New A Level Support

This page provides links to support the teaching of some of the new topics in A Level Mathematics. More general resources are featured at the bottom of the page.

My list of the main additions to the specification is not exhaustive. Some of the topics listed might have featured in previous specifications, but not for all exam boards. I've categorised topics as 'Year 12' and 'Year 13' as a guide, but timings will differ by school.

Free resources are listed for each new topic. This page is work in progress and will be updated regularly. Please email any additional resources to resourceaholic@gmail.com. Note that I haven't linked to any resources which require subscription or purchase (eg Integral and Solomon), though I do recommend them if you have access.

My A level resource libraries will continue to be organised as 'AS' and 'A2' for school year 2017/18 (while the legacy specification is still being taught to Year 13).


Proof
Year 12: Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion and disproof by counter example. 

Year 13: Proof by contradiction (including proof of the irrationality of √2 and the infinity of primes, and application to unfamiliar proofs).


Resources: Proof delivery guide | Check-in testThe irrationality of root 2 | When is 6×7=426×7=42 a counter-example? | Proof worksheet | Proof and Reasoning | Triangle number differences | Root 2 is irrational | more to come...



Inequalities
Year 12: Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions. Express solutions through correct use of ‘and’ and ‘or’, or through set notation. Represent linear and quadratic inequalities such as y > x + 1 and y > ax2 + bx + c graphically.

Note: fractions in inequalities are new (e.g. a/x < b becomes ax < bx2) and graphical inequalities are new


Resources: Inequalities on graphsRational inequalities | Inequalities sample chapter (legacy FP2) | Inequalities for some occasions | Inequations: regionsCIMT Inequalities (for graphical inequalities) | more to come...

Additional inequalities resources are available in my AS Core library.



Graphs
Year 12: Understand and use proportional relationships and their graphs.

Year 12: Understand and use graph of functions; sketch curves defined by simple equations including polynomials such as quartic functions and sketch the curve y = a / x² (including their vertical and horizontal asymptotes).

Year 13: The modulus of a linear function. Students should be able to sketch the graphs of y =|ax + b|. They should be able to use their graph. For example, sketch the graph with equation y = |2x – 1| and use the graph to solve the equation |2x – 1| = x or the inequality |2x – 1| > x


Resources: Functions Stack | Modulus Function Worksheets | Curve Match | Translating or not? | more to come...

Additional graphing resources are available in my AS Core library.


Sequences
Year 13: Increasing sequences; decreasing sequences; periodic sequences (recurrence relations).


Resources: Increasing, decreasing and not monotonic sequences video | Recurrence relations worksheet | Types of sequence and series | Final digit | more to come...






Trigonometry
Year 13: Understand and use the standard small angle approximations of sine, cosine and tangent.



Resources: Testing the small angle approximationVideo: small angle approximations | Video: applying small angle approximations | Sample chapter: The small angle approximations | What do functions do for tiny x?



Exponentials and Logarithms
Year 12: Use logarithmic graphs to estimate parameters in relationships of the form y = axn and y = kbx , given data for x and y.

Resources:  
Plotting the planets | Linearizing data | more to come...






Differentiation
Year 12: Sketching the gradient function for a given curve.

Year 12: Differentiation from first principles for small positive integer powers of x.

Year 13: Second derivative's connection to convex and concave sections of curves and points of inflection.

Year 13:
Differentiation from first principles for sin x and cos x.



Resources: Differentiation from first principles | Gradient match | Slippery slopes | Zooming in | Gradients of gradients | Trig gradient match | more to come...




Integration
Year 13: Use of definite integral to find the area between two curves.



Resources: Meaningful areas | more to come...







Numerical Methods
Year 13: Solve equations approximately using simple iterative methods; be able to draw associated cobweb and staircase diagrams.

Year 13Solve equations using the Newton-Raphson method and other recurrence relations of the form xn+1= g(xn) Understand how such methods can fail.


Resources: Numerical Methods | Numerical Methods Notes | Graphical iteration (staircase and cobweb) | more to come...


Sampling
Year 12: Understand and use sampling techniques, including simple random sampling and opportunity sampling. Students will be expected to be familiar with: simple random sampling, stratified sampling, systematic sampling, quota sampling and opportunity (or convenience) sampling.

Resources: Edexcel Teaching Guide: Statistics for A level Maths | Methods of samplingSampling techniquesCensus or sample? | CIMT sampling | Sampling methods slides | An Exercise in Sampling: Rolling Down the River | Data types and sampling methods | more to come...


Hypothesis Testing
Year 13: Hypothesis testing for correlation coefficients as measures of how close data points lie to a straight line. Be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded).

Year 13: Conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context.

Resources: Edexcel Teaching Guide: Statistics for A level Maths | Psychology - Correlation Study | Hypothesis Testing Notes | more to come...









9 comments:

  1. As a working mum I don't know how you find the time to do this but I'm extremely glad that you do!! (Mine are 11 and 16 and fairly self sufficient these days but I barely have time to read other people's blogs let alone maintain such a fabulous one!) I'm moving to a new school (selective grammar) in September and will have three year 12 classes and it seems your blog will be as helpful then as it has been during my training and NQT years and this year as my first year as a fully fledged teacher Thank you :-)

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  2. Thanks for another enormously helpful post!

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  3. I shall be keeping a tag to this page handy, thank you so much. Any thoughts on how the data set in Statistics is going to work? Jenny

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    1. Hi. I've not thought about it much yet. I won't get to the statistics part of the course until February 2018 so I will look into it then.

      I'm still sulking about the impracticalities tbh. IT rooms are hard to book and the computers are unreliable at my school. But a bigger issue is that many students these days don't even know the basics of Excel. They study computing instead of ICT so they no longer learn Office skills. Given that the time constraints are ridiculous in Year 12, I can't imagine I'll have time to teach them Excel from scratch (or geogebra, or something else) and spend time leisurely exploring a data set in an IT room. It would be nice to do, but it's going to be a challenge. Perhaps it might be best done in Year 13 - reviewing statistical techniques using the large data set.

      I'm sure it will all turn out ok! Edexcel have published some teaching materials here: https://qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/Teaching%20and%20learning%20materials/Data_set_activities_for_AS_and_A_level_Mathematics.zip

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    2. Jenny - it would be worth looking out for any FMSP training on statistics that might be taking pkace near to your school. We are doing loads re technology and the large data set as CPD days and at network meetings. http://furthermaths.org.uk/cpd_events

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  4. Thank you for your helpful reply. The knowledge of Excel(or lack of it) is certainly a big factor. I shall keep an eye out for any gems later in the year. In the meantime I am enjoying investigating your website, having recently found it, so many great resources, thank you for those too.

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  5. To get you in the mood for February, a fun introduction to the Edexcel Large Data Set (also on TES) https://youtu.be/KOdx12uFEQI

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