2024 JPJC Chapter 3_Equation and Inequalies

Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2023 Chapter 3 Equations and Inequalities / Pg 1 Chapter 3: Equations and Inequalities Content Outline Include:  formulating an equation, a system of linear equations, or inequalities from a problem situation  solving an equation exactly or approximately using a graphing calculator  solving a system of linear equations using a graphing calculator  solving inequalities of the form f ( ) g( ) x x > 0 where f(x) and g(x) are linear or quadratic expressions that are either factorisable or always positive  concept of |x| and use of relations x a b a b x a b       and or x a b x a b x a b       in the course of solving inequalities  solving inequalities by graphical methods References  Further Pure Mathematics by Brian and Mark Gaulter (Oxford)  My First Step in using TI-84Plus CE for H1 and H2 Math by Dr Spario Soon (Interactive Math Exploration Centre) Prerequisites  Basic rules for manipulating inequalities  Ability to sketch graphs of quadratic, cubic and quartic functions and use the graphing calculator to find the x-intercepts of these graphs  Determine the equations of vertical, horizontal asymptotes and restrictions on the possible values of x and y 1. Properties of Inequalities (Recap from O Level Mathematics) 1.1 Addition & Subtraction (a) Any quantity can be added to or subtracted from both sides of an inequality without changing the inequality sign. If a b , then a c b c   and a – c > b – c For example, If x > 3, then x + 7 > 3 + 7 and x – 8 > 3 – 8 (b) Inequalities of the same kind can be added together . If a > b and c > d , then a + c > b + d For example, If x > 3 and y > 4, then x + y > 3 + 4

Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2023 Chapter 3 Equations and Inequalities / Pg 2 (c) NEVER SUBTRACT inequalities. For example, If x > 2 & y > 0, then x y may not be greater than 2 Counter example: For 3x and 4y  , 3 4x y   1 ≯2 1.2 Multiplication & Division (a) Both sides of an inequality can be multiplied or divided by any positive quantity without changing the inequality sign. If c > 0 and a b , then ac > bc and a b c c For example: If x > 3, then x × 2 > 3 × 2 and 3 2 2 x  (b) Both sides of an inequality can be multiplied or divided by any negative quantity but the inequality sign must be reversed. If d < 0 and a > b , then ad < bd and a b d d For example: If x > 3, then 2 2(3)x  and 3 2 2 x   Note: Greater care must be taken when dealing with logarithmic terms. When solving the inequality, ln 5 .(Since )ln 0. ln 0.2 ln 5 ln 0.2 2 0 n n   When solving the inequality, ln 5.(Since )ln 2 ln 2 ln 5