TMJC H2 Chapter 4 Equations & Inequalities Learning Package 2024

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Chapter 4 Equations and Inequalities TMJC 2024 Page 1 of 26 H2 Mathematics (9758) Chapter 4 Equations and Inequalities Core Concept Notes Success Criteria: SURFACE DEEP TRANSFER Solving an equation  Solve polynomial equations by factorisation and/or quadratic formula  Solve polynomial equations using graphing calculator  Use of graphing calculator to solve a non-polynomial equation by sketching graphs System of linear equations  Solve the system of linear equations using the graphing calculator Inequalities  Represent inequalities on a real number line (e.g. 3x ) using open/closed circle  Interpret the mathematical language “and” and “or” on a real number line  Solve linear or quadratic inequalities by hand or graphical methods  Solve simple inequalities involving modulus by hand or graphical methods  Use of graphing calculator to solve inequalities (graphical methods) System of linear equations  Interpret the solutions found using a graphing calculator Inequalities  Solve inequalities of the form f ( ) 0g( ) x x  (< , ≥ , ≤ ) by hand or graphical methods, where f ( )x and g( )x are linear or quadratic expressions.  Solve inequalities of the form a < f ( )xb (≤ ) by hand or graphical methods System of linear equations  Formulate a contextual problem into possible mathematical equations and provide possible solutions, and interpret/reflect the solutions in the real world context Inequalities  Formulate a contextual problem into possible mathematical inequalities and provide possible solutions, and interpret/reflect the solutions in the real world context (Examples can be in subsequent topics such as Arithemtic and Geometric Series, and Binomial / Normal Distributions.)

Chapter 4 Equations and Inequalities TMJC 2024 Page 2 of 26 §1 Finding the Numerical Solution of an Equation Recap: The solution (roots/zeros) to an equation is/are the value(s) which satisfies (satisfy) the equation. To find the solution (roots/zeros) of an equation, we can use one of the following methods : (a) Algebraic Factorisation/ Formula (b) Using Application: PlySmlt2 on a Graphing Calculator (GC) (c) Sketching graphs using a Graphing Calculator (GC) (a) Algebraic Factorisation/Formula (When a question needs an EXACT solution) Example 1 Find the values of x satisfying the equation 2 20xx+ − = . Algebraic Factorisation 2 20xx+ − = ( )( )2 1 0 2 or 1 xx xx + − =  =− = Formula 2 2