Currently Covered Mathematics

Mathematical Expressions in the Calculio App

Expression Manipulation

  • Simplifying Numerical Expressions
  • Polynomials – Addition, Subtraction, Multiplication
  • Fractions – Simplification, Addition, Subtraction, Multiplication, Division
  • Compound Fractions
  • Rationalizing Fractions
  • Exponents – With Natural, Integer, and Fractional Exponents, with a Variable in the Exponent
  • Radicals – With Natural Indices, with a Variable in the Index
  • Simplifying Trigonometric, Exponential, and Logarithmic Expressions
  • Expressions with Factorials and Binomial Coefficients
  • Complex numbers - Simplification, Absolute value, Power
  • Factoring Expressions – Factoring Out, Factoring Formulas, Quadratic Expressions, Tricks for More Complex Factorizations

Equations, Inequalities, and Systems

  • Linear Equations and Inequalities
  • Quadratic Equations and Inequalities
  • Equations and Inequalities in Product and Quotient Forms
  • Equations and Inequalities with Absolute Values
  • Irrational Equations and Inequalities (with Radicals)
  • Exponential Equations and Inequalities
  • Logarithmic Equations and Inequalities
  • Trigonometric Equations and Inequalities
  • Reciprocal Equations
  • Equations and Inequalities Using Substitution
  • Equations and Inequalities with Factorials
  • Systems of Equations – Addition Method, Comparison Method, Substitution Method
Equations, Inequalities, and Systems in the Calculio App
Equations and Inequalities with Parameters in the Calculio App

Equations and Inequalities with Parameters

  • Supported Types:
    • Linear Equations and Inequalities with Parameters
    • Quadratic Equations and Inequalities with Parameters
    • Irrational Equations and Inequalities with Parameters (with Radicals)
    • Equations and Inequalities with Parameters and Absolute Values
    • Equations and Inequalities with Parameters in Product and Quotient Forms

Word Problems

  • We solve only word problems leading to equations, inequalities, and systems (i.e., we do not support construction problems, visual problems, proofs, etc.)
  • Focused on solving word problems at elementary and high school levels with average difficulty
  • Supported Types of Word Problems:
    • Word problems on direct and inverse proportionality (and their combinations)
    • Word problems on motion
    • Word problems on collaborative work
    • Word problems on mixtures and solutions
    • Word problems on sequences (arithmetic, geometric)
    • Word problems on sets (Venn diagrams, Cartesian product)
    • Word problems on combinatorics
    • Word problems involving geometric calculations (perimeters, areas, volumes, etc.)
    • Word problems on extrema using derivatives
    • Specific problems (age, LCM, GCD, percentages, scale, clock hands, etc.)
    • General problems
  • Supported Types of Mathematical Operations:
    • Word Problems Leading to a Linear Equation
    • Word Problems Leading to a Linear Inequality
    • Word Problems Leading to a Quadratic Equation
    • Word Problems Leading to a System of Equations
    • Word Problems Leading to an Exponential Equation/Inequality
    • Word Problems Leading to a Trigonometric Equation
    • And more
  • Not primarily intended for physics problems, though we can handle simple ones as well.
  • More about word problems can be found on this page
Word Problems in the Calculio App