Five Things You Lot Mightiness Non Know Almost The Novel Gcse Content #2

I lately wrote a post about v changes to the content of maths GCSE. In today's ship service I listing v to a greater extent than changes that may non move widely known.

1. Invariance

When didactics shape transformations to Higher Tier students, you'll instantly demand to ensure that students are move able to pose invariant points. This is described inwards the specification every bit follows: "Describe the changes as well as invariance achieved past times combinations of rotations, reflections as well as translations".

We are given this instance enquiry from AQA:

"Write downwards the coordinates of a dot that is invariant when it is reflected inwards the business y = x".

Here, students volition demand to know that the points (1,1), (2,2) etc prevarication on the business y = x as well as would so move unchanged if reflected inwards this line.

There's a laid of resources for this topic inwards the Mind the Gap Maths Toolbox and Peter Mattock has shared a resources 'Invariance activeness sheet'.

2. Geometric Sequences
When I saw that geometric sequences instantly appear on the GCSE specification I assumed I'd move making usage of my AS score (C2) resources. This is non the case.

In C2 nosotros detect the nth term of a geometric sequence using the formula U_n = ar^n-1.  This gives us a 'position-to-term' rule. For instance if nosotros bring the sequence

3,  6,  12,  24,  48, ... 

so nosotros bring a = three (the start term) as well as r = 2 (the mutual ratio), so the nth term is U_n = 3(2^n-1).

Although geometric sequences create come upwards up at GCSE, there's 2 points from the specification that are worth noting when didactics this content:

1. Geometric sequences volition move inwards the cast rⁿ , for example:

2,  4,  8,  16,  ...  

3,  9,  27,  81, ...

√5,  5,  5√5,  25,  ...  (Higher Tier only)

2. Students are non required to detect expressions for the nth term of these sequences. They alone bring to create that for linear as well as quadratic sequences.

Examples of novel GCSE questions include:

The nth term of a sequence is (√3)ⁿ. What is the 5^th term of this sequence?

and...

U_n = 2U_n-1     U₁ = 2     Write downwards the start 4 price of this sequence.

In both examples students are using an nth term formula but non deriving the formula themselves. So when you lot learn this topic I propose that you lot focus on:

• recognising geometric sequences
• finding a mutual ratio as well as using this to proceed a sequence
• substituting into both position-to-term as well as term-to-term rules (including those using subscript notation). 

If you've spotted this enquiry inwards OCR's Practice Paper 5 you lot may intend that it contradicts what I've written hither most geometric sequences:

Here is a sequence.

2,  2√7,  14,  14√7,  ... 

a) Work out the adjacent term   (1)

b) Find the nth term   (3)

c) Find the value of the 21st term divided past times the 17th term.   (2)

I asked OCR for clarification as well as they sent a helpful reply:

"...the Assessment Objectives around making deductions, inferences as well as work solving hateful that some questions may involve taking known elements of content as well as taking them that fleck further, every bit seen inwards the question. Given that students at Higher tier bring to know how to detect the formula for the nth term of a quadratic sequence as well as too to 'recognise as well as usage sequences of... geometric progressions (r^n where n is a... surd) as well as other sequences', the enquiry is an instance of how higher powerfulness students powerfulness move expected to brand a deduction from known content. I don't await this to move a enquiry we'd regularly examine inwards alive assessment, but is the kind of affair we'd desire to include inwards sample assessment to hand an indication of how the content as well as Assessment Objectives are brought together inwards writing questions."

3. Scatter Graphs

There's a fleck to a greater extent than to scatter graphs now, though some teachers may bring already been roofing these things. Students volition demand to know:

• that correlation does non necessarily signal causation
• the deviation betwixt interpolation as well as extrapolation, as well as the dangers of extrapolation.

Although I volition usage the words interpolate as well as extrapolate inwards class, I incertitude these words volition move used inwards exams. Questions are probable to move inwards the cast of this instance from Edexcel:

You should non usage a business of best gibe to predict the let out of units of electricity used for heating when the exterior temperature is 30°C. Give 1 argue why. 

Students may too bring to pose an outlier from a scatter graph (note that this is informal identification of outliers - ie past times eye) as well as determine whether to ignore it when drawing a business of best fit.

The Scatter Graphs: True or False activeness from MathsPad covers all of this content as well as is absolutely excellent.

Don't forget that some statistics content has been removed from the novel GCSE, such every bit questionnaires as well as stratified sampling. It's worth looking at these previous post).

Also, inwards my ship service most real life graphs, I said that I was surprised to run into sketching cubics inwards my novel GCSE textbook - including identifying roots from factorised expressions.

Cubic graphs from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book 

This is what the specification says most cubic graphs:

recognise, sketch as well as translate graphs of ... simple cubic functions ...

This is on both the Foundation as well as Higher Tier. The AQA Teaching Guidance provides farther details, stating that students should move able to:

draw, sketch, recognise as well as translate graphs of the cast y = x³ + k where k is an integer

There's for certain no advert of the type of cubic graphs that characteristic inwards my textbook, as well as I intend this is 1 of the things that volition likely move removed from subsequent editions.

A few to a greater extent than clarifications
I asked OCR what they are oftentimes asked most the novel GCSE. In improver to questions regarding grading as well as didactics time, they are often asked to clarify the following:

• whether students volition move expected to differentiate to detect the slope of a crease (no, they volition bring to approximate slope from a tangent at a point, or potentially a chord betwixt 2 suitable points) - run into my blog post most this. 
• whether Foundation Tier students are required to calculate turning points of quadratic graphs (no, at Foundation they’ll only demand to read from the graph. At Higher they volition detect turning points past times completing the square).
• if Higher Tier students bring to know most the equations for whatever circle (no, alone those centred around the origin).

This is actually helpful data from OCR.

So that's it - I promise you're instantly feeling to a greater extent than informed most the novel GCSE content. Do allow me know your thoughts as well as questions.