Year 1: P2 – Algebra and Functions
P2.1 Indices and Surds
Step One:
Learn
The first in a series of videos on indices and surds. In this video we look at laws of indices at a Year 1 A level standard
The second in a series on indices and surds. This video extends the use of index laws to include negative and fractional indices
The third video in the series on indices and surds. This video deals with simplifying surds and using the four operations; addition, subtraction, multiplication and division with surds
Step Two:
Check
This stuff is the foundations for what’s to come, so it needs to be solid. Although much of it can be done with a calculator, examiners can always find a way around it in order to be able to check your skills, so it is well worth spending the time to ensure you know what you are doing.
P2.2 Quadratics
Step One:
Learn
The second video in a series on quadratics. In this video we see how the principles of factorising quadratics can be applied to polynomials of a particular form
The third in a series on quadratics. Here we review and and extend skills on solving quadratics by factorising, quadratic formula and completed square
The fourth in a series on quadratics. This video introduces the discriminant and how it is used to identify the number and type of roots of a quadratic equation
Step Two:
Check
Check your knowledge of the basics of manipulating a factorised quadratic
Check your knowledge of discriminants by sketching quadratics
P2.3 Simultaneous equations
Step One:
Learn
The first video in the series which recaps the knowledge from GCSE then extents further into more complex forms. Essentially, the video gives guidance on which technique is most appropriate to use given the form of the equations in the question.
The second video in the series on simultaneous equations. This video show you how to solve simultaneous equations when one of the equations is not linear (i.e quadratic or a circle or a reciprocal).
Step Two:
Check
All lot of this stuff can be done using the functions on your calculator … however, you need to know the skills, so do as much as possible without the numerical life support machine
P2.4 Inequalities
Step One:
Learn
The first video in the series on inequalities. This video gives an introduction to solving basic linear inequalities and explores the issues surrounding multiplying and dividing by negatives when solving.
The second video in the series on inequalities. This video looks at solving quadratic inequalities and how to describe the range of possible solutions.
Step Two:
Check
This is where we are starting to see a real step up from GCSE. The section extends the quadratic inequality work from GCSE as we all combining it with your understanding of discriminants and roots.
P2.5 Polynomials
Step One:
Learn
The first in the series on polynomials. Initially we will be looking at simplifying algebraic fractions.
The second in the series on polynomials. Here we will recap long division and then look at how to apply this techniques when dividing polynomials. Finally, we will see how this can be used to fully factorise a polynomial expression and use the factorised version to sketch the curve.
Step Two:
Check
We are well beyond GCSE now … you’ll need to be able to factorise cubic expressions and equations as well as be able to complete algebraic long division and apply your understanding of factor theorem. Lots to think about!
P2.6 Graph sketching
Step One:
Learn
The first in the series on sketching polynomial curves. This video runs quickly through quadratics and then extends to look at power 3 (cubic) curves and power 4 (quartic) curves.
The second video on curve sketching. This video focuses on reciprocal curves and introduces the idea of curves tending to zero and also what an asymptote is.
Step Two:
Check
This links together all you know about roots, equations and curves. You can make it easier by using your graphical calculator (and you absolutely should when it comes to the exam), but for now, you would be only be cheating yourself if you took the easy option now. Bottom line – you need to know and understanding this stuff properly so you are equipped with the skills to deal what’s to come later in the course.
Step One:
Learn
Step Two:
Check
