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Maths Syllabus Link to specification: https://qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/a-level-l3-mathematics-specification-issue4.pdf Papers Paper 1 & 2: Pure Mathematics AS-Level [[Maths - Straight Line Graphs]]S [[Maths - Triangles in a Co-ordinate System]]S [[Maths - Linear Models]]S [[Maths - Quadratic and Straight Line Intersections]]S [[Maths - Surds]]S [[Maths - Proof Roots of Primes are Irrational]]S [[Maths - Quadratics Tips and Tricks]]S [[Maths - Sketching Graphs]]S [[Maths - Integration]]S [[Maths - Differentiation]]S [[Maths - Quartics]]S [[Maths - Completing the Square]]S [[Maths - Quadratic Modelling]]?

What is the role of an operating system?? Hide the complexities of the hardware from the user. Where is the OS stored on a computer?? On the hard drive. How is the BIOS stored?? On the ROM. What is ROM?? Read only memory. How is the OS loaded when the computer is switched on?? The bios. What is a virtual machine?? A layer of software that allows one computer to simulate another and to run more than one operating system.

Here, using $z$ instead of $x$ means that the variable is complex. $w$ is also sometimes used. The first step is to find the one real solution. Since it’s a cubic, there will be three solutions and by examining the graph you can see that there always must be at least one real solution (cubics always cross the $y$-axis at least once). For $z = 1$: $$ z^3 + 9z^2 + 33z + 25 1^3 + 9\times1^2 + 33\times1 + 25 \neq 0 $$

A complex number is a number with both a real and imaginary part. See Also [[Further Maths - Polar Form]]S [[Further Maths - Argand Diagrams]]S [[Further Maths - Loci in the Argand Diagram]]S [[Further Maths - Regions in the Argand Diagram]]S [[Further Maths - Exponential Form of Complex Numbers]]S [[Further Maths - Trig Equations with Complex Numbers]]S [[Further Maths - Roots of Complex Numbers]]S Introducing $i$ First, a couple of definitions:

Polyphasic Sleeping is the practice of sleeping more than once throughout the day. This is in contrast to monophasic sleep which is sleeping once like most people do. Pros The main benefit of polyphasic sleep is that you can spend less time sleeping to gain the same amount of rest. For example, a popular sleeping pattern is called Everyman 2: Base sleep 4 hours 30 minutes 2x 20 minute naps For at total of 5 hr 10 minutes People can live on 5 hr 10 minutes of sleep!

Spark: The Revolutionary New Science of Exercise and the Brain Spark is a book about how exercise affects not just the physical aspects of the body, but also mental health and the capacity to learn. If exercise came in pill form, it would be plastered across the front page, hailed as the blockbuster drug of the century. Chapters Chapter 1: [[Spark - Welcome to the Revolution]]?? Chapter 2: [[Spark - Learning]]?

Invictus, by William Ernest Henley: Out of the night that covers me, Black as the pit from pole to pole, I thank whatever gods may be, For my unconquerable soul. In the fell clutch of circumstance, I have not winced nor cried aloud, And under the bludgeonings of chance, My head is bloodied but unbowed. Beyond this place of wrath and tears, Looms but the horror of the shade, And yet the menace of the years, Finds and shall find me unafraid.

“Flow” is a book by Mihlay Csikzentmilhalyi about the idea of flow, or the feeling of [[Optimal Experience]]?? . It examines how a feeling of happiness can be achieved through a feeling of control over one’s life. Times when we feel masters of our own fate instead of the bi-products of the external forces around us. A sense that one’s skills are adequate to cope with the challenges at hand, in a goal-directed, rule-bound action system that provides clear clues as to how well one is performing.