GSCE

GSCE - OCR - Physics Combined Sciences

Physics Combined Sciences

GSCE - OCR - Physics Combined Sciences - P1: Matter

Matter

GSCE - OCR - Physics Combined Sciences - P2: Forces

Forces

GSCE - OCR - Physics Combined Sciences - P3: Electricity and Magnetism

Electricity and Magnetism

GSCE - OCR - Physics Combined Sciences - P4: Waves and Radioactivity 

Waves and Radioactivity 

GSCE - OCR - Physics Combined Sciences - P5: Energy

Energy

GSCE - OCR - Physics Combined Sciences - P6: Global Challenges 

Global Challenges 

GSCE - AQA - Physics Combined Sciences

GSCE - AQA - Physics Combined Sciences - P1: Matter

GSCE - AQA - Physics Combined Sciences - P2: Forces

GSCE - AQA - Maths

Maths

GSCE - AQA - Maths - M1: HCF and LCM

HCF and LCM

GSCE - AQA - Maths - M2: Equation of Straight Line

Equation of Straight Line

GSCE - OCR - Physics

Physics

GSCE - Edexcel - Physics

GSCE - AQA - Physics

GSCE - OCR - Maths

GSCE - Edexcel - Maths

A-Level

A-Level - OCR - Math

Math

A-Level - OCR - Biology

Biology

A-Level - AQA - Physics

A-Level - AQA - Physics - P6: Further mechanics and Thermal Physics

Further mechanics and Thermal Physics

A-Level - OCR - Physics

A-Level - OCR - Physics - P5: Newtonian world and astrophysics

Newtonian world and astrophysics

AS-Level

AS-Level - Edexcel - Maths

AS-Level - Edexcel - Maths - M1: Integration

Integration

AS-Level - Edexcel - Maths - M3: Differentiation 

Differentiation 

AS-Level - Edexcel - Physics

AS-Level - Edexcel - Physics - P1: Circular Motion

Circular Motion

AS-Level - AQA - Physics

AS-Level - AQA - Physics - P2: Particles and radiation

Particles and radiation

AS-Level - AQA - Physics - P3: Waves

Waves

AS-Level - AQA - Physics - P4: Mechanics and materials

Mechanics and materials

AS-Level - AQA - Physics - P1: Measurements and their errors

Measurements and their errors

AS-Level - OCR - Maths

IGSCE

IGSCE - Edexcel - Maths

IGSCE - Edexcel - Physics

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GSCE - AQA - Physics Combined Sciences - P1: Matter - P1.1 The Particle Model

<h3>P1-1-1 Structure of an atom</h3>Plum Pudding model:In 1897 J.J. Thompson discovered the electron is much lighter than the atom, and hence realised the atom is not the smallest particle. So he proposed the Plum Pudding model:<figure class="image"><img style="aspect-ratio:400/400;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/P1_1a_Plum_pudding_atom_svg_99b0e23a89.png" alt="P1.1a Plum_pudding_atom.svg.png" width="400" height="400"></figure>&nbsp;The pudding is positive, and the plums in it are negative!&nbsp;JJ Thompson did not think of neutrons!&nbsp;Nuclear Model (Rutherford Model):&nbsp;In 1909 Geiger and Marsden fired some alpha particles towards a thin sheet of gold (alpha particle is made of two protons and two neutrons, so it has a positive charge!).Because they thought material is made of atoms that are like a plum pudding and hence it is soft like a pudding, they expected all of the alpha particles to pass through the metal sheet. But they saw some alpha particles bounce back! So their supervisor, Ernest Rutherford, said there is a positive nucleus at the centre of the atom which repels the positive alpha particles. He said electrons randomly orbit around the nucleus.&nbsp;

The Particle Model

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GSCE - AQA - Physics Combined Sciences - P2: Forces - P2.1 Motion

<h3>P2.1-1 Speed</h3>P2.1b<img src="file:///C:\Users\pedro\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png">&nbsp;P2.1aDevices used to measure distance: tape measure, metre rule, light gates, ticker tape machine, odometer of a car, GPSHow to measure time: stopwatch, data-logger connected to light gatesP2.1cConvert units of speed:Example 1: a car is moving with a speed of 12 m/s. calculate its speed in km/h.&nbsp;P2.1d<h3>P2.1-2 Scalar and Vector:</h3>&nbsp;

Motion

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GSCE - AQA - Maths - M1: HCF and LCM - M1.1 Highest Common Factor

<h3>HCF</h3>Write both numbers in terms of their prime factors.For HCF we choose the common factors with lowest powers.Example:<img src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/HCF_f3168463fe.jpg" alt="HCF.jpg"><h3>LCM</h3>We choose all the common and uncommon factors, but for common factors, we chose the highest powers!<img src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/LCM_2532a7b674.jpg" alt="LCM.jpg">

Highest Common Factor

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GSCE - AQA - Maths - M2: Equation of Straight Line - M2.1 Gradient

Gradient or Rate of Change!It is always important to know how fast some thing changes!&nbsp;&nbsp;gradient: m = rise/runm = ∆y/ ∆x<img src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/Straight_line_graph_c13137f354.png" alt="Straight_line_graph.png">

Gradient

GSCE - AQA - Maths - M2: Equation of Straight Line - M2.2 Parallel Lines

Two lines are parallel if they have the same gradient:m1 = m2&nbsp;<h3>Perpendicular Lines</h3>Two lines are perpendicular if their gradient are negative reciprocal of each other:For example if gradient of one of the lines is 3, gradient of the perpendicular line is -1/3

Parallel Lines

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AS-Level - AQA - Physics - P2: Particles and radiation - P2.1 Particles

<h3>2.1.1 Some definitions:</h3>&nbsp;Atoms are made of protons, neutrons and electrons. Protons and electrons are in the nucleus of the atom and electrons orbit the nucleus.&nbsp;Nucleon: term used for protons and neutrons.&nbsp;&nbsp;In a neutral atom number of protons equals the number of electrons.Ion: when an atom loses (positive&nbsp;ion) or gains&nbsp;(negative&nbsp;ion) electrons.&nbsp;Isotope: atom of an element with different number of neutrons, but same number of protons.Specific charge =&nbsp;<img src="data:image/png;base64,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" width="135" height="36">&nbsp;; unit: C/kgAtomic Mass Unit (u): 1/12 of mass of an atom of carbon-12 (<img src="data:image/png;base64,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" width="28" height="24">). So “u” of carbon-12 is 12!Mass of a proton ≈ mass of a neutron ≈ 1 u (≈ : almost equal)&nbsp;The “atomic mass unit” of all nuclei ≈ nucleon number.Nuclei: plural of nucleus!&nbsp;Fundamental Forces:<ol><li>Electromagnetic force: keeps electrons in orbit, intermolecular bonds, repulsion or attraction between charged particles, friction, drag, tension in a rope are all electromagnetic too, it has infinite range;</li><li>Gravity: attractive force between all masses, infinite range;</li><li>Strong nuclear force: holds nucleons in a nucleus together, attractive from 3 fm to 0.5 fm; repulsive below 0.5 fm;</li><li>Weak nuclear force: affects all particles, range of order 10-18 m, responsible for nuclear reactions.&nbsp;</li></ol>&nbsp;Strong nuclear force: force that holds protons together, otherwise the protons would repel each other because of the electrostatic force.It is attractive from 3 fm to 0.5 fmIt is repulsive below 0.5 fm. (f: femto = 10-15), otherwise protons would crush into each other.Strong nuclear force acts between any two nucleons.&nbsp;Electron-volt (eV): small unit of energy used in nuclear physics instead of Jules.1 eV = energy needed to move an electron in PD of 1 volt.&nbsp;Radiation:Elements such as uranium, thorium, and radium have unstable nuclei and emit radiation.&nbsp;Radiation:<ol><li>Alpha (α): 2 protons + 2 neutrons short range in air (few of cm), can be stopped with a paper, highly ionising, happens in a nucleus with too many protons &amp; neutrons;</li><li>Beta minus (β-): an electron, range of several meters in air, can pass through paper or think plastic, happens when a neutron&nbsp;in the nucleus changes to a proton&nbsp;and electron, then the electron is emitted at high speed;&nbsp;</li><li>Beta plus (β+):&nbsp;anti particle of electron, called positron. Happens&nbsp;when a proton&nbsp;in the nucleus changes to a neutron&nbsp;and positron, then the positron is emitted at high speed;</li><li>Gamma (γ): electromagnetic radiation (photon), no charge, no mass, highly penetrative, ionising power less than that of alpha and beta. A photon is produced when&nbsp;a charged particle loses energy such as an electron falling to lower energy orbit (closer to the nucleus).</li><li>Neutron:&nbsp;itself can be emitted from a neutron rich nucleus. It is highly ionising too!</li></ol>

Particles

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AS-Level - AQA - Physics - P3: Waves - P3.3 Progressive and Stationary Waves

Wave is a transfer of energy, not matter!And that is true for progressive waves! Because they actually move from one point to another. For example water wave!But stationary waves are trapped between two points and the energy only goes back and forth between those two points! For example a guitar string vibrating. Or the sound wave in a flute.&nbsp;&nbsp;We have two types of progressive waves: transverse and longitudinal&nbsp;Transverse waves: the direction of oscillation of particles is perpendicular to the direction of the energy transfer.&nbsp;Longitudinal waves: the direction of oscillation of particles is parallel to the energy transfer.&nbsp;

Progressive and Stationary Waves

AS-Level - AQA - Physics - P3: Waves - P3.2 Refraction, diffraction and interference

Refraction happens when waves goes through a different medium.&nbsp;Diffraction is when it travels through a narrow slit.&nbsp;Interference is when two waves superpose each other.&nbsp;

Refraction, diffraction and interference

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AS-Level - AQA - Physics - P4: Mechanics and materials - P4.2 Materials

Density: ρ=m V&nbsp;&nbsp;Hooke’s law: F=k∆L , k as stiffness and spring constant&nbsp;Stress = force / Area&nbsp;Strain = change in length / original length

Materials

AS-Level - AQA - Physics - P4: Mechanics and materials - P4.1 Force, energy and momentum

Force: a push or a pullenergy: capacity to do workWork: force x distance in line with the force (cos x)momentum = mass x velocity ; momentum is a vector quantity.&nbsp;

Force, energy and momentum

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AS-Level - AQA - Physics - P1: Measurements and their errors - P1.1 Use of SI units and their prefixes

Basic SI Units:mass kglength mtime s&nbsp;current Atemperature KGiga 109Mega 106Kilo 103deci 10-1centi 10-2mili 10-3micro 10-6nano 10-9&nbsp;

Use of SI units and their prefixes

AS-Level - AQA - Physics - P1: Measurements and their errors - P1.2 Limitation of physical measurements

Random errors are those human make. By taking an average of the measurements or readings we can reduce their effect on results.&nbsp;Systematic errors are because of a faulty device and show up in every single measurement or reading. They cannot be averaged out.

Limitation of physical measurements

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A-Level - AQA - Physics - P6: Further mechanics and Thermal Physics - P6.2 Thermal Physics

<h3>6.3.1 Ideal Gases</h3>Assumptions we make for a gas to be ideal:<ul style="list-style-type:disc;"><li>Gas particles are identical, spherical, and hard;</li><li>Volume of a particles is negligible compared to volume of the container;</li><li>Collisions between the particles, and particles and walls of the container is elastic with no friction;</li><li>Time of collisions is negligible compared to time spent between collisions;</li><li>There are no intermolecular bonds between particles, the only force is due to collisions;</li><li>The particles are in constant random motion (Brownian motion), with variety of velocities, with a certain mean (average) velocity.</li></ul>We change 3 parameters in ideal gases:<ol><li>Pressure: originates from force from collision of particles with walls of the container. As particles’ motion is random and we assume an average velocity for them, the collision force is distributed uniformly on walls of the container.</li></ol>&nbsp;<figure class="image image_resized" style="width:75.74%;"><img style="aspect-ratio:1280/627;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_Gas_Pressure_a0aff89d67.jpg" alt="6-2-2 Gas Pressure.jpg" width="1280" height="627"></figure>&nbsp;2. Volume: because of Brownian motion, the molecules fill up the container and volume of a gas is the volume of the container.&nbsp;3. Temperature: increasing the temperature increases the KE of the particles (only KE! as we assume no bond between particles) and average velocity. In a fixed volume this increases the pressure. Or if we allow volume to change we can keep pressure constant.&nbsp;<h4>6.3.2-1 The Gas Laws</h4>&nbsp;Boyle’s Law: if we keep temperature constant, volume and pressure are inversely proportional (for a fixed mass of ideal gas of course!):&nbsp;<figure class="image image_resized" style="width:71.85%;"><img style="aspect-ratio:922/545;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_1_Boyles_Formula_6e3bf1abd2.jpg" alt="6-2-2-1 Boyles Formula.jpg" width="922" height="545"></figure>&nbsp;Charles’ Law: if we keep pressure constant, the volume is directly proportional to absolute temperature (for a fixed mass of ideal gas of course!).&nbsp;<figure class="image image_resized" style="width:88.27%;"><img style="aspect-ratio:1391/487;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_1_Charles_Formula_2c1ff6d18e.jpg" alt="6-2-2-1 Charles Formula.jpg" width="1391" height="487"></figure>&nbsp;Pressure- Temperature Law (Amonton’s Law): if we keep volume constant, the pressure is directly proportional to absolute temperature (guess what!)&nbsp;<figure class="image image_resized" style="width:83.19%;"><img style="aspect-ratio:1310/587;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_1_Pressure_Temperature_Formula_9d53a6306b.jpg" alt="6-2-2-1 Pressure-Temperature Formula.jpg" width="1310" height="587"></figure>&nbsp;Gas Laws Combined:&nbsp;<figure class="image image_resized" style="width:70.99%;"><img style="aspect-ratio:780/383;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_1_combining_gas_laws_51085ceec8.jpg" alt="6-2-2-1 combining gas laws.jpg" width="780" height="383"></figure>&nbsp;Remember:Unit of temperature for all gas laws is Kelvin: 0oC = 273oKUnit of pressure is usually pascals (Pa) which is the same as N/m2Another unit of pressure: atm (atmospheres) 1 atm = 101’325 Pa = 1.01 x 105 PaSTP means: Standard Temperature and Pressure: 273oK and 1.01 x 105 PaRTP: Room Temperature and Pressure: 25oC = 278K and 1.01 x 105 Pa&nbsp;<h4>6.3.1-2 Moles and Avogadro constant&nbsp;</h4>&nbsp;1 mole of a substance contains 6.02 x 1023 particles = NA (Avogadro’s constant).&nbsp;The definition of mole is the number of atoms carbon-12 that add up to have a mass of 12 grams.&nbsp;Also for other elements, 1 mole has a mass equal to their mass number (nucleon number) in grams!e.g.&nbsp;<figure class="image image_resized" style="width:73.91%;"><img style="aspect-ratio:882/442;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_2_Mass_Number_aeacebca5d.jpg" alt="6-2-2-2 Mass Number.jpg" width="882" height="442"></figure>&nbsp;Avogadro’s Law: Under same pressure and temperature, equal volume of gases contain the same number of particles (atoms or molecules).&nbsp;&nbsp;<figure class="image image_resized" style="width:75.09%;"><img style="aspect-ratio:1042/582;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_2_Avogadro_Law_56dad989d0.jpg" alt="6-2-2-2 Avogadro Law.jpg" width="1042" height="582"></figure>&nbsp;Combining all four gas laws above, we get the following formulae:&nbsp;<figure class="image"><img style="aspect-ratio:1450/640;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_2_Four_gas_laws_P_Vn_RT_62d9e00104.jpg" alt="6-2-2-2 Four gas laws PVnRT.jpg" width="1450" height="640"></figure>&nbsp;or:&nbsp;<figure class="image image_resized" style="width:81.9%;"><img style="aspect-ratio:1137/585;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_2_Four_gas_laws_PV_Nk_T_Boltzmann_337b79b5b9.jpg" alt="6-2-2-2 Four gas laws PVNkT Boltzmann.jpg" width="1137" height="585"></figure>&nbsp;This shows that pressure of an ideal gas does not depend on mass of its particles.&nbsp;&nbsp;Molar and Molecular Mass:Molar mass (Mm): mass of 1 mole of a substanceMolecular mass (m): mass of a molecule of a substanceMm = NA m&nbsp;<figure class="image"><img style="aspect-ratio:1532/593;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_2_Molecular_and_molar_mass_7235d918d8.jpg" alt="6-2-2-2 Molecular and molar mass.jpg" width="1532" height="593"></figure>&nbsp;<h4>6.3.1-3 Work Done on Gas</h4>&nbsp;<figure class="image image_resized" style="width:82.98%;"><img style="aspect-ratio:1277/456;" src="https://effortless-creativity-dd2bae31d9.media.strapiapp.com/6_2_2_3_Work_Done_on_Gas_137ea47f70.jpg" alt="6-2-2-3 Work Done on Gas.jpg" width="1277" height="456"></figure>&nbsp;<h3>6.3.2 Molecular kinetic theory model</h3>All four gas laws explained before are empirical&nbsp;(based on experiments) but the Kinetic Theory Model is theoretical.&nbsp;Brownian motion is instrumental to explain the relationship between p, V, and T; and as a reason for existence of atoms.&nbsp;

Gas Laws

<h3>6.2.1 Thermal Energy Transfer</h3>&nbsp;&nbsp;Q = m c ΔTQ: heat energy (J)m: mass (kg)c: Specific heat capacityΔT: change in temperature (oC or oK)&nbsp;Specific heat capacity: the amount of energy needed to change the temperature of 1 kg of a material by 1 oC.&nbsp;Specific Latent Heat: amount of energy needed to change the state of 1 kg of a material.

Thermal Physics

A-Level - AQA - Physics - P6: Further mechanics and Thermal Physics - P6.1 Periodic Motion

Circular motioncircular acceleration: a = v2/r&nbsp;centripetal force: F = mv2/r (coming from Newton's second law)&nbsp;There is not such thing as centrifugal force!The centripetal force, is not a new force created when the object is rotating in a circular path. Rather, it is a force which we already have and now is acting as the Centripetal Force for the object.examples:&nbsp;tension in the string for a bub at the end of a string being rotated.&nbsp;friction between tyres and road for a car in a roundaboutpull of gravity for a satellite in the orbit around the Earthforce from a magnetic field on a moving charge.&nbsp;

Periodic Motion

AQA Physics Combined Sciences

Motion

P2.1-1 Speed

P2.1-2 Scalar and Vector:

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