GCSE: Quadratic Inequalities Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com @Dr. Frost. Maths Last modified: 7 th May 2017
Reminder: Inequalities ? ? Bro Side Notes: Equations and inequalities are not limited to just one solution: we have seen that quadratics equations often have 2 solutions, and in this example it would not be possible to ‘list’ all the solutions because there are infinitely many! In this particular example, known as a linear inequality, the range of solutions was simple. But for quadratic inequalities, this might be more complex…
Quadratic Inequalities By trial and error (or otherwise!), try and think of the range (or ranges) of values that satisfies the following inequality. Your values need not be whole numbers. ?
Solving Quadratic Inequalities Step 1: Get 0 on one side (already done!) ? Step 2: Factorise Step 3: Sketch and reason Click to Bro-Bolden > ? ? ?
Solving Quadratic Inequalities Step 1: Get 0 on one side (already done!) Step 2: Factorise Step 3: Sketch and reason ? Sketch with highlighted region ? Final solution
Further Examples ? ? Bro Note: The most common error I’ve seen students make with quadratic inequalities is to skip the ‘sketch step’. Sod’s Law states that even though you have a 50% chance of getting it right without a sketch (presuming you’ve factorised correctly), you will get it wrong.
Test Your Understanding 1 ? 2 ?
Exercises 1 a b c d e 2 a b c d e f ? ? ? ? ? 3 a b ? ? ? c ? N a b c ? ? ?