New Gcse: Inequalities

The new GCSE specification has 2 additions nether the heading Inequalities:

a) using gear upwards musical note to correspond solutions

b) solving quadratic inequalities.

This post service explains these changes as well as provides education back upwards as well as resources.

Set Notation

Students volition straightaway hold upwards required to correspond solutions to inequalities using gear upwards notation. This is inwards add-on to representing solutions on publish lines as well as graphs. The OCR specification gives us 2 examples of gear upwards notation:

If you're non familiar alongside gear upwards notation, it's explained here (it's unremarkably referred to equally 'set-builder notation'). Note that either a vertical trouble or a colon tin move hold upwards used to correspond 'such that'.

Image source: coolmath.com

The examples from the OCR specification imply that GCSE students volition not postulate to know symbols representing publish types (eg ℤ for integers), as well as thence volition non hold upwards required to limited their answers similar this:

Image source: mathsinsfun.com

Set musical note comes upwards elsewhere inwards the novel GCSE specification - nether the championship 'Venn Diagrams as well as Sets' nosotros lead maintain this:

Source: OCR specification

So create nosotros lead maintain whatsoever resources to exercise this? There's enough of resources relating to gear upwards musical note as well as probability inwards my Data library. I've also made this simple worksheet so students tin move exercise using gear upwards musical note to correspond inequalities. 

Quadratic Inequalities

Here's a enquiry from OCR's Sample Assessment Materials Higher Paper five (non-calculator):

Find the gain of values of x for which x² - 3x - 10 ≤ 0

If y'all haven't taught AS score maths or iGCSE so y'all mightiness non lead maintain taught this topic before. There's a few dissimilar methods for solving quadratic inequalities. H5N1 mutual method involves sketching a graph of the quadratic component so identifying the required part (see event below). To role this method, our GCSE students volition postulate to hold upwards confident inwards sketching quadratics (this is covered inwards the novel specification). I oftentimes honor that my Year 12 students brand mistakes inwards their end reply because they don't bother sketching the graph. To me, sketching the graph is essential.

Desmos is a fantastic tool for exploring quadratic inequalities - cheers to Cathal (@CGA_PGS) for sharing this example.

An choice method for solving quadratic inequalities involves using a publish trouble as well as assay out points. In this method students even so lead maintain to honor the critical values, but instead of sketching the graph they depository fiscal establishment fit the value of a assay out indicate inwards each region.

Given that this topic has been taught inwards iGCSE as well as H5N1 score courses for unopen to time, there's surprisingly few resources available. There's a few resources inwards my Algebra library, including a 'Spot the Mistake' action I made, but I postulate more! If y'all know of anything else so delight part it. 

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