Standard Algebra – Linear relationships

This lesson comprises four (4) master classes focusing on:

• Reviewing algebraic expressions and formula
• Constructing and analysing linear models
• Solving linear equations
• Using formulae to calculate speed, distance and time
• Using formulae to calculate blood alcohol levels and medication dosage

Content:

MS-A1

• Review the substitution of numerical values into linear and non-linear algebraic expressions and equations
  • review evaluating the subject of a formula, given the value of other pronumerals in the formula
  • change the subject of a formula
  • solve problems involving formulae, including calculating distance, speed and time (with change of units of measurement as required) or calculating stopping distances of vehicles using a suitable formula
• Develop and solve linear equations, including those derived from substituting values into a formula or those developed from a word description
• Calculate and interpret blood alcohol content (BAC) based on drink consumption and body weight
  • use formulae, both in word form and algebraic form, to calculate an estimate for blood alcohol content (BAC), including \( BAC_{Male}=\frac{10N-7.5H}{6.8M} \) and \( BAC_{Female}=\frac{10N-7.5H}{5.5M} \) where \( N \) is the number of standard drinks consumed, \( H \) is the number of hours of drinking, and \( M \) is the person’s weight in kilograms
  • determine the number of hours required for a person to stop consuming alcohol in order to reach zero BAC, eg using the formula \( time=\frac{BAC}{0.015} \)
  • describe the limitations of methods estimating BAC
• Calculate required medication dosages for children and adults from packets, given age or weight, using Fried’s, Young’s or Clark’s formula as appropriate
  • Fried’s formula: \( Dosage\ for\ children\ 1-2\ years=\frac{age\ (in\ months) \times adult\ dosage}{150} \)
  • Young’s formula: \( Dosage\ for\ children\ 1-12\ years=\frac{age\ of\ child\ (in\ years) \times adult\ dosage}{age\ of\ child\ (in years) + 12} \)
  • Clark’s formula: \( Dosage=\frac{weight\ in\ kg \times adult\ dosage}{70} \)

MS-A2

• Model, analyse and solve problems involving linear relationships, including constructing a straight-line graph and interpreting features of a straight-line graph, including the gradient and intercepts
  • recognise that a direct variation relationship produces a straight-line graph
  • determine a direct variation relationship from a written description, a straight-line graph passing through the origin, or a linear function in the form \( y=mx \)
  • review the linear function \( y=mx+c \) and understand the geometrical significance of \( m \) and \( c \)
  • recognise the gradient of a direct variation graph as the constant of variation
  • construct straight-line graphs both with and without the aid of technology
• Construct and analyse a linear model, graphically or algebraically, to solve practical direct variation problems, including the cost of filling a car with fuel or a currency conversion graph
  • identify and evaluate the limitations of a linear model in a practical context