numberandalgebra path adv

📖 Prior Knowledge

ContentPrerequisite relationships
Equations- Verify equation solutions by substitution → Model and solve word problems with quadratics
Linear Relationships- Find the intersection of two lines → Solve simultaneous equations graphically
Equations A- Solve 3-step linear equations → Change the subject of a formula
- Solve 3-step linear equations → Solve simultaneous equations algebraically
- Solve linear equations with one algebraic fraction → Solve linear equations with two or more fractions
Algebraic Techniques B- Factorise by taking out a common algebraic factor → Change the subject when it appears twice
Algebraic Techniques C- Prove and apply special products → Complete the square
- Factorise using special products and grouping → Solve quadratic equations by factorisation
Indices C- Simplify expressions involving surds → Solve quadratics by completing the square
- Simplify expressions involving surds → Apply the quadratic formula
Equations B- Solve monic quadratic equations by factorising → Solve quadratic equations by factorisation
- Solve linear inequalities → Find unknown coefficients using the discriminant

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

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

Rearrange literal equations.pdf

  • Change the subject of a formula

Solve quadratic equations using a variety of methods.pdf

  • Solve equations of the form  by factorisation and by completing the square
  • Apply the quadratic formula  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