Solving Simultaneous Equations Graphically

? Video Tutorial Setting Up Equations from Word Problems: Define variables for unknowns and write equations based on relationships, e.g., $x + y = 20$ and $x – y = 10$. Solving Systems of Linear Equations Graphically: Learn to find solutions by plotting linear equations to identify points of intersection. Types of Solutions for Systems […]

Simultaneous Equations: Equal Values and Substitution Method

? Video Tutorial Equal Values Method: Isolate the same variable in both equations, set the expressions equal, and solve for the remaining variable. This method reduces a system to a single-variable equation. Example of Equal Values: For equations $y = x – 1$ and $y = 2x + 3$, set $x – 1 = 2x […]

Simultaneous Equations: Elimination Methods

? Video Tutorial The Elimination Method: Simplifies solving systems of linear equations by removing one variable, making it easier to find the solution. Elimination Techniques: Adding or subtracting two equations to eliminate a variable (e.g., $y$) and solve for the other (e.g., $x$) Transforming Equations: Sometimes, equations must be multiplied to align terms for elimination. […]

Introduction to Functions and Graphs

? Video Tutorial What is a Function?: A function maps each input to exactly one output, often written as $f(x) = text{expression}$ (e.g., $f(x) = 2x + 1$). Function Table and Graph: Create a table of input-output pairs (e.g., $f(1) = 3$, $f(2) = 5$) to visualise the function on a graph, making it easier […]

Gradient and Y-Intercept in Linear Equations

? Video Tutorial Linear equation basics: In $y = mx + c$, $m$ is the gradient (slope) and $c$ is the y-intercept. Understanding $m$ and $c$ is essential for graphing straight lines. Interpreting the gradient $m$: The gradient ($m$) shows how steep the line is. A positive $m$ means an upward slope, while a negative […]

Finding the Equation of a Straight Line

? Video Tutorial Understanding the Linear Equation: For $y = mx + c$, $m$ represents the slope and $c$ is the y-intercept, where the line crosses the y-axis. Calculating the Slope $m$ from Two Points: Use the formula $m = large frac{{y_2 – y_1}}{{x_2 – x_1}}$ to find the slope between two points. Finding the […]

y-Intercepts and x-intercepts of Linear Equations

? Video Tutorial Understanding Y-Intercept and X-Intercept: The y-intercept is where $x = 0$; the x-intercept is where $y = 0$. Example of Finding Intercepts: For $y = 200 – 50x$, the y-intercept is $200$, and the x-intercept is $4$. Finding the Intersection of Two Lines: Set equations equal to solve for $x$ and substitute […]

Solving Equations with 2 Variables

? Video Tutorial Equations with Two Variables: In equation $x + 2y = 20$, $x$ represents cookies, $y$ represents sandwiches, and £20 budget. Substituting Values: By plugging in $x = 10$ to find $y = 5$, meaning you can afford 10 cookies and 5 sandwiches. Similarly, substitute $y = 8$ to get $x = 4$. […]

Determining Quadratic Equations

? Video Tutorial Forming Quadratic Equations Using Vertex Form: When the vertex $(h, k)$ is known, substitute directly into the vertex form, $y = a(x – h)^2 + k$, and use an additional point to solve for $a$. Forming Quadratic Equations Using General Form: For cases without a known vertex, use the general form $y […]

Solving Simple Quadratic Equations

? Video Tutorial Solving Simple Quadratic Equations: For $x^2 = k$, there are two solutions: $x = pm sqrt{k}$. Note that $k$ must be non-negative, as $x^2$ cannot be negative. No Real Solutions for Negative Numbers: If $k$ is negative, such as in $x^2 = -25$, there are no real solutions. Solving $x^2 – d […]