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Algebra Masterclass 2026: Zero to Pre-Calculus (Demo Only)
46 students

Algebra Masterclass 2026: Zero to Pre-Calculus (Demo Only)

This Demo Course Is part of the main course Algebra Masterclass 2026: Zero to Pre-Calculus
Created byOmar Koryakin
Last updated 5/2026
English
English [Auto],

What you'll learn

  • Solve every type of equation, linear, quadratic, polynomial, rational, radical, exponential, and logarithmic, using the right method for each
  • Graph any function by hand or with a calculator, and read its slope, intercepts, roots, asymptotes, and end behavior at a glance
  • Translate any word problem into algebra with a repeatable 4-step process that works on test problems and real-world problems alike
  • Master factoring with every method (GCF, grouping, trinomials, special products, sum and difference of cubes) so polynomials never block you
  • Work fluently with functions: composition, inverses, transformations, piecewise, even and odd, and see why they're the central object of algebra
  • Solve systems of equations and inequalities (substitution, elimination, three-variable, linear programming) with confidence
  • Use complex numbers to find every root of any polynomial, including roots that don't exist in the real numbers
  • Recognize all four conic sections (circles, ellipses, parabolas, hyperbolas) from their equations and graph them
  • Apply algebra to real careers: pharmacy dosing, contracting estimates, compound interest, depreciation, half-life, and more
  • Pass standardized algebra tests (SAT, ACT, GRE, GMAT, GED, ASVAB) with the complete toolkit each one requires

Explore related topics

Course content

2 sections • 19 lectures • 1h 22m total length

  • S11 L01: Introduction to Quadratic Equations4:22

    Quadratic equations have the form a x squared plus b x plus c equals 0, degree 2, exactly two roots in the complex numbers (counting multiplicity). We introduce the four standard solving methods (factoring, square root method, completing the square, quadratic formula), the discriminant, and the parabola as the geometric picture.


  • S11 L02: Square Root Method4:11

    For quadratics of the form x squared equals k, take the square root of both sides. We cover the plus-or-minus rule, the no-real-solution case (when k is negative, sets up complex numbers in Section 12), and the slightly-extended form (x minus h) squared equals k that bridges to completing the square.


  • S11 L03: Solving Quadratics by Factoring4:23

    Combining factoring (Section 8) with the zero product property, the fastest method when the quadratic factors cleanly. We cover the full routine: factor, set each factor to zero, solve. We also identify when factoring won't work and you need to switch methods.


  • S11 L04: Completing the Square4:10

    Turning a x squared plus b x plus c into (x minus h) squared plus k, the technique that derives the quadratic formula and unlocks vertex form for graphing. We cover the systematic "halve b, square it" routine, the leading-coefficient case (a not equal to 1), and apply completing the square to both equation solving and graph analysis.


  • S11 L05: The Quadratic Formula4:22

    x equals (negative b plus or minus root of (b squared minus 4 a c)) over 2 a, the universal solver for any quadratic equation. We derive it from completing the square (so you understand why it works), apply it to dozens of examples, and discuss the discriminant b squared minus 4 a c and what each sign tells you about the roots.


  • S11 L06: Choosing a Quadratic Method4:16

    A diagnostic for picking among square root, factoring, completing the square, and the quadratic formula. We work through 8 to 10 quadratics and apply the diagnostic in real time. The right-method choice cuts solution time dramatically on tests.


  • S11 L07: Vertex Form4:29

    The form y equals a times (x minus h) squared plus k, where (h, k) is the vertex. We cover the connection to completing the square, reading the vertex and direction off the equation, and the transformations from y equals x squared that produce any vertex-form parabola.


  • S11 L08: Graphing Parabolas4:24

    Graphing quadratic functions by identifying the four key features: direction (sign of a), vertex (from vertex form or formula negative b over 2 a), axis of symmetry, x and y intercepts. We cover plotting from any of the three quadratic forms (standard, vertex, factored) and the connection to projectile motion in physics.


  • S11 L09: Quadratic Applications4:42

    The rich application set: projectile motion (height vs time), maximum profit and minimum cost, area optimization, supply-demand curves, and the famous "rectangle inscribed in a parabola" problems. Each translates a real situation into a quadratic equation we solve.


  • S11 L10: Quadratic Inequalities4:17

    Quadratic inequalities (a x squared plus b x plus c greater than 0), find where the parabola is above (or below) the x-axis. We cover the standard "find roots, test intervals" technique, graph the solution on the number line, and apply quadratic inequalities to constraint problems in optimization.


  • S11 L11: Nonlinear Systems4:26

    Systems where at least one equation is nonlinear, line-circle intersections, parabola-line intersections, two-conic intersections. We cover substitution and elimination adapted for these systems, the geometric interpretation (point-of-intersection counts), and the connection to conic sections in Section 15.


  • S11 L12: Sum and Product of Roots3:58

    The Vieta's formulas: for a x squared plus b x plus c equals 0, sum of roots equals negative b over a, product equals c over a. We use these to construct quadratics with given roots, check answers on tests, and connect to higher-degree polynomial root patterns. A subtle but powerful tool.


  • S11 L13: Section 11 Marathon4:01

    A consolidating marathon for Section 11: all four solving methods, the discriminant, vertex form, graphing parabolas, applications, inequalities, nonlinear systems, and Vieta's formulas. Work before any test covering quadratics or as a review before complex numbers.


Requirements

  • Basic arithmetic. Comfortable adding, subtracting, multiplying, and dividing whole numbers and simple fractions.
  • A calculator. Any standard scientific calculator works. No graphing calculator required, though it helps for some lessons.
  • Pencil, paper, and the willingness to work through problems alongside the instructor. This is a hands-on course, not a lecture series.
  • No prior algebra experience required. The first sections start from the absolute beginning.

Description

Note: This Demo Course Is part of my main course: Complete Algebra Masterclass 2026: Zero to Pre-Calculus

Algebra is the language of every quantitative field, and most courses teach it badly. This course doesn't. Complete Algebra Masterclass 2026 walks you through every algebra topic the way a patient one-on-one tutor would: visual diagrams on screen, every step worked out clearly, and a real worked example for every concept. Not a generic find x problem with no context.


WHAT MAKES THIS COURSE DIFFERENT


  • Every concept is shown visually first. When you see a parabola open up, watch a triangle's rise and run get measured, or see a polynomial's roots land on the number line, the math stops feeling abstract.

  • Worked examples that actually look like test problems. Each section ends with a marathon lesson where I works through real problems start to finish, the same kind of multi-step problems you will see on the SAT, ACT, GRE, GMAT, GED, or your final exam.

  • Roleplay lessons that connect math to real careers. A pharmacy tech computing dosages. A contractor estimating materials. Slope as a wheelchair-ramp gradient. Compound interest as a 401(k). You will never wonder when will I use this again.

  • No filler. Every lesson has a single sharp learning objective. If the topic takes 12 minutes to teach properly, the lesson is 12 minutes. Not stretched to 30 to look impressive.

  • Structured for real retention. The course follows a deliberate sequence: foundations (Sections 1 to 5), linear methods (Sections 3 to 6), polynomials and factoring (Sections 7 to 8), rationals and radicals (Sections 9 to 10), quadratics and complex numbers (Sections 11 to 12), exponentials and sequences (Sections 13 to 14), conics and synthesis (Sections 15 to 16). Each section builds on the last.


REAL-WORLD APPLICATIONS YOU WILL WORK THROUGH


  • Engineering and physics: slope as gradient, polynomial roots as system stability, exponential decay as half-life, conic sections as orbital mechanics.

  • Finance: compound interest, exponential growth, linear depreciation, system-of-equations break-even analysis.

  • Data science: function transformations, exponential modeling, logarithmic scaling, sequences and series.

  • Test prep: every topic on the SAT, ACT, GRE Quantitative, GMAT, GED, ASVAB, and Accuplacer math sections is covered explicitly, with the kinds of multi-step problems those exams favor.

  • Trades and applied work: pharmacy dosing, contracting estimates, ramp gradients, electrical formulas, conversion problems.


BY THE END OF THIS COURSE YOU WILL


  • Solve any linear, quadratic, polynomial, rational, radical, exponential, or logarithmic equation with confidence.

  • Translate any word problem into algebra and solve it step by step.

  • Graph any function: linear, quadratic, polynomial, rational, exponential, logarithmic. And read its key features at a glance.

  • Recognize and apply 10 core algebra techniques that solve more than 90 percent of all algebra problems.

  • Pass any standardized algebra test (SAT, ACT, GRE, GMAT, GED, ASVAB) with the math toolkit it requires.

  • Move into pre-calculus, calculus, statistics, or any quantitative discipline with the algebra fluency they assume you have.


WHO THIS COURSE IS FOR


  • High school students taking Algebra 1, Algebra 2, or pre-calculus, who want extra practice or an alternative explanation.

  • College students in College Algebra, Quantitative Reasoning, or any course with an algebra prerequisite.

  • Adult returners going back to school or switching careers into a STEM, finance, or data field.

  • Test prep candidates preparing for SAT, ACT, GRE, GMAT, GED, ASVAB, Accuplacer, or college placement exams.

  • Parents and tutors who want a complete, well-sequenced reference to teach from.

  • Self learners who want a single course that covers everything in order, without gaps.


WHO THIS COURSE IS NOT FOR


  • Pure beginners who don't yet know basic arithmetic. You should be comfortable with addition, subtraction, multiplication, division, and simple fractions before starting.

  • Students who want a quick 1.5-hour cram.

  • Calculus or higher math seekers. This course covers algebra in full. Calculus is the next step but is not included.

  • Enroll now and start with the first lesson, the number line. Everything else builds from there.

Who this course is for:

  • High school students taking Algebra 1, Algebra 2, or pre-calculus
  • College students in College Algebra, Finite Math, or any quantitative course
  • Adults returning to school or switching careers into engineering, finance, data science, or any STEM field
  • Test prep candidates for SAT, ACT, GRE, GMAT, GED, ASVAB, accuplacer, or college placement exams
  • Parents and tutors who want a complete, well-sequenced algebra reference
  • Self learners who want one course that covers every algebra topic from start to finish

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