Year 7 Maths • AC9M7A05
Patterns, Tables, Rules and Graphs — Homework
Show tables, algebraic rules and graph reasoning clearly. Use step number as the independent variable unless another variable is specified.
Part A • 5 × 2 marks
Short questions
For y=4x−3, complete the table entry when x=4.
A function machine says “multiply by 6 then add 2”. Find the output for input 7 and write the rule.
The pattern 3, 8, 13, 18, … has what constant difference? Is its step-number graph linear?
What type of graph is produced by y=5x? State where it crosses the y-axis.
For C=2πr, identify the dependent variable and explain what changes when r increases.
Part B • 5 × 5 marks
Deep reasoning
A pattern is 10, 16, 22, 28, … . (a) Find the constant difference. (b) Make a table for steps 1–5. (c) Write y=mx+b. (d) Give the five ordered pairs. (e) Describe the graph.
A function machine says “subtract 4, then triple”. (a) Write the rule. (b) Find outputs for 2, 5, 8 and 11. (c) List the ordered pairs. (d) State the slope. (e) Explain why the graph is linear.
A tile pattern has 7, 11, 15 and 19 tiles at steps 1–4. (a) Identify the growth. (b) Extend to step 6. (c) Write T in terms of n. (d) Explain the meaning of slope and intercept. (e) Predict step 20.
An algorithm has term 1=3 and adds 9 each new term. (a) Generate six terms. (b) Create a table. (c) Write the explicit rule. (d) Give the graph shape. (e) Explain why repeated addition creates a linear rule.
The relationship C=2πr models circumference. (a) Make a table for r=1–5. (b) Give ordered pairs. (c) Describe the graph. (d) Explain why it is proportional. (e) Interpret the slope 2π.
Part C • Enrichment
Seasonal water-hole model
A hypothetical water-hole model has 12 L at cycle 1 and gains 7 L each wet-season cycle. Build a table for cycles 1–8, write a general rule, describe or sketch the Cartesian graph, interpret the slope and intercept, and explain how a simple linear model could help compare seasonal observations. Finally, state one limitation of assuming the same 7 L gain every cycle.