@?school

Flashcards What is a parametric equation?? An equation where $x$ and $y$ are defined in terms of a parameter $t$. How do you work out points for a parametric curve?? Plug in a value for $t$ and see what co-ordinate $(x, y)$ it generates. How can you convert a parametric curve to a Cartesian one?? Rearrange $x$ or $y$ to $t = …$ and then substitute. Backlinks [[Maths - Syllabus]]S Metadata date: 2021-10-05 18:04 tags: - '@?

Flashcards Parabolas How can you form a parabola from a cone?? Slice it parallel to its slope. Why must you slice a cone PARALLEL to the slope to form a parabola?? Otherwise you’d either get an ellipse or intersect the cone twice and get a hyperbola. What is the parametric equation that defines a parabola?? $$ x = at^2 $$ $$ y = 2at $$ When thinking about parabolas as a conic section, is it better to think of them symmetrical around the $x$-axis or $y$-axis?

Flashcards Backlinks [[Further Maths - Syllabus]]S Metadata date: 2021-10-05 16:31 tags: - '@?public' - '@?school' - '@?further-maths' - '@?inequalities' - '@?further-pure-1' - '@?safe-to-post-online' title: Further Maths - Inequalities

See Also Flashcards 2021-09-18 What’s the format of a general arithmetic sequence term $U_n$ for common difference $d$ and start term $a$?? $$ U_n = (n - 1)d + a $$ What’s the formula for the sum $S_n$ up to term $n$ of a sequence with start $a$ and common difference $d$?? $$ S_n = \frac{n}{2}\left( (n - 1)d + 2a \right) $$ What’s the formula for the sum $S_n$ of an arithmetic sequence between terms $a$ and $l$?

See Also Flashcards 2021-09-10 What is the general process for solving a coupled first-order differential equation?? Eliminating one of the variables to form a single second-order differential equation. $$\frac{\text{d}x}{\text{d}t} = x + y \\ \frac{\text{d}y}{\text{d}t} = x - y$$ What are the 3 first steps?? Rewriting it as $y = …$, differentiating and then substituting. $$\frac{\text{d}x}{\text{d}t} = x + y \\ \frac{\text{d}y}{\text{d}t} = x - y$$ You’ve discovered $$x = Ae^{\sqrt{2}t} + Be^{-\sqrt{2}t}$$ What do you now do to find $y$ in terms of $t$?

See Also Flashcards 2021-09-07 How can you solve modulus questions like $$5|x + 2| - 1 = \frac{1}{2}x + 1$$?? Pretend that it’s $(x + 2)$ and then pretend it’s $-(x + 2)$. When worried about which “sign” of a modulus function to use when solving an equation, what should you do?? Draw a graph. Backlinks [[Maths - Syllabus]]S Metadata date: 2021-09-07 17:23 tags: - '@?maths' - '@?school' - '@?modulus' - '@?

See Also Flashcards What two points define the Kelvin scale?? Absolute zero Triple point of water What is the triple point of water?? The point at which water is a solid, liquid and gas simultaneously. How can you have a solid, liquid and a gas simultaneously?? By setting an exact pressure and temperature. What is $0K$ in Celsius?? $$ -273.15^\circ $$ What is $0^\circ$ in Kelvin?? $$ 273.15K $$ What is the equation for converting Kelvin $T$ to Celsius $\theta$?

Flashcards What is the time period $T$ of an object in uniform circular motion?? The time taken to complete one rotation. What are the SI units of angular velocity?? $$ \text{rad},s^{-1} $$ How can you conceptualise angular velocity in terms of derivatives?? It’s the rate of change of angle. What is the formula for a radian angle $\theta$ in terms of arc and radius?? $$ \theta = \frac{\text{arc}}{\text{radius}} $$ What is the formula for angluar speed?

Flashcards What is this in interval notation?? $$ (a, b) $$ What is this in interval notation?? $$ [a, b] $$ What is this in interval notation?? $$ [a, b) $$ What is this in interval notation?? $$ (a, b] $$ $$(a, b)$$ What is this as an inequality for $x$?? $$ a < x < b $$ $$[a, b]$$ What is this as an inequality for $x$?? $$ a \le x \le b $$

lets do some stuff with inequalities and trig functions because we hate fun

Recall Questions What is a photon?? A quantum of energy of electromagnetic radiation. What is the photoelectric effect?? The emission of electrons from a metal surface when illuminated with light. What is a photoelectron? An electron that has been removed from a metal by absorbing a photon. What is the work function?? The minimum energy required to release an electron from the surface of a metal. What is the threshold frequency?? The minimum frequency of light required to produce photoelectrons from a metal.

Recall Questions State what is meant by the superposition principle?? When two or more waves meet at a point, the resultant displacement is the vector sum of the displacements of the individual waves. State what is meant by coherent waves?? Waves that have a constant phase difference. State the conditions for two waves to be coherent?? The waves must be of the same type and have the same frequency. State what is meant by interference?? The superposition of waves from coherent sources.