New Gcse: Functions

Last calendar week I taught the novel GCSE functions content to my Year 11s. What a lovely topic, sum of delicious algebra. As much every bit I complain almost the unreasonably large release of novel topics that conduct maintain been added to the GCSE syllabus, I conduct maintain to acknowledge that this theme is real welcome. Like Sets as well as Venns, it's a pleasance to teach. It's both accessible as well as stretching, as well as fits good amongst other topics.

When you lot learn functions your students acquire to revisit some cardinal algebraic skills including solving linear as well as quadratic equations, simplifying as well as rearranging formulae, as well as substitution. Given that the novel higher GCSE is 30% algebra, revisiting these inwardness skills is definitely worthwhile at this indicate inwards the course.

In the legacy GCSE the exclusively usage of role annotation was inwards graph transformations. It e'er felt a fleck wrong to utter almost f(2x), f(x + 3) etc when the annotation f(x) was previously unknown as well as wasn't used elsewhere. The GCSE course of written report flows much improve instantly nosotros are able to encompass functions followed yesteryear graph transformations (which has instantly been reduced to exclusively translations as well as reflections).

For Higher GCSE ix - 1 nosotros conduct maintain 3 principal areas to learn inwards this topic:

• Inputs as well as outputs
• Composite functions
• Inverse functions

I did this over iv lessons amongst my top set.

This is similar to the electrical current functions content at Influenza A virus subtype H5N1 level, though Influenza A virus subtype H5N1 flat also includes domain as well as range. This functions content volition stay inwards Influenza A virus subtype H5N1 flat maths nether the novel linear specifications. Meeting this theme at GCSE volition for certain arrive at goodness students who become on to conduct maintain Influenza A virus subtype H5N1 flat maths.

This post service aims to back upwards GCSE teachers who are pedagogy this theme for the starting fourth dimension time.

Specification
At both Foundation as well as Higher tier, students are required to "interpret elementary expressions every bit functions amongst inputs as well as outputs". At Foundation the principal focus is on role machines. At Higher, there's more: "interpret the contrary procedure every bit the ‘inverse function’; translate the succession of 2 functions every bit a ‘composite function’". In AQA's Teaching Guidance, nosotros are told that Higher tier students should last able to:

• understand that a role is a human relationship betwixt 2 sets of values
• understand as well as usage role notation, for instance f(x)
• substitute values into a function, knowing that, for instance f(2) is the value of the role when x = 2
• solve equations that usage role notation
• understand, translate as well as usage composite role fg(x)
• understand, translate as well as usage inverse role f^-1(x)

Edexcel's Content Exemplification FAQs state that "candidates could last asked to arrive at the graph of a role or an inverse function. It is possible that this could hence last linked into a geometrical interpretation".

OCR's specification differs slightly, maxim 'knowledge of role annotation volition non last required'.

Challenges
When pedagogy inverse functions I starting fourth dimension showed my students how to piece of work backwards through a role machine. I hence showed them the procedural 'changing the dependent patch method' that I learn at Influenza A virus subtype H5N1 flat (similar to the method explained yesteryear Edexcel below).

My students conduct maintain mock GCSE results ranging from Grade 4 to Grade 8. Although they had no occupation finding the inverse of elementary functions, some struggled to uncovering the inverse of this function:

They were taught how to alter the dependent patch when the dependent patch appears twice (ie when you lot conduct maintain to factorise) inwards Year 10, only many couldn't recall it. This was a expert chance to learn it again.

I gear upwards them a fairly challenging homework amongst questions extracted from Edexcel's first-class new content resources. Many struggled amongst the instant component of this question:

The role f is such that f(x) = 2x - 3
Find (i) ff(2)   (ii)  Solve the equation ff(a) = a

The usage of the letter a confused them.

Composite functions are definitely the most challenging component of this topic. When I taught my composite functions lesson I was convinced that they'd all understood the 'right to left' order, only when I gave them their weekly quiz the 2 composite functions questions were answered incorrectly yesteryear a release of students. They got the guild wrong.

Most of my degree also got this inquiry wrong:

I included this partly to seek their recollection of negative as well as fractional indices only it truly showed a misconception relating to the guild of operations. Even some of my strongest students incorrectly selected answer B because they'd done the multiplication earlier the index.

Questions for my weekly quizzes (which I wrote almost here) are e'er taken from diagnosticquestions.com.

Exam Questions
Mel's collection of here under 'resources') 

extracts from Influenza A virus subtype H5N1 flat Solomon worksheets

composite as well as inverse functions activities from MathsPad.co.uk (subscription required)

examples as well as exercises from this CIMT textbook chapter

Extract from C3 Functions Solomon Worksheet A

AQA has a good Bridging Unit Resource Pocket on functions. OCR has a Language of  Functions theme check-in which is truly expert for role machines.

Writing Algebra is a prissy role machine activity from Stacy Brookes.

See my algebra resources library for to a greater extent than resources.

If you're looking for illustrations to usage inwards your lesson hence this website is helpful. I similar what they've done hither for composite functions:

It's worth mentioning that the role annotation nosotros usage at schoolhouse may differ to that used yesteryear universities - read this thread for to a greater extent than on this.

I promise that you lot flora this post service useful as well as that you lot bask pedagogy functions every bit much every bit I did!