##
A level, I/GCSE, & Functional Skills Tutoring

in Physics & Maths

One-to-one tuition in-person or on-line from

Michael Andrew Smith

MInstP BSc(Hons) NatSciPhys & Math

son of David Michael Smith

A tutor with sixteen years of experience & dedication with extensive knowledge of both physics & maths

at A level, IGCSE, GCSE, & Functional Skills Maths

Introductory session: free & without obligation

Bookings now being taken for June 2023 onwards

Contact Michael on

0 77 86 69 56 06

or via mike.smith

"Michael has tutored my twin daughters throughout this year & has helped them tremendously with their GCSE Exam/Assessments, during the pandemic. He has been a great tutor to both of them, patient, thorough & always well prepped with the maths subjects that they needed to cover. We really appreciate all the help that he has given them & would highly recommend him as a tutor."

"MS has been a great success in both re-engaging & encouraging my son's confidence in mathematics. He quickly saw where the weaknesses were, which were addressed & supported with great patience, & carefully developed my son's learning capabilities. Very much appreciated!"

See more ...

###
Newsletters

September '22

August '22

February '22

###
Maths Problem of the Week:

What is the perimeter of this rectangle?

Previously,

How many times was I late?

Now with solution.

### 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.

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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 $B=\{x:{x}^{2}+5|x\in \mathbb{N}\}$

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### 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.

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### 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 ...

Further details can be found at Wikipedia: Equations of motion - Uniform acceleration

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### Useful Physics Websites

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

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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 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).

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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 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]

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-oOo-