Year 7 Maths • AC9M7A01

Variables, Formulas and Substitution — Homework

Show substitution clearly, preserve units, and interpret each unknown in its context.

5 × 2
Short questions
5 × 5
Deep questions
1
Enrichment

Part A • 10 marks

Five 2-mark questions

  1. Use A=lw. A rectangle has l=12.5 cm and w=8 cm. Calculate A and include units. [2]
  2. Use p=6g+b. A team scores 3 goals and 7 behinds. Find p. [2]
  3. Use d=m/v. Mass m=240 g and volume v=80 cm³. Find d with units. [2]
  4. Use W=b+1.5rh. If b=$540, r=$20/h and h=3, calculate W. [2]
  5. Use HRmax=220−age. Find the predicted maximum heart rate for age 14. [2]

Part B • 25 marks

Five 5-mark questions

  1. A rectangular garden has A=lw, l=18 m and A=162 m². (a) Write the formula. (b) Substitute known values. (c) Find w. (d) Explain why using a variable is useful. (e) Interpret the result with units. [5]
  2. A football team uses p=6g+b. It scores 5 goals and 47 total points. (a) Substitute known values. (b) Find b. (c) Check by substitution. (d) Explain what the coefficient 6 represents. (e) Interpret b in context. [5]
  3. A worker has W=b+1.5rh, where b=$720, r=$24/h and W=$900. (a) Substitute. (b) Isolate the overtime component. (c) Find h. (d) Check your value in the original formula. (e) Explain the fixed and variable parts of this wage model. [5]
  4. A substance has d=m/v, density 4.5 g/cm³ and mass 360 g. (a) Substitute. (b) Rearrange for v. (c) Calculate v. (d) Check using units. (e) Interpret the result. [5]
  5. Use HRmax=220−age and HRtarget=0.7HRmax for a 15-year-old. (a) Find HRmax. (b) Substitute it into the target formula. (c) Find HRtarget. (d) Explain why linked formulas must be used in the correct order. (e) Interpret the numerical result as a prediction from the given model, not a personalised medical recommendation. [5]

Enrichment

Formula modelling on Country/Place

In a hypothetical classroom model, water flow through a channel is represented by Q=Av, where Q is flow rate (m³/s), A is cross-sectional area (m²) and v is measured water velocity (m/s). At one observation point A=12 m² and v=1.8 m/s.

Calculate Q; explain what each variable represents; interpret the units; investigate how Q changes if A or v changes; and explain how a formula can support environmental observation while recognising that real Country/Place knowledge and management involves additional environmental, cultural and local knowledge beyond this simple mathematical model.