Linear modelling

A gym charges $20 joining fee plus $8 per week. Write the cost equation.

For C = 5n + 12, find C when n = 10 and interpret the result.

Choose whether a table with constant differences represents a linear relation.

A student uses a curved graph for a fixed cost plus constant rate. Explain why a straight line is expected.

Write the rule or formula most useful for Linear modelling.

Show how to check one answer using estimation, substitution or inverse operations.

Write one common mistake students make in Linear modelling and correct it.

Create a small table, diagram or equation that represents this topic.

State where units, exact form or rounding matter in this topic.

Write one exam-style short question on Linear modelling and solve it.

Compare two hire plans: A costs $15 + $4h and B costs $9 + $6h. Find the break-even time.

Model the cost of printing posters with a setup fee and per-poster charge, then interpret the equation and graph.

Solve a multi-step problem involving Linear modelling and explain every step clearly.

Create a realistic word problem for Linear modelling, solve it and interpret the answer.

Compare two methods for a problem in Linear modelling and explain which is more efficient.

Write a worked solution that includes a check for reasonableness.

Create a problem with a deliberate trap, then solve it correctly and explain the trap.

Use a diagram, table, graph or equation to model a situation involving Linear modelling.

Explain how this topic connects to a previous Year 7 or Year 8 maths skill.

Write a full-mark response to a challenging Linear modelling question, including reasoning and final answer.