Year 7 Maths • AC9M7A06 • Homework
Multi-variable Formulas & Sensitivity
Vary inputs systematically, hold other variables constant where appropriate, and explain what each change means.
Part A • 5 × 2 marks
Short multistep questions
- V = lwh. If l=10 cm, w=4 cm and h=7 cm, calculate V and include units.
- A spreadsheet uses =A1*B1. If A1=12 and B1=9, calculate the output and state the operation being performed.
- Using d=st, find the distance travelled at 60 km/h for 3 h. Then state which variable was held constant if speed alone were being tested.
- For y=3a+2b, a increases by 5 while b stays fixed. Find the change in y and explain how you know without calculating the full new value.
- Explain what one-variable-at-a-time sensitivity analysis is designed to reveal and why other variables are held constant.
Part B • 5 × 5 marks
Extended reasoning
- A prism has l=12 cm and w=6 cm. Height h varies from 1 to 5 cm. Create a table of V values, describe the pattern, identify the relationship between V and h, explain why it is linear, and define what “holding variables constant” means.
- For d=st, time is fixed at 2 h and speed takes 40, 60 and 80 km/h. Generate a table, describe the change in d, identify independent/dependent variables, explain why the relationship is proportional, and interpret systematic variation.
- For y=4x−2z+10, vary x from 1 to 5 while z=3. Generate a table, describe the effect of x, explain why this one-variable slice is linear, calculate the change in y for a 3-unit increase in x, and explain what sensitivity means here.
- For d=st, build a 3×3 table for speeds 30,60,90 km/h and times 1,2,3 h. Describe row and column patterns, explain simultaneous variation, identify why d depends on two variables, and predict what happens if both s and t double.
- For P=2a+5b−c, set a=4 and c=10, then vary b from 1 to 5. Generate a table, describe the effect of b, calculate the change in P from b=1 to b=5, explain what the coefficient 5 means, and state why coefficient size should be compared carefully when variables use different scales.
Part C • Enrichment
Model sensitivity investigation
For F=3x+2y−4z+15, create three tables: vary x from 1–5 with y=2,z=1; vary y from 1–5 with x=2,z=1; vary z from 1–5 with x=2,y=2. Compare the output changes, identify direction and magnitude of each per-unit effect, explain what the experiment reveals about this mathematical model, and discuss why sensitivity analysis can improve explainability without proving that a model is accurate, fair or causal.