Year 8 Mathematics Essentials

This cheat sheet covers fundamental Year 8 mathematics topics including solving linear and simple quadratic equations, and understanding linear graphs and their applications.

Core Principles

• Linear equations have one variable and one solution.
• Quadratic equations involve a squared term and can have up to two solutions.
• Linear graphs are straight lines represented by y = mx + c.
• Graphs visualize relationships between variables.

Action Steps

• Isolate the variable in linear equations using inverse operations.
• Factorize or use the quadratic formula for simple quadratics.
• Identify slope (m) and y-intercept (c) for linear graphs.
• Substitute values to find points on a graph.
• Plot points and connect them to draw a linear graph.
• Interpret graph intercepts and slopes in real-world contexts.

Formulas

• Linear Equation: ax + b = c
• Quadratic Equation: ax^2 + bx + c = 0
• Slope-Intercept Form: y = mx + c (m=slope, c=y-intercept)
• Point-Slope Form: y - y1 = m(x - x1)

Key Terms

• Variable: A symbol representing an unknown quantity (e.g., x, y).
• Equation: A statement that two expressions are equal.
• Solution: The value(s) of the variable(s) that make an equation true.
• Quadratic Term: A term in an equation containing a variable raised to the power of two (e.g., x^2).
• Slope (Gradient): The steepness of a line, calculated as the change in y over the change in x.
• Y-intercept: The point where a line crosses the y-axis (where x=0).

Real World Examples

• Calculating total cost based on a fixed fee and a per-item charge.: Represented by a linear equation: Cost = (price per item * number of items) + fixed fee.
• Tracking distance traveled over time at a constant speed.: A linear graph where time is on the x-axis and distance is on the y-axis.
• Finding the break-even point where revenue equals cost.: Intersection point of two linear graphs representing cost and revenue functions.