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Flashcards What does $fg(x)$ mean?? $$ f(g(x)) $$ What does $f^2(x)$ mean?? $$ f(f(x)) $$ What does $\alpha \circ \beta (x)$ mean?? $$ \alpha(\beta(x)) $$ If the domain for $g(x) = x^2 - 3$ is $$x \in \mathbb{R}, x \ge 0$$ What is the domain for $gf(x)$ where $f(x) = 5x - 2$?? $$ x \ge \frac{2}{5} $$ Backlinks [[Maths - Syllabus]]S Metadata date: 2021-07-05 11:15 tags: - '@?maths' - '@?

Flashcards 2021-07-05 When is a photon emitted from an atom?? When an electron makes a transition. What is the energy of the photon created when an electron drops an energy level?? The difference in energy between the initial state and the new state. What happens when an electron drops an energy level?? A photon is emitted. Why do simple elements have simpler emission spectra?? There are less electron shells and therefore less possible transitions. What type of spectrum is this?

Flashcards What is the domain of a function?? The set of all possible inputs. What is the range of a function?? The set of all possible outputs. What is the range of a function sometimes called?? The codomain. What is a mapping?? A transformation from one set of numbers into a different set of numbers. When is a mapping a function?? When every input has a distinct output. Other than a one-to-one function, what’s another type of mapping that is also a function?

See Also [[Physics - Waves]]S Flashcards When is a standing wave formed?? When two waves with the same frequency and amplitude travelling in opposite directions are superimposed. What are the points of total constructive interference in a standing wave called?? Antinodes. What are the points of total destructive interference in a standing wave called?? Nodes. What is the seperation between adjacent nodes or antinodes in a standing wave?? $$ \frac{\lambda}{2} $$

Flashcards $$\frac{24\pi (t - 1)}{1 + \sqrt{t}}$$ How can you integrate this?? Rewrite as $$ \frac{24\pi (\sqrt{t} - 1)(\sqrt{t} + 1)}{\sqrt{t} + 1} = 24\pi (\sqrt{t} - 1) $$ When checking if something is a counterexample, what should you do?? Make sure that the counterexample follows the definition of what is valid. $$\log(ab^2c) = 7$$ If you have 3 sets of equations of something like this, how can you rewrite it?? As a set of simultaneous equations in the form $\log a + 2\log b + \log c = 7$

See Also [[Physics - Quantum Physics]]S [[Physics - The Photoelectric Effect]]S Flashcards What’s the evidence that light exists as a particle?? The photoelectric effect. What’s the evidence that light exists as a wave?? They form diffraction patterns. What’s the evidence that electrons exist as a wave?? They form diffraction patterns. What would you expect when firing electrons through two slits if they are a particle?? There should be two bright spots and no inteference pattern.

See Also [[Maths - Proof by Contradiction]]S [[Maths - Proof Roots of Primes are Irrational]]S Backlinks [[Maths - Proof by Contradiction]]S [[Maths - Syllabus]]S Metadata date: 2021-06-06 11:39 tags: - '@?public' - '@?school' - '@?maths' - '@?proof' title: Maths - Proof

See Also [[Maths - Proof Roots of Primes are Irrational]]S [[Maths - Proof]]S Flashcards How can you prove a statement is FALSE by contradiction?? Find a counterexample. How can you prove a statement is TRUE by contradiction?? Negate the statement and assume it’s false. Prove this leads to a contradiction. What would be the negated statement for “if $n^2$ is even, $n$ must be even”?? “there exists an odd number $n$ such that $n^2$ is even”

See Also [[Maths - Integration]]S [[Maths - Differentiation]]S Flashcards What type of answer do you normally get for differential equation questions?? A family of curves. What’s the general process for solving a differential equation question like $$\frac{dy}{dx} = \frac{y + 1}{x}$$?? Seperate the two variables and put them on either side of the equation. Integrate both sides with respect to $x$. Rearrange. $$\int \frac{1}{y + 1} \frac{dy}{dx} dx$$ What does this simplify down to?

See Also [[Physics - Waves]]S [[Physics - Standing Waves]]S Flashcards At what phase differences does total constructive superposition occur?? $$ 0, 2\pi, 4\pi, 6\pi, 8\pi, … $$ At what phase differences does total destructive superposition occur?? $$ \pi, 3\pi, 5\pi, 7\pi, 9\pi $$ What requirement other than phase difference is there for total destructive superposition?? Both waves need to have the same amplitude. 2021-05-27 What does it mean for two wave sources to be coherent?

See Also [[Stats - Binomial Distribution]]S Flashcards What is the notation for $X$ being a random variable following a normal distribution with mode $\mu$ and standard deviation $\sigma$?? $$ X ~ N(\mu, \sigma^2) $$ What is this?? The normal distribution. What is the area under the normal distribution?? $$ 1 $$ What is required for a random variable $X$ to follow a normal distribution?? It has to be continious. How would you find $P(170 < X < 190)$ for the normal distribution?

See Also [[Physics - Quantum Physics]]S [[Physics - Electromagnetic Radiation]]S Flashcards What is the photoelectric effect?? The release of an electron when a photon is incident on a metal surface. When does the photoelectric effect occur?? When the photons incident on a material have a frequence above a threshold frequence $f_0$. Why was the discovery of the photoelectric effect significant?? It showed that light was a particle as well as a wave.