Equations, formulas and inequalities - advanced

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

• Quadratic equations
• Simple cubic equations
• Inequalities

Content:

MA5-EQU-P-01

Solve monic quadratic equations

• Solve quadratic equations of the form \( ax^2+bx+c=0 \), limited to \( a=1 \), using factors

Solve cubic equations

• Determine that for any value of  \( k \) there is a unique value of \( x \) that solves a cubic equation of the form  \( ax^3=k \) where \(a \ne 0 \)
• Solve cubic equations of the form , leaving answers in exact form and as decimal approximations

Solve linear inequalities and graph their solutions on a number line

• Represent inequalities on a number line
• Solve linear inequalities, including those with negative numbers, and graph the solutions
• Recognise that an inequality has an infinite number of solutions unless other restrictions are introduced

MA5-EQU-P-02

Solve linear equations involving algebraic fractions and equations of more than 3 steps

• Solve linear equations involving more than 3 steps
• Solve equations that involve 2 or more fractions

Rearrange literal equations

• Change the subject of a formula

Solve quadratic equations using a variety of methods

• Solve equations of the form \( ax^2+bx+c=0 \) by factorisation and by completing the square
• Apply the quadratic formula \( x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \) to solve quadratic equations
• Apply the most appropriate method to solve a variety of quadratic equations
• Use substitution to verify solutions to quadratic equations
• Identify whether a given quadratic equation has real solutions, and if there are real solutions, whether or not they are equal
• Solve quadratic equations resulting from substitution into formulas in various contexts
• Model and solve word problems using quadratic equations in various contexts
• Solve equations that are reducible to quadratics

Solve linear simultaneous equations, both algebraically and graphically

• Solve linear simultaneous equations by finding the point of intersection of their graphs
• Solve linear simultaneous equations using algebraic techniques including substitution and elimination methods
• Model and solve word problems using simultaneous equations and interpret their solutions
• Describe an identity as an equation that is true for all values of the pronumeral and relate the identity to coincident lines
• Describe a contradiction as an equation that has no solutions and relate the contradiction to parallel lines