Mathematics>Year 9>Unit 3

Functions & Graphs

This 20-lesson unit explores the mathematics of graphs and relationships. You will master gradient, sketch linear and non-linear graphs, solve simultaneous equations, and model real-world situations with parabolas, exponentials and circles.

20 Lessons 4 Checkpoints 1 Unit Quiz Stage 5 Core
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Syllabus Outcomes

MA5-LIN-C-01

Calculates distance, midpoint and gradient on the number plane and graphs linear relationships using gradient-intercept form.

MA5-LIN-C-02

Solves linear simultaneous equations and models linear relationships in practical contexts.

MA5-NLI-C-01

Graphs and interprets parabolas, exponentials and circles on the number plane.

MA5-NLI-C-02

Recognises and uses features of non-linear relationships including transformations.

Block A — Linear Foundations
01

Gradient of a Line

Rise over run, positive and negative gradient

02

Intercepts and Sketching

x-intercept, y-intercept and quick sketching

03

Equation of a Line

y = mx + c and rearranging to gradient-intercept form

04

Equation from Two Points

Using gradient formula and point-gradient form

05

Parallel and Perpendicular Lines

m1 = m2 and m1 × m2 = −1

Checkpoint 1 — Linear Foundations

Covers Lessons 1–5

Block B — Linear Applications
06

Simultaneous Equations — Graphical

Intersection point of two lines

07

Simultaneous Equations — Algebraic

Substitution and elimination methods

08

Linear Modelling

Real-world problems: cost, distance and speed

09

Distance, Midpoint and Length

Formulas and applications on the number plane

10

Linear Inequalities

Graphing inequalities on the number plane

Checkpoint 2 — Linear Applications

Covers Lessons 6–10

Block C — Non-linear Relationships
11

Introduction to Parabolas

y = x2, basic shape and vertex at origin

12

Features of Parabolas

Vertex, axis of symmetry, concavity and y-intercept

13

Sketching Parabolas

From y = ax2 + bx + c using key features

14

Exponential Functions

y = ax, growth and decay graphs

15

Circles and Their Equations

x2 + y2 = r2, centre and radius

Checkpoint 3 — Non-linear Relationships

Covers Lessons 11–15

Block D — Synthesis & Problem Solving
16

Comparing Linear and Non-linear

Tables of values, shapes and rates of change

17

Transformations of Parabolas

Vertical shift, horizontal shift and dilation

18

Mixed Graphing Review

All graph types: linear, parabola, exponential, circle

19

Problem Solving with Relationships

Word problems requiring graph selection and analysis

20

Unit Synthesis: The Graphing Challenge

Integrated capstone project

Checkpoint 4 — Synthesis & Problem Solving

Covers Lessons 16–20

Unit Quiz

Full unit assessment