Physics & Maths Tutoring

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Set Notation

A set is a collection of objects, elements or members. The objects can be any collection you can think of. This collection can be described by listing the elements, or by giving a rule. The list or rule is given in a pair of curly brackets {}. For example: $A=\{6,9,14\}$ or $B=\{x:x^2+5|x\in \mathbb{N}\}$

Physics Equations & Data

Equations are central to understanding physics. Each examination boards issues a list of equations for use in their tests which are either to be memorised or given to the candidate in a booklet.

Mathematics Transition
from GCSE to A Level.

A page of links to materials to help the transition from GCSE Mathematics to A Level over the summer leave. Sources include the examination boards, some schools, books and more...

Rules for Divisibility

Divisible By" means "when you divide one number by another the result is a whole number. Numbers like 555 are clearly divisible by five, but could you see that 555 is also divisible by three, fifteen, 37, 111, & 185? Methods are given here to identify divisibility by integers 2 to 12 & more should you wish.

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SUVAT

The Equations of Constant Acceleration

Let s be the displacement, u be the initial velocity, v be the final velocity, a be the constant acceleration, & t be the time taken, then …

Useful Physics Websites

A list of websites grouped according to qualifications that students may find useful in revision & preparation for exams.

Quadratic Sequences

A quadratic sequence has $n^2$ & no higher powers of $n$ in its $n^{\mathrm{th}}$ term ($U_n$). The general form of a quadratic sequence is given by $$U_n=a{n}^2+bn+c$$ where $a$, $b$ & $c$ are numbers that can be thought of as characterising the quadratic sequence & often are to be found.

An example of a quadratic sequence is 1, 4, 9, 16, 25, ... which happens to be the square numbers. Another is 3, 6, 13, 24, 39, ... which is less easily identified as a particular sequence. To determine if a given sequence is indeed a quadratic sequence the second difference needs to be shown to be constant.

All measurements we make have a level of uncertainty

the Limitation of Physical Measurements

But how do we combine uncertainties?

● Adding / subtracting - ADD ABSOLUTE UNCERTAINTIES
e.g. A ruler with an uncertainty of $0.5\mathrm{mm}$ shows a spring extends from $50.0\mathrm{mm}$ to $63.5\mathrm{mm}$, so the extension is $63.5-50.5=13.5$ with an uncertainty of $0.5+0.5=1$. The calculated extension is $(13.5\pm 1)\mathrm{mm}$

● Multiplying / dividing - ADD RELATIVE UNCERTAINTIES
e.g. a force of $(45\pm 5)\mathrm{N}$ is applied to a mass of $(9\pm 3)\mathrm{kg}$, what is the acceleration? Using Newton's 2^nd Law, the acceleration is given by $a=\frac{F}{m}$, so $a=\frac{45}{9}=5\mathrm{m}{\mathrm{s}}^{-2}$ with an certainty given by $\frac{5}{45}+\frac{3}{9}=\frac{4}{9}$. The calculated acceleration is $5\mathrm{m}{\mathrm{s}}^{-2}\pm \frac{4}{9}$ or $(5\pm 2)\mathrm{m}{\mathrm{s}}^{-2}$

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Recommended Calculators

A list of calculators that are useful for I/GCSE & A Level Maths or physics

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Moments

In physics, a moment is an expression involving the product of a distance & physical quantity, & in this way it accounts for how the physical quantity is located or arranged.
Moments are usually defined with respect to a fixed reference point; they deal with physical quantities located at some distance relative to that reference point. For example, the moment of force, often called torque, is the product of a force on an object & the distance from the reference point to the object. In principle, any physical quantity can be multiplied by a distance to produce a moment. Commonly used quantities include forces, masses, & electric charge distributions. [scraped from en.wikipedia.org/wiki/Moment_(physics)]

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Photoelectric Effect

The Photoelectric effect provides evidence that electromagnetic waves have particle-like behaviour. In the photoelectric effect, electrons are emitted from a metal’s surface when it absorbs electromagnetic radiation.

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Fraction, Decimals & Percents

You're unlikely to be asked to convert between one seventh & the decimal equivalent of 0.1428571428571 ...
These are, however, the same number, but in different presentations.
See more at mathsisfun.com

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Evolution of Large Mass Stars

The evolution of stars with a mass higher than about 1.4M_Sun is different from that of smaller mass stars. Stars between 1.4M_Sun & 3M_Sun also evolve into red giants, but they end their life as supernovae, leaving behind a neutron star. Stars with a main-sequence mass of more than 3MSun evolve into red supergiants, & when these explode as supernovae they leave behind a black hole.

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Internal Resistance emf & Potential Difference

In any circuit there are components that put energy into the circuit, they provide an electo-motive force (emf), & components that take energy out, they have a potential difference (pd) across them. Both emf & pd are measure in volts (V).

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Types of Homework

There are seven types of homework. These are practice, preparation, extension, integration, research, application, & flipped homework.
Each type of homework has its own role for students learning. The important task for teachers is to select homework that will best provide holistic support to a student.

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12 Female Physicists

Marie Curie - only person to have Nobel Prizes in multiple sciences;
Lise Meitner - the 1^st woman to be appointed Professor of Physics in Germany;
Maria Goeppert Mayer - proposed the nuclear shell model;
Ruby Payne-Scott - discovered several types of radiation bursts originating from the sun;
Rosalind Franklin - her expertise was instrumental in producing the 1^st X-ray diffraction images of DNA, confirming its double helix structure;
Vera Rubin - conducted pioneering work on galaxy rotation rates, providing evidence for the existence of dark matter;
Dame Jocelyn Bell Burnell - co-discovered the 1^st radio pulsars;
Katherine Johnson - her calculations of orbital mechanics made possible the 1^st & subsequent manned U.S. spaceflights;
Helen Quinn - developed the theory, which is related to matter-antimatter symmetry & explains a possible source of dark matter;
Margaret Reid - is carrying out pioneering on fundamental tests of quantum theory, applications include teleportation & cryptography;
Amanda Barnard - she became the 1^st woman & the 1^st person in the Southern Hemisphere to win the Feynman Prize in nanotechnology for her work on diamond nanoparticles;
Michelle Simmons - She has established a large research group dedicated to the fabrication of atomic scale devices, the only group worldwide that can create atomically precise devices in silicon.

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Abu Rayhan al-Biruni a polymath
from the Islamic Golden Age

Al-Biruni was well versed in physics, mathematics, astronomy, & natural sciences, & also distinguished himself as a historian, chronologist & linguist. He studied almost all the sciences of his day & was rewarded abundantly for his tireless research in many fields of knowledge. Royalty & other powerful elements in society funded Al-Biruni's research & sought him out with specific projects in mind. Influential in his own right, Al-Biruni was himself influenced by the scholars of other nations, such as the Greeks, from whom he took inspiration when he turned to the study of philosophy. A gifted linguist, he was conversant in Khwarezmian, Persian, Arabic, Sanskrit, & also knew Greek, Hebrew & Syriac. He spent much of his life in Ghazni, then capital of the Ghaznavids, in modern-day central-eastern Afghanistan. In 1017 he travelled to the Indian subcontinent & wrote a treatise on Indian culture entitled Tārīkh al-Hind (History of India), after exploring the Hindu faith practiced in India. He was, for his time, an admirably impartial writer on the customs & creeds of various nations, his scholarly objectivity earning him the title al-Ustadh ("The Master") in recognition of his remarkable description of early 11th-century India.
[Scraped from en.wikipedia.org/wiki/Al-Biruni]

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The Conic Sections Collected

Circle,
Ellipse,
Parabola
&
Hyperbola

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