Physics and Maths Tutoring

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.

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.

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.

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.

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 a 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 $(5\pm 2)\mathrm{m}{\mathrm{s}}^{-2}$

Recommended Calculators

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

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)]

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.

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

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.

Internal Resistance emf & Potential Difference

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

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.

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.

Abu Rayhan al-Biruni a polymath
from theIslamic 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]