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Geometry

How to Find the Area of a Triangle: Formula, Steps, and Examples

Find the area of a triangle with A = (1/2)bh. See the formula worked step by step, plus a right-triangle example and common mistakes to avoid.

By Lernos Team • 2026-08-04

Algebra 2

How to Factor Quadratics When a Is Not 1 (AC Method, Step by Step)

Factor ax² + bx + c when a ≠ 1 using the AC method: split the middle term, group, and pull out common factors. Two full worked examples.

By Lernos Team • 2026-07-17

Algebra 1

How to Find the Discriminant of a Quadratic Equation (Step by Step)

The discriminant of ax² + bx + c = 0 is b² − 4ac. Plug in a, b, c, simplify, and read off how many real solutions the equation has.

By Lernos Team • 2026-07-31

Geometry

How to Find the Hypotenuse of a Right Triangle (Step-by-Step)

Find the hypotenuse using c = √(a² + b²). For legs 3 and 4, the hypotenuse is 5. See two worked examples and the exact steps.

By Lernos Team • 2026-08-04

Algebra 1

How to Find the Slope From Two Points (Formula + Examples)

Find the slope between two points using m = (y₂ − y₁)/(x₂ − x₁). Step-by-step method, two worked examples, and common mistakes to avoid.

By Lernos Team • 2026-07-31

Algebra 2

How to Find the Vertex of a Parabola (Formula & Examples)

Find the vertex of a parabola using x = -b/(2a) or by completing the square. Two fully worked examples with steps for standard and vertex form.

By Lernos Team • 2026-07-31

Prealgebra

How to Add and Subtract Fractions: Step-by-Step Method

Learn how to add and subtract fractions by finding a common denominator, converting, then combining numerators. Two fully worked examples.

By Lernos Team • 2026-08-28

Algebra 2

How to Complete the Square: Step-by-Step Method with Examples

Learn how to complete the square in algebra 2. Convert x² + bx + c into (x + b/2)² form with two fully worked examples and clear steps.

By Lernos Team • 2026-08-31

Algebra 2

How to Factor Quadratic Equations: Step-by-Step Method with Examples

Learn how to factor quadratic equations like x² + 5x + 6 = 0 using the AC method. Step-by-step worked examples and common mistakes explained.

By Lernos Team • 2026-08-31

SAT Prep

How to Find the Discriminant on the SAT (Formula & Examples)

Compute the SAT discriminant b² − 4ac and use its sign to count real solutions. Two SAT-style worked examples, the three cases, and Desmos shortcut.

By Lernos Team • 2026-08-17

SAT Prep

How to Find the Vertex of a Parabola on the SAT (Formula & Steps)

Find the vertex of an SAT parabola using x = -b/(2a) or vertex form (h, k). Two SAT-style worked examples, the method, and Desmos traps to avoid.

By Lernos Team • 2026-08-17

Algebra 1

How to Graph a Linear Equation: Step-by-Step Method

Graph any linear equation by plotting the y-intercept, using the slope for a second point, and drawing the line. Two worked examples inside.

By Lernos Team • 2026-08-27

SAT Prep

How to Improve Your SAT Math Score: A Complete Guide for 2025

Struggling with SAT Math prep? Learn proven strategies from someone who moved from Ireland with zero prep. Includes study plans, common mistakes & AI solutions.

By Ella, Lernos Co-founder • Dec 29, 2025

Algebra 1

How to Solve Linear Equations Step by Step (Algebra 1 Guide)

Solve any linear equation in three steps: simplify, isolate the variable term, then divide by its coefficient. Two full worked examples inside.

By Lernos Team • 2026-08-26

Algebra 1

How to Solve Two-Step Equations With Fractions (Step-by-Step)

Learn how to solve two-step equations with fractions by clearing denominators with the LCD, then isolating the variable. Worked examples included.

By Lernos Team • 2026-07-17

Algebra 1

How to Solve Two-Step Equations: Method, Examples, and Steps

Learn how to solve two-step equations by undoing addition or subtraction first, then multiplication or division. Two fully worked examples included.

By Lernos Team • 2026-07-10

For Parents

How to Tell If Your Kid Is Using ChatGPT for Homework

The behavioral signs your kid is using ChatGPT to do their homework, what to look for in their work, and a short conversation to have tonight.

By The Lernos Team • Aug 10, 2026

Algebra 2

How to Use the Quadratic Formula: Step-by-Step With Examples

Learn how to use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a to solve any quadratic equation, with two fully worked examples.

By Lernos Team • 2026-07-10

For Parents

My Child Gets Good Homework Grades but Fails Tests: What's Actually Going On

The three real reasons a student aces homework and bombs tests, how to figure out which one is happening in your house, and what to do about it tonight.

By The Lernos Team • Aug 10, 2026

Prealgebra

Order of Operations Explained: PEMDAS Rules with Examples

Order of operations means: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. See PEMDAS worked step by step with examples.

By Lernos Team • 2026-08-31

Founder Story

Why Three Siblings Are Building an AI Tutor: The Lernos Story

From Ireland to California with no SAT prep. From precalculus without prerequisites to building an AI tutor. The honest story behind Lernos.

By Ella, Lernos Co-founder • Dec 29, 2025

Geometry

Pythagorean Theorem Explained With Examples (Step-by-Step)

The Pythagorean Theorem says a² + b² = c² for right triangles. See two fully worked examples, the method, and common mistakes to avoid.

By Lernos Team • 2026-07-10

SAT Prep

SAT Quadratic Formula Problems (Worked Examples & Steps)

Solve SAT quadratic-formula problems with x = (-b ± √(b² - 4ac))/(2a). Two SAT-style worked examples, when to use it vs factoring, and Desmos tips.

By Lernos Team • 2026-08-17

SAT Prep

SAT Right Triangle Trigonometry: SOHCAHTOA (Worked Examples)

Solve SAT right-triangle trig with SOHCAHTOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj. Two worked examples, cofunction identity, and Desmos tips.

By Lernos Team • 2026-08-17

For Parents

Signs Your Kid Is Struggling in Math (Before the Report Card Says So)

The observable signs your kid is falling behind in math, what to notice at the kitchen table this week, and how to spot a foundational gap before the grade drops.

By The Lernos Team • Aug 10, 2026

Algebra 1

How to Solve Equations With Variables on Both Sides (Step by Step)

Learn how to solve equations with variables on both sides: move variables to one side, constants to the other, then divide. Two worked examples included.

By Lernos Team • 2026-08-04

Algebra 1

How to Solve Systems of Equations by Substitution (Step by Step)

Solve a system of equations by substitution: isolate one variable, plug it into the other equation, solve, and back-substitute. Full worked examples.

By Lernos Team • 2026-08-27

Algebra 1

How to Solve Systems of Equations Word Problems Step by Step

Turn word problems into two equations, solve by substitution or elimination, and check. Full worked examples with numbers included.

By Lernos Team • 2026-07-17

Education

Why Your Child Is Struggling with Math (And It's Probably Not Their Fault)

Is your child struggling with math homework every night? Learn why the education system fails students and how AI tutoring builds genuine understanding.

By Ella, Lernos Co-founder • Dec 29, 2025