Core math areas covered by this workspace
This page is designed as a compact hub for everyday math. It does not try to replace full learning platforms like Khan Academy or MathWorld, but it gives you a fast way to compute, visualize, and check your work across the most common topics.
1. Arithmetic & number sense
- Operations with integers, fractions, and decimals.
- Percentages, percentage change, discounts, and markups.
- Order of operations (PEMDAS): parentheses, exponents, multiplication/division, addition/subtraction.
Key percentage formulas
Percentage of a value:
\(\text{part} = \text{whole} \times \frac{\text{percent}}{100}\)
Percentage change:
\(\text{percent change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%\)
2. Algebra
- Simplifying expressions and combining like terms.
- Solving linear equations such as \(2x + 5 = 17\).
- Factoring quadratics like \(x^2 - 5x + 6\).
- Evaluating functions \(f(x)\) at specific values.
Quadratic formula
For \(ax^2 + bx + c = 0\):
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. Functions & graphing
Many real problems can be modeled as a function \(y = f(x)\). The quick graph on this page lets you see the shape of polynomials, exponentials, and trigonometric functions on a standard window.
- Linear functions: \(y = mx + b\).
- Quadratic functions: \(y = ax^2 + bx + c\).
- Basic trig functions: \(\sin x\), \(\cos x\), \(\tan x\).
4. Calculus (intro level)
The workspace supports basic symbolic derivatives and integrals for common functions. This is helpful for checking homework or verifying manual work.
- Derivatives of polynomials, exponentials, and simple trig functions.
- Indefinite integrals of basic functions where closed forms exist.
Fundamental derivative rules
- \(\dfrac{d}{dx} (x^n) = n x^{n-1}\)
- \(\dfrac{d}{dx} (\sin x) = \cos x\)
- \(\dfrac{d}{dx} (e^x) = e^x\)
5. Statistics (basics)
While CalcDomain has dedicated tools for advanced statistics, this workspace can help with simple descriptive statistics such as mean and standard deviation for small data sets.
Sample mean and standard deviation
Mean:
\(\bar{x} = \dfrac{1}{n} \sum_{i=1}^{n} x_i\)
Sample standard deviation:
\(s = \sqrt{\dfrac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}\)
When to use a dedicated calculator
For specialized tasks—like matrix operations, geometry of specific shapes, or probability distributions—use the dedicated tools in the Math & Conversions category (see the sidebar). This workspace is ideal for quick, mixed, or exploratory work where you do not want to switch tools.