Year 8 Mathematics: Equations and Problem Solving

VOCABULARY flashcards covering algebraic equations, solution types, and problem-solving concepts based on the Year 8 Mathematics lecture notes.

Identity

An equation that is true for all possible values of the variable, such as $5(a + 2) = 5a + 10$.

Single solution

An equation that has exactly one value for the variable that makes the statement true, such as $2y + 7 = 21$.

No solution

An equation that has no value for the unknown variable that makes the statement true, such as $4(d + 2) = 9 + 4d$.

Solving by inspection

Determining the solution to an equation through mental observation and logical deduction without traditional written steps.

Substitution

The process of replacing a variable with a specific numerical value to check if the equation holds true, such as checking if $x = 6$ satisfies $\frac{x}{2} + 1 = 4$.

Defining a variable

The first step in problem solving where a letter is assigned to represent an unknown quantity, such as letting $x$ represent a certain number.

Algebraic Equation

A mathematical statement showing the equality of two expressions, typically involving numbers and variables, such as $5y - 8 = 19 - 4y$.

Perimeter of a rectangle

The total length of the boundary of a rectangle; in the provided exercise, the perimeter is given as $30\,\text{cm}$.

Area of a rectangle

The measure of the space inside a rectangle, calculated as length times width; in the provided exercise, the area is given as $50\,\text{cm}^2$.