How to Write Math Formulas
Wrap your formula with "$" (dollar signs) to display it.
Example: Writing $x^2 + 3x - 4 = 0$ displays as $x^2 + 3x - 4 = 0$.
Table of Contents
Powers and Roots
Square (Power of 2)
Code:
$x^2$
Display:
$x^2$
Cube (Power of 3)
Code:
$a^3$
Display:
$a^3$
Square Root
Code:
$\sqrt{2}$
Display:
$\sqrt{2}$
Complex Square Root
Code:
$\sqrt{x^2 + y^2}$
Display:
$\sqrt{x^2 + y^2}$
Cube Root
Code:
$\sqrt[3]{8}$
Display:
$\sqrt[3]{8}$
Equations
Linear Equation
Code:
$2x + 5 = 13$
Display:
$2x + 5 = 13$
Quadratic Equation
Code:
$x^2 - 5x + 6 = 0$
Display:
$x^2 - 5x + 6 = 0$
Quadratic Formula
Code:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Display:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
System of Equations
Code:
$\begin{cases} 2x + y = 7 \\ x - y = 2 \end{cases}$
Display:
$\begin{cases} 2x + y = 7 \\ x - y = 2 \end{cases}$
Inequalities
Linear Inequality
Code:
$3x - 4 > 8$
Display:
$3x - 4 > 8$
Greater/Less Than or Equal
Code:
$-2 \leq x \leq 5$
Display:
$-2 \leq x \leq 5$
Not Equal
Code:
$x \neq 0$
Display:
$x \neq 0$
Factorization
Factoring Out Common Factor
Code:
$6x + 9 = 3(2x + 3)$
Display:
$6x + 9 = 3(2x + 3)$
Factoring Quadratics
Code:
$x^2 + 5x + 6 = (x + 2)(x + 3)$
Display:
$x^2 + 5x + 6 = (x + 2)(x + 3)$
Difference of Squares
Code:
$x^2 - 9 = (x + 3)(x - 3)$
Display:
$x^2 - 9 = (x + 3)(x - 3)$
Perfect Square Trinomial
Code:
$x^2 + 6x + 9 = (x + 3)^2$
Display:
$x^2 + 6x + 9 = (x + 3)^2$
Functions
Linear Function
Code:
$y = 2x + 3$
Display:
$y = 2x + 3$
Quadratic Function
Code:
$y = x^2 - 4x + 3$
Display:
$y = x^2 - 4x + 3$
Inverse Proportion
Code:
$y = \frac{12}{x}$
Display:
$y = \frac{12}{x}$
Rate of Change
Code:
Rate of Change = $\displaystyle\frac{\Delta y}{\Delta x}$
Display:
Rate of Change = $\displaystyle\frac{\Delta y}{\Delta x}$
Geometry
Pythagorean Theorem
Code:
$a^2 + b^2 = c^2$
Display:
$a^2 + b^2 = c^2$
Area of Circle
Code:
$S = \pi r^2$
Display:
$S = \pi r^2$
Volume of Sphere
Code:
$V = \frac{4}{3}\pi r^3$
Display:
$V = \frac{4}{3}\pi r^3$
Volume of Cone
Code:
$V = \frac{1}{3}\pi r^2 h$
Display:
$V = \frac{1}{3}\pi r^2 h$
Probability and Statistics
Basic Probability
Code:
Probability = (Favorable Outcomes) $\div$ (Total Outcomes)
Display:
Probability = (Favorable Outcomes) $\div$ (Total Outcomes)
Mean (Average)
Code:
Mean = $\frac{x_1 + x_2 + \cdots + x_n}{n}$
Display:
Mean = $\frac{x_1 + x_2 + \cdots + x_n}{n}$
Combinations
Code:
${}_n C_r = \frac{n!}{r!(n-r)!}$
Display:
${}_n C_r = \frac{n!}{r!(n-r)!}$
Special Symbols
Plus-Minus
Code:
$x = 3 \pm 2$
Display:
$x = 3 \pm 2$
Infinity
Code:
$\infty$
Display:
$\infty$
Approximately Equal
Code:
$\pi \approx 3.14$
Display:
$\pi \approx 3.14$
Absolute Value
Code:
$|x| = 5$
Display:
$|x| = 5$
Expanding Expressions
Square of Sum
Code:
$(a + b)^2 = a^2 + 2ab + b^2$
Display:
$(a + b)^2 = a^2 + 2ab + b^2$
Square of Difference
Code:
$(a - b)^2 = a^2 - 2ab + b^2$
Display:
$(a - b)^2 = a^2 - 2ab + b^2$
Product of Sum and Difference
Code:
$(a + b)(a - b) = a^2 - b^2$
Display:
$(a + b)(a - b) = a^2 - b^2$
Calculations with Radicals
Multiplying Radicals
Code:
$\sqrt{2} \times \sqrt{3} = \sqrt{6}$
Display:
$\sqrt{2} \times \sqrt{3} = \sqrt{6}$
Dividing Radicals
Code:
$\frac{\sqrt{8}}{\sqrt{2}} = 2$
Display:
$\frac{\sqrt{8}}{\sqrt{2}} = 2$
Simplifying Radicals
Code:
$\sqrt{18} = 3\sqrt{2}$
Display:
$\sqrt{18} = 3\sqrt{2}$
Geometric Symbols
Similar Triangles
Code:
$\triangle ABC \sim \triangle DEF$
Display:
$\triangle ABC \sim \triangle DEF$
Congruent Triangles
Code:
$\triangle ABC \cong \triangle DEF$
Display:
$\triangle ABC \cong \triangle DEF$
Area of Sector
Code:
$S = \pi r^2 \times \frac{\theta}{360}$
Display:
$S = \pi r^2 \times \frac{\theta}{360}$
Arc Length
Code:
$l = 2\pi r \times \frac{\theta}{360}$
Display:
$l = 2\pi r \times \frac{\theta}{360}$
Permutations
Permutation Notation
Code:
$_nP_r = \frac{n!}{(n-r)!}$
Display:
$_nP_r = \frac{n!}{(n-r)!}$
Example (Choose 3 from 5)
Code:
$_5P_3 = 5 \times 4 \times 3 = 60$
Display:
$_5P_3 = 5 \times 4 \times 3 = 60$
Usage Examples in Reading Notes
Example 1: Equation Problem
Code:
p.78 problem: Solve $x^2 - 7x + 12 = 0$. Factoring: $(x-3)(x-4)=0$, so $x=3, 4$
Display:
p.78 problem: Solve $x^2 - 7x + 12 = 0$. Factoring: $(x-3)(x-4)=0$, so $x=3, 4$
Example 2: Pythagorean Theorem Application
Code:
When a right triangle has legs of $3$ and $4$, the hypotenuse is $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$
Display:
When a right triangle has legs of $3$ and $4$, the hypotenuse is $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$
Example 3: Function Graph
Code:
The vertex of $y = 2x^2 - 8x + 6$ is found by completing the square: $y = 2(x-2)^2 - 2$, so vertex is $(2, -2)$
Display:
The vertex of $y = 2x^2 - 8x + 6$ is found by completing the square: $y = 2(x-2)^2 - 2$, so vertex is $(2, -2)$
Common Symbol Reference
\times→ multiplication ×\div→ division ÷\pm→ plus-minus ±\leq→ less than or equal ≤\geq→ greater than or equal ≥\neq→ not equal ≠\sqrt{}→ square root √\frac{numerator}{denominator}→ fraction^→ exponent (e.g., x^2 gives x²)\pi→ pi π\infty→ infinity ∞\approx→ approximately ≈
Chemical Formulas & Equations (Grade 8)
Electrolysis of Water
Code:
$2\text{H}_2\text{O} \rightarrow 2\text{H}_2 + \text{O}_2$
Display:
$2\text{H}_2\text{O} \rightarrow 2\text{H}_2 + \text{O}_2$
Combustion of Hydrogen (Water Synthesis)
Code:
$2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$
Display:
$2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$
Reduction of Copper Oxide
Code:
$2\text{CuO} + \text{C} \rightarrow 2\text{Cu} + \text{CO}_2$
Display:
$2\text{CuO} + \text{C} \rightarrow 2\text{Cu} + \text{CO}_2$
Combustion of Magnesium (Oxidation)
Code:
$2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$
Display:
$2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$
Decomposition of Sodium Bicarbonate
Code:
$2\text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2$
Display:
$2\text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2$
Combination of Iron and Sulfur
Code:
$\text{Fe} + \text{S} \rightarrow \text{FeS}$
Display:
$\text{Fe} + \text{S} \rightarrow \text{FeS}$
Tips for Writing Chemical Formulas
• Wrap element symbols with \text{} (e.g., \text{H})
• Use _ for subscripts (e.g., \text{H}_2 → $\text{H}_2$)
• Use \rightarrow for arrows (→)