Parabolas, Rates of Change and Variation
Parabolas, rates of change, and direct and inverse variation.
Active lessons
10
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
10 of 10 active
Lesson 1
Introduction to Parabolas
Recognise basic parabola features including vertex, symmetry, opening direction and y-intercept.
Lesson 2
Sketching Parabolas
Sketch simple parabolas using tables, symmetry, y-intercepts and factorised x-intercepts.
Lesson 3
7C Sketching by Factorisation
Sketch a parabola by factorising to find its x-intercepts, y-intercept and axis of symmetry.
Lesson 4
7D Sketching by Completing the Square
Use completed-square form to read off the vertex and minimum value of a parabola.
Lesson 5
7E Sketching by Quadratic Formula and Discriminant
Use the discriminant to count the real roots (x-intercepts) of a quadratic.
Lesson 6
7F Applications
Apply parabolas to real situations: maximum height at the vertex, landing at the x-intercepts.
Lesson 7
7G Intersection of Lines and Parabolas
Find where a line meets a parabola by solving the two equations simultaneously.
Lesson 8
7H Rates of Change
Find an average rate of change as change in output per change in input.
Lesson 9
7I Average and Instantaneous Rates
Distinguish the average rate over an interval from the instantaneous rate at a point.
Lesson 10
7J Direct and Inverse Variation
Model direct variation (constant ratio) and inverse variation (constant product).
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