Non-Linear Relationships, Functions and Their Graphs — NSW Year 10 Core Maths
Parabolas, exponential curves and graphs that describe change. Three subtopics and 60 practice questions, each with a worked solution, aligned to NESA MA5-NLI-C-01, MA5-NLI-C-02 and MA5-NLI-P-01.
Non-Linear Relationships, Functions and Their Graphs in NSW Year 10 Core
Not every relationship is a straight line. In Year 10 Core, students explore parabolas and their features and study exponential growth and decay. The topic finishes by reading real situations from graphs, using rates of change and direct and inverse variation. Sketching parabolas by transformations and graphing circles are studied in Year 10 Advanced.
The three subtopics below follow that order. Non-Linear Relationships, Functions and Their Graphs is one of the 11 topics in NSW Year 10 Maths Core and sits within NESA's Number and Algebra strand (NESA outcomes MA5‑NLI‑C‑01 and MA5‑NLI‑C‑02, with the Path outcomes MA5‑NLI‑P‑01, MA5‑RAT‑P‑01 and MA5‑RAT‑P‑02). These graphs are the starting point for the functions studied in Stage 6 Advanced maths.
Subtopics
Non-Linear Relationships, Functions and Their Graphs: common questions
What is a parabola?
A parabola is the U-shaped graph of a quadratic relationship such as \(y = x^2 - 1\). It has a turning point and an axis of symmetry, and it is either concave up or concave down.
What is the axis of symmetry of a parabola?
It is the vertical line through the turning point that splits the parabola into two mirror-image halves. If a parabola crosses the \(x\)-axis at \(x = -1\) and \(x = 5\), its axis of symmetry is halfway between them, at \(x = 2\).
What does the gradient of a distance-time graph show?
It shows the speed. A steeper section means faster travel, a flat section means the object has stopped, and a curved section means the speed is changing.
What does an exponential graph look like?
A graph such as \(y = 2^x\) passes through \((0, 1)\), rises more and more steeply as \(x\) increases, and gets closer and closer to the \(x\)-axis as \(x\) decreases without touching it. \(y = 2^{-x}\) is its reflection and shows decay.
Which NESA outcomes cover non-linear relationships in Year 10 Core?
Graphing parabolas and exponential curves comes under MA5‑NLI‑C‑01 and MA5‑NLI‑C‑02, and rates of change and variation belong to the Path outcomes MA5‑RAT‑P‑01 and MA5‑RAT‑P‑02.