Worked problem pages
Each page explains the idea, then works through real problems from the Mathyessy bank step by step.
One-variable linear equations practiceSolving a linear equation means undoing what was done to x, in reverse order, while keeping both sides balanced.Algebra word problems practiceThe hard part of a word problem is the translation. Once it is an equation, the algebra is quick.Systems of equations practiceTwo unknowns need two equations. Contest problems often reward finding what is asked without solving for each variable.Ratio practice problemsA ratio compares quantities. Most ratio problems become easy once you find the size of one 'part'.Percent practice problemsPercent means 'per hundred'. Turning percents into multipliers makes discounts and percent changes quick.Rate problems practiceDistance, work and production problems all use one idea: amount = rate × time.Arithmetic sequences and series practiceAn arithmetic sequence adds the same amount each time. Two formulas handle almost every contest question.Factoring quadratics practiceTo factor x² + bx + c, find two numbers that multiply to c and add to b.Quadratic formula and discriminant practiceThe quadratic formula solves any quadratic. The discriminant tells you what kind of roots to expect before you solve.Simon's Favorite Factoring Trick practiceAn equation like xy + 3x + 4y = 24 looks stuck, until you add one number to both sides and it factors.Exponent laws practiceA few exponent rules cover almost everything: same base means add, subtract or multiply the exponents.
Every Algebra practice set in Mathyessy
Each link opens that topic's question set in the free app. Questions get harder as you go, and you get instant feedback after each answer.
- Prerequisites - Arithmetic Review
- Prerequisites - Exponent Laws · worked problems
- Prerequisites - Square Roots
- Prerequisites - Fractional Exponents
- Evaluating Expressions
- Simplifying One-Variable Expressions
- One-Variable Distribution
- One-Variable Linear Equations · worked problems
- Word Problems in One Variable · worked problems
- Linear Equations in Disguise
- Solving Two-Variable Systems · worked problems
- Two-Variable Word Problems
- Advanced Systems of Equations
- Ratios · worked problems
- Unit Conversions
- Percents · worked problems
- Direct Proportion
- Inverse Proportion
- Rate Problems · worked problems
- Distance in the Plane
- Midpoint of a Segment
- Graphing Lines
- Graphing Multiple Lines
- Solving Linear Inequalities
- Multiplying Binomials
- Factoring Monic Quadratics · worked problems
- Factoring General Quadratics
- Sum and Product of Roots
- Square of a Binomial
- Difference-of-Squares
- Rationalizing Denominators
- Simon's Favorite Factoring Trick · worked problems
- Complex Number Arithmetic
- Quadratic Formula/Discriminant · worked problems
- Completing the Square
- Quadratic Optimization
- Advanced Quadratics
- Graphing Quadratics
- Graphing Circles
- Quadratic Inequalities
- Evaluating Functions
- Domain and Range
- Function Composition
- Inverse Functions
- Functional Operations
- Graphing Functions
- Polynomial Basics
- Polynomial Multiplication
- Exponential and Logarithm Basics
- Interest Rates
- Logarithm Basics
- Radical Expressions and Functions
- Absolute Value
- Floor and Ceiling
- Rational Expressions of Polynomials
- Piecewise-Defined Functions
- Arithmetic Sequences
- Arithmetic Series · worked problems
- Geometric Sequences
- Geometric Series
- Clever Algebraic Manipulations
- All Topics in Algebra