Physics homework
What is the force between two charges $q_1$ and $q_2$ separated by a distance $r$? $$F = \frac{kq_1q_2}{r^2}$$ What is the electric field due to a point charge $q$ at a distance $r$? $$E = \frac{kq}{r^2}$$ What is the energy stored in a capacitor of...
Mathematics form one
Mathematics Guide Algebra To solve for \[x\], follow these steps: \begin{aligned} 2x - 5 &= 15 \\ 2x &= 20 \\ x &= 10 \end{aligned} Factorize $$x^2 - 4x + 4$$: $$(x - 2)(x - 2)$$ Simplify $$(x + 2)(x - 3)$$: $$x^2 - x - 6$$ Expand $$(2x - 1)^3$$: $$8...
Calculus equations
Find the derivative of the function $$f(x) = x^3 + 2x^2 - 5x + 1$$. Evaluate the integral $$\int_{0}^{1} (x^2 + sin(x)) dx$$. Determine the critical points of the function $$f(x) = x^4 - 2x^2 + 1$$. Sketch the graph of the function $$f(x) = |x-2|+1$$...
Mermaid modified
Here is the modified cube with an additional cube with green faces: $$ \begin{tikzpicture}[scale=0.5] \draw[thick] (-1,-1,-1) -- (-1,-1,1) -- (1,-1,1) -- (1,-1,-1) -- cycle; % front face \draw[thick] (-1,1,-1) -- (-1,1,1) -- (1,1,1) -- (1,1,-1) -- cy...
Mermaid js code 2
Refactored Mermaid Code graph LR start --> design design --> code code --> test test --> deploy deploy --> finish Explanation This refactored code creates a flowchart with the same nodes as the original code: start: The starting point of the process...
Mermaid js code
Refactored Code Example Here is a refactored version of the Mermaid.js code example: graph LR A --> B B --> C C --> A D --> E E --> F F --> D This code creates a directed graph with six nodes (A-F) and eight edges. The -->> symbol indicates a directe...
Test more diagrams
$$ \usetikzlibrary{quotes,arrows.meta} \tikzset{ annotated cuboid/.pic={ \tikzset{every edge quotes/.append style={midway, auto},/cuboid/.cd,#1} \draw[every edge/.append style={pic actions, densely dashed, opacity=.5}, pic actions] (0,0,0) coordinate...
Cubes
The image provided is a 3D representation of a cube, with each face colored yellow and the edges colored red. The cube is composed of eight triangular faces, with each face being a triangle. The edges of the cube are thick and red, connecting the ver...
Area of a circle
$$\begin{tikzpicture} \draw[thick] (0,0) circle (2cm); \end{tikzpicture}$$ The area of a circle is given by the formula: $$A = \pi r^2$$ where \[A\] is the area and $$r$$ is the radius of the circle. For example, if the radius of the circle is 4 cm,...
Form 4 holiday practice questions
Algebra Simplifying Expressions Simplify the expression: $$2x + 5 + 3x$$ Solving Equations Solve the equation: $$x + 2 = 7$$ Graphs Sketch the graph of the equation: $$y = 2x - 3$$ Statistics The scores of 5 students in a mathematics test are: 80, 70...
Fully math diagrams
Upmath: Math Online Editor Create web articles and blog posts with equations and diagrams Upmath significantly simplifies this task by using Markdown and LaTeX. It converts Markdown syntax extended with LaTeX equations support into HTML code you can...
Chemistry form one
Form One Chemistry Questions for Holiday Question 1: Atomic Structure What is the atomic number of an element that has 6 protons in its atomic nucleus? Question 2: Chemical Bonding What type of bond is formed between two atoms when they share one or...
Grade 8 may holiday homework
English Questions for Grade 8 Vocabulary What does the word "perspicacious" mean? $$\text{______________}$$ Grammar Identify the correct form of the verb "to be" in the sentence: "By the time I ________ (to be) at the party, it was already over." $$\...
Mathematics grade 8
Question 1: Algebra Solve for x in the equation: 2x + 5 = 11 Question 2: Geometry In the figure below, ABC is a right triangle with AB = 5 cm and BC = 12 cm. Find the length of AC. $$\begin{tikzpicture}[scale=0.5] \draw (0,0) -- (5,0) -- (0,4) -- cyc...
Form one maths course outline
Mathematics Course Outline Course Title: Introduction to Calculus Course Description: This course provides an introduction to the fundamental concepts of calculus, including limits, derivatives, and integrals. Students will learn to apply these conce...
Science grade 4 outline
Exploring the Wonders of Science: Grade 2 Topics Outline As young minds begin to explore the world around them, science becomes an exciting and essential part of their educational journey. In Grade 2, students are introduced to fundamental concepts t...
Science grade 4
The Amazing World of Science Hey there, young explorers! Today, we're going on an adventure to discover the amazing world of science! What is Science? Science is like being a detective. We use our curiosity and observation skills to figure out how th...
Academic competitions
Academic Competitions: Fostering Excellence and Collaboration Academic competitions have become an integral part of the educational landscape, providing a platform for students to showcase their knowledge, skills, and creativity. These competitions n...
Principles speech
Closing Day Address Fellow students, esteemed faculty members, and honored guests, As we gather here today to mark the closing of another academic year, I am filled with a mix of emotions - pride, gratitude, and a hint of sadness. We have accomplishe...
Sports
The Thrilling Victory of the Wildcats The Wildcats, led by their star quarterback, Jack Harris, have taken the league by storm with their impressive winning streak. In their latest match against the Panthers, the Wildcats emerged victorious, securing...
Mathematics sample calculus
Finding the Derivative of a Function Let's consider the function: $$f(x) = 3x^2 + 2x - 5$$ To find the derivative of this function, we'll apply the power rule and the sum rule of differentiation. $$f'(x) = \frac{d}{dx} (3x^2 + 2x - 5)$$ Using the pow...
Last calculus equations
Example 1: Finding the Derivative of a Function Let's consider the function f(x) = 3x^2 + 2x - 5. We want to find its derivative using the power rule and the sum rule. $$f'(x) = \frac{d}{dx} (3x^2 + 2x - 5)$$ Step 1: Differentiate the first term usin...
More maths ➗➖
Here are five examples of linear algebra problems with their solutions, presented step by step using KaTeX notation. Example 1: Solving a System of Linear Equations Solve the following system of linear equations: Step-by-Step Solution: Solve the seco...
Test math ➗➖
Markdown Sure! Here are five examples of linear algebra problems with their solutions, presented step by step using KaTeX notation. ### Example 1: Solving a System of Linear Equations Solve the following system of linear equations: \[ \begin{cases}...
Integration calculus
Example 1: $$\int x^2 dx = \frac{x^3}{3} + C$$ Step 1: Use the power rule of integration: $\int x^n dx = \frac{x^{n+1}}{n+1} + C$. Example 2: $$\int \sin x dx = -\cos x + C$$ Step 1: Use the substitution method: let $u = \sin x$, then $du = \cos x dx...
PDE I
1. Poisson Equation $$ \nabla^2 u = f(x,y) $$ Solution: $$ u(x,y) = \iint\limits_DG(x,y;\xi,\eta)f(\xi,\eta)d\xi d\eta $$ where $G(x,y;\xi,\eta)$ is the Green's function for the Laplacian operator. 2. Heat Equation $$ \frac{\partial u}{\partial t} =...
Linear algebra
Example 1: $$ \begin{align} A &= \begin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix}, B &= \begin{bmatrix} -1 & 2 \ 1 & 3 \end{bmatrix} \ A + B &= \begin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix} + \begin{bmatrix} -1 & 2 \ 1 & 3 \end{bmatrix} \ &= \begin{bmatrix}...
Symposium
Example 1: Solving a System of Linear Equations $$ \begin{aligned} 2x + 3y &= 5 \ x - y &= 1 \end{aligned} $$ Solution: Multiply the second equation by 3 to get: $$3x - 3y = 3$$ Add this to the first equation to get: $$5x = 8$$ Solve for x: $$x = \fr...
Mathletes
Mathematics Academic Competitions: Nurturing Mathematical Excellence Mathematics academic competitions serve as a platform for students to showcase their exceptional mathematical abilities and foster a spirit of intellectual curiosity. These competit...
Calculus equations
Question 1: Find the derivative of: $$f(x) = x^3 - 2x^2 + 5x - 1$$ Working: $$f'(x) = \frac{d}{dx}(x^3 - 2x^2 + 5x - 1)$$ $$= \frac{d}{dx}x^3 - \frac{d}{dx}2x^2 + \frac{d}{dx}5x - \frac{d}{dx}1$$ $$= 3x^2 - 4x + 5$$ Question 2: Find the indefinite in...