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See also: [[Further Maths - Determinants]]S [[Further Maths - Inverting Matricies]]S [[Further Maths - Solving Systems of Equations Using Matricies]]S [[Further Maths - Linear Transformations]]S If a matrix is $m \times n$, how many columns does it have?? $m$ columns. If a matrix is $m \times n$, how many rows does it have?? $n$ rows. What are the dimensions of a matrix?? $$ \text{rows} \times \text{columns} $$

See Also [[Maths - Proof by Contradiction]]S Flashcards When proving irrationality of a surd $x$, what is the setup?? Assume $x = \frac{a}{b}$ where $a$ and $b$ are integers that do not share any factors. Why can’t $a$ and $b$ share any factors when proving the irrationality of a surd?? Because it would mean you could simplify $\frac{a}{b}$. How do you get rid the square root over $x$ when proving it’s irrationality?

What are integers?? All numbers without a fractional component. What are numbers without a fractional component called?? Integers. What are rational numbers?? Numbers that can be written in the form $\frac{a}{b}$. What are numbers that can be written as $\frac{a}{b}$ called??' Rational numbers. What are irrational numbers?? Non-recurring decimals. What are non-recurring decimals called?? Irrational numbers. What are real numbers?? Rational and irrational numbers. What the term for rational and irrational numbers?? Real numbers. Backlinks [[Maths - Syllabus]]S Metadata date: 2020-09-23 17:28 tags: - '@?

Physics Syllabus Link to specification: https://www.ocr.org.uk/Images/171726-specification-accredited-a-level-gce-physics-a-h556.pdf Exams: [[Physics - Exams]]?? AS-Level [[Physics - Units and Prefixes]]S [[Physics - Vectors and Scalars]]S [[Physics - Distance and Velocity Time Graphs]]?? [[Physics - Vernier Callipers and Micrometers]]S [[Physics - Uncertainty]]S [[Physics - Galileo's Slope Experiment]]S [[Physics - Combining Vectors]]S [[Physics - Resolving Vectors]]S [[Physics - Syllabus]]S [[Physics - SUVAT Equations]]S [[Physics - Force and Newtons]]S [[Physics - Stopping Distances]]S [[Physics - Free Fall]]S [[Physics - Moments]]S [[Physics - Calculating Acceleration Due To Gravity]]S [[Physics - Equilibrium]]S [[Physics - Projectiles]]S [[Physics - Density]]S [[Physics - Pressure]]S [[Physics - Archimedes' Principle]]S [[Physics - Hooke's Law]]S [[Physics - Work Done]]S [[Physics - Energy]]S [[Physics - Power]]S [[Physics - Elastic Potential Energy]]S [[Physics - Momentum]]S [[Physics - Charge and Current]]S [[Physics - Circuits]]S [[Physics - Electron Drift Velocity]]S [[Physics - Collisions in 2D]]S [[Physics - Voltage and Potential Difference]]S [[Physics - Resistance and Ohm's Law]]S [[Physics - Resistivity]]S [[Physics - Waves]]S [[Physics - Thermistors and LDRs]]S [[Physics - Oscilliscopes]]S [[Physics - Reflection and Refraction]]S [[Physics - Diffraction]]S [[Physics - Polarisation]]S [[Physics - Intensity]]S [[Physics - Electromagnetic Waves]]S [[Physics - Young's Modulus]]S [[Physics - Internal Resistance]]S [[Physics - Potential Dividers]]S [[Physics - Quantum Physics]]S [[Physics - Electromagnetic Radiation]]S [[Physics - The Photoelectric Effect]]S [[Physics - Superposition]]S [[Physics - Wave-Particle Duality]]S [[Physics - Standing Waves]]S Recall Questions for AS-Level [[Physics - Recall for Chapter 3: Motion]]S [[Physics - Recall for Chapter 4: Forces in Action]]S [[Phyiscs - Recall for Chapter 5: Work, Energy and Power]]S [[Physics - Recall for Chapter 6: Materials]]S [[Physics - Recall for Chapter 7: Laws of Motion and Momentum]]S [[Physics - Recall for Chapter 8: Current and Charge]]S [[Phyiscs - Recall for Chapter 9: Energy, Power and Resistance]]S [[Physics - Recall for Chapter 10: Electrical Circuits]]S [[Physics - Recall for Chapter 11: Waves I]]S [[Physics - Recall for Chapter 12: Waves II]]S [[Physics - Recall for Chapter 13: Quantum Physics]]S A-Level [[Physics - Spectra]]S [[Physics - Circular Motion]]S [[Physics - Thermal Physics]]S [[Physics - Oscillations]]S [[Physics - Moles]]S [[Physics - Ideal Gases]]S [[Physics - Gravitational Fields]]S [[Physics - Kepler's Laws]]S [[Physics - Satellites]]S [[Physics - Gravitational Potential]]S [[Physics - Stellar Evolution]]S [[Physics - Objects in the Universe]]S [[Physics - The Nuclear Atom]]S [[Physics - Hertzsprung-Russell Diagrams]]S [[Physics - Black-Body Curves]]S [[Physics - Standard Model]]S [[Physics - Beta Decay]]S [[Physics - Cosmology]]S [[Physics - Radioactivity]]S [[Physics - Misc]]S Spec Module 1: Development of Practical Skills in Physics (Y12 & Y13) Practical skills assessed in a written exam Practical skills assessed in the practical endorsement Module 2: Foundations in Physics (Y12 & Y13) Physical quantities and units Making measurements and analysing data Nature of quantities Module 3: Forces and Motion (Y12) Motion Forces in action Work, energy and power Materials Newton’s laws of motion and momentum Module 4: Electrons, Waves and Photons (Y12) Charge and current Energy, power and resistance Electrical circuits Waves Quantum physics Module 5: Newtonian World and Astrophysics (Y13) Thermal physics Circular motion Oscillations Gravitational fields Astrophysics and cosmology Module 6: Particles and Medical Physics (Y13) Capacitors Electric fields Electromagnetism Nuclear and particle physics Medical imaging Info This page was last updated 2022-02-21.

What is $\hat{i}$?? The unit vector in the x direction. What is $\hat{j}$?? The unit vector in the y direction. What is the unit vector in the x direction?? $$ \hat{i} $$ What is the unit vector in the y direction?? $$ \hat{j} $$ What is $\begin{matrix}-2 \ 3\end{matrix}$ in unit vector form?? $$ -2\hat{i} + 3 \hat{j} $$ What is $4\hat{i} - 2\hat{j}$ in column vector form?? $$ \begin{matrix}4 \ -2\end{matrix} $$ What is the magnitude of displacement?

Resolving Vectors This links to [[Physics - Combining Vectors]]S , since it’s like doing it in reverse. What is resolving vectors?? Finding the horizontal and vertical component of a vector. What is resolving vectors opposite to…?? Combining a vector. How is the the horizontal component of $F$ written?? $F_x$. What is $F_x$?? The horizontal component of vector $F$. How is the the vertical component of $F$ written?? $F_y$. What is $F_y$?? The vertical component of vector $F$.

Combining Vectors Combining Vectors is [[Physics - Resolving Vectors]]S in reverse, or vice-versa. What is the golden rule for adding vectors?? Always add vectors tip to tail. Combine these vectors, a boat moving $10kmh^{-1}$ across a $10kmh^{-1}$ flowing river PHOTO?? PHOTO $\sqrt{10^2 + 10^2} = \sqrt{200} = 10\sqrt{2} kmh^{-1}$ When can Pythagoras be used to combine two vectors?? When two known forces are at a right angle. How can you work out the angle between two forces?

How do you find the intersection for something like $y = 5 - 2x$ and $y = 3x^2 + 5x - 3$?? Set them equal to each other and simplify. $5 - 2x = 3x^2 + 5x - 3$ What’s the most amount of times a straight line and a quadratic could intersect?? What’s the least amoount of times a straight line and a quadratic could intersect?? A line of the form $y = mx+c$ with one point of intersection with a quadratic has what relationship?

What is a linear model?? A model which works with a straight line. When creating a linear model, how do you need to change $y = mx + c$?? Instead of using $y$ and $x$ you use variables which reflect the context. What is the general ice cream sales equation?? $\text{ice cream sales} = m \times \text{weather} + c$ What’s a common critique of a linear model?? It predicts impossible negative values. What does the gradient in a linear model reflect?

When working with triangles in a co-ordinate system, the most important step is?? Drawing a sketch. How can you prove that a triangle is right-angled in a co-ordinate system?? Find the gradients of the lines and prove two are perpindicular. How can you prove two lines are perpindicular?? Show their gradients multiply to give $-1$. How can you prove that a triangle is isoceles in a co-ordinate system?? Show two lines have the same length.

The sole purpose of this entry being seperate is so that I don’t have to re-load the other [[Further Maths - Series]]S into Anki because it’s got some formatting issues that are down to underscores inside Latex formulas being recognised as italics rather than subscripts. How can you rewrite $\sum^{n}_{r=1} (r+4)^3$?? $$ \sum^{n+4}{r=1} r^3 + \sum{4}{r=1} r^3 $$ Why can you rewrite $\sum^{n}_{r=1} (r+4)^3$?? Because it’s the same as a $r^3$ sequence starting at $5$.

Programming Languages What is a low level programming language?? A programming language that provides little or no abstraction of a computer’s instruction set. What are the two parts of an instruction in machine code?? The opcode The operand What is the purpose of having an opcode and an operand?? What do you have (operand) and what do you want do with it (opcode). What is an instruction set?? All the instructions that a computer can understand and exectue.