polar graphs
• Right triangle trigonometry, the law of sines, and the law of cosines
• Matrices, determinants, and Cramer's rule
• Logarithms, exponential models, the normal distribution, and regression

What your student will be able to do

• Compute with complex numbers in both standard and polar form
• Find the terms and sums of arithmetic and geometric sequences and series
• Divide polynomials, find all roots, and sketch a polynomial or rational graph
• Identify, write, and graph any conic section from its equation
• Solve an oblique triangle with the law of sines or the law of cosines
• Solve a linear system with matrices and work with logarithmic and exponential models

Scope and sequence

All 15 units of Mathematics for Grade 10, in the order they are taught.

Every lesson, by title

All 180 lesson titles are listed here — nothing is withheld until you download. Open a unit to read its contents.

One whole lesson, exactly as it comes

This is a real lesson taken from the middle of the course — the teaching text, the practice, the homework, and the first three quiz questions with their answers. It is not a marketing excerpt.

What you will need

Drawn from the materials named across all 180 lessons of this course. Most families already own most of it.