Five Things You Lot Mightiness Non Know Well-Nigh The Novel Gcse Content #2

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

1. Invariance

When pedagogy shape transformations to Higher Tier students, you'll straightaway demand to ensure that students are travel able to seat invariant points. This is described inward the specification equally follows: "Describe the changes in addition to invariance achieved past times combinations of rotations, reflections in addition to translations".

We are given this instance inquiry from AQA:

"Write downward the coordinates of a dot that is invariant when it is reflected inward the line of piece of work y = x".

Here, students volition demand to know that the points (1,1), (2,2) etc prevarication on the line of piece of work y = x in addition to would thence travel unchanged if reflected inward this line.

There's a laid of resources for this topic inward 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 straightaway appear on the GCSE specification I assumed I'd travel making exercise of my AS marking (C2) resources. This is non the case.

In C2 nosotros uncovering 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 accept the sequence

3,  6,  12,  24,  48, ... 

so nosotros accept a = iii (the showtime term) in addition to r = 2 (the mutual ratio), so the nth term is U_n = 3(2^n-1).

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

1. Geometric sequences volition travel inward the shape 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 uncovering expressions for the nth term of these sequences. They solely accept to produce that for linear in addition to 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 downward the showtime 4 damage 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 advise that you lot focus on:

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

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

Here is a sequence.

2,  2√7,  14,  14√7,  ... 

a) Work out the side past times side 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 in addition to they sent a helpful reply:

"...the Assessment Objectives around making deductions, inferences in addition to work solving hateful that some questions may involve taking known elements of content in addition to taking them that chip further, equally seen inward the question. Given that students at Higher tier accept to know how to uncovering the formula for the nth term of a quadratic sequence in addition to equally good to 'recognise in addition to exercise sequences of... geometric progressions (r^n where n is a... surd) in addition to other sequences', the inquiry is an instance of how higher powerfulness students mightiness travel expected to brand a deduction from known content. I don't await this to travel a inquiry we'd regularly evidence inward alive assessment, but is the form of matter we'd desire to include inward sample assessment to hand an indication of how the content in addition to Assessment Objectives are brought together inward writing questions."

3. Scatter Graphs

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

• that correlation does non necessarily shout out for causation
• the departure betwixt interpolation in addition to extrapolation, in addition to the dangers of extrapolation.

Although I volition exercise the words interpolate in addition to extrapolate inward class, I incertitude these words volition travel used inward exams. Questions are probable to travel inward the shape of this instance from Edexcel:

You should non exercise a line of piece of work of best jibe to predict the seat out of units of electricity used for heating when the exterior temperature is 30°C. Give 1 argue why. 

Students may equally good accept to seat an outlier from a scatter graph (note that this is informal identification of outliers - ie past times eye) in addition to create upward one's heed whether to ignore it when drawing a line of piece of work of best fit.

The Scatter Graphs: True or False activeness from MathsPad covers all of this content in addition to is absolutely excellent.

Don't forget that some statistics content has been removed from the novel GCSE, such equally questionnaires in addition to stratified sampling. It's worth looking at these previous post).

Also, inward my postal service close real life graphs, I said that I was surprised to come across sketching cubics inward 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 close cubic graphs:

recognise, sketch in addition to translate graphs of ... simple cubic functions ...

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

draw, sketch, recognise in addition to translate graphs of the shape y = x³ + k where k is an integer

There's sure no cite of the type of cubic graphs that characteristic inward my textbook, in addition to I intend this is 1 of the things that volition in all probability travel removed from subsequent editions.

A few to a greater extent than clarifications
I asked OCR what they are often asked close the novel GCSE. In add-on to questions regarding grading in addition to pedagogy time, they are often asked to clarify the following:

• whether students volition travel expected to differentiate to uncovering the slope of a crease (no, they volition accept to guess slope from a tangent at a point, or potentially a chord betwixt 2 suitable points) - come across my blog post close this. 
• whether Foundation Tier students are required to calculate turning points of quadratic graphs (no, at Foundation they’ll simply demand to read from the graph. At Higher they volition uncovering turning points past times completing the square).
• if Higher Tier students accept to know close the equations for whatever circle (no, solely those centred around the origin).

This is actually helpful data from OCR.

So that's it - I promise you're straightaway feeling to a greater extent than informed close the novel GCSE content. Do permit me know your thoughts in addition to questions.